%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWV910-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n006.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 09:01:00 AM UTC 2026
% Result : Unsatisfiable 16.31s 4.93s
% Output : Refutation 17.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 498
% Syntax : Number of formulae : 997 ( 327 unt; 0 typ; 0 def)
% Number of atoms : 2027 ( 626 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 17220 (1006 ~;1030 |; 0 &;15184 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 95 ( 93 usr; 14 con; 0-9 aty)
% Number of variables : 3700 ( 0 ^;3700 !; 0 ?;3700 :)
% Comments :
%------------------------------------------------------------------------------
thf(hBOOL_decl,type,
hBOOL: $i > $o ).
thf(hAPP_decl,type,
hAPP: $i > $i > $i ).
thf(v_P_decl,type,
v_P: $i ).
thf(v_x_decl,type,
v_x: $i ).
thf(v_xa_decl,type,
v_xa: $i ).
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(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(v_c_decl,type,
v_c: $i ).
thf(c_Orderings_Obot__class_Obot_decl,type,
c_Orderings_Obot__class_Obot: $i > $i ).
thf(tc_fun_decl,type,
tc_fun: $i > $i > $i ).
thf(tc_bool_decl,type,
tc_bool: $i ).
thf(c_Com_Ocom_OSKIP_decl,type,
c_Com_Ocom_OSKIP: $i ).
thf(c_Com_Ocom_OWhile_decl,type,
c_Com_Ocom_OWhile: $i > $i > $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(class_Lattices_Olower__semilattice_decl,type,
class_Lattices_Olower__semilattice: $i > $o ).
thf(c_Finite__Set_Ofun__left__comm__idem_decl,type,
c_Finite__Set_Ofun__left__comm__idem: $i > $i > $i > $o ).
thf(c_Lattices_Olower__semilattice__class_Oinf_decl,type,
c_Lattices_Olower__semilattice__class_Oinf: $i > $i ).
thf(c_Fun_Ofcomp_decl,type,
c_Fun_Ofcomp: $i > $i > $i > $i > $i > $i ).
thf(c_Fun_Oid_decl,type,
c_Fun_Oid: $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_Ocomp_decl,type,
c_Fun_Ocomp: $i > $i > $i > $i > $i > $i ).
thf(class_Orderings_Opreorder_decl,type,
class_Orderings_Opreorder: $i > $o ).
thf(c_lessequals_decl,type,
c_lessequals: $i > $i > $i > $o ).
thf(class_Orderings_Oorder_decl,type,
class_Orderings_Oorder: $i > $o ).
thf(class_OrderedGroup_Oab__group__add_decl,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
thf(c_HOL_Ominus__class_Ominus_decl,type,
c_HOL_Ominus__class_Ominus: $i > $i > $i > $i ).
thf(c_Fun_Oinj__on_decl,type,
c_Fun_Oinj__on: $i > $i > $i > $i > $o ).
thf(c_COMBI_decl,type,
c_COMBI: $i > $i ).
thf(c_Fun_Ofun__upd_decl,type,
c_Fun_Ofun__upd: $i > $i > $i > $i > $i > $i ).
thf(class_OrderedGroup_Opordered__ab__group__add_decl,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
thf(class_Orderings_Olinorder_decl,type,
class_Orderings_Olinorder: $i > $o ).
thf(c_Finite__Set_Ofold1_decl,type,
c_Finite__Set_Ofold1: $i > $i > $i > $i ).
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(class_Lattices_Oupper__semilattice_decl,type,
class_Lattices_Oupper__semilattice: $i > $o ).
thf(c_Lattices_Oupper__semilattice__class_Osup_decl,type,
c_Lattices_Oupper__semilattice__class_Osup: $i > $i ).
thf(class_Finite__Set_Ofinite_Ofinite_decl,type,
class_Finite__Set_Ofinite_Ofinite: $i > $o ).
thf(c_Finite__Set_Ofinite_decl,type,
c_Finite__Set_Ofinite: $i > $i > $o ).
thf(tc_Option_Ooption_decl,type,
tc_Option_Ooption: $i > $i ).
thf(c_in_decl,type,
c_in: $i > $i > $i > $i ).
thf(class_Lattices_Olattice_decl,type,
class_Lattices_Olattice: $i > $o ).
thf(c_Set_Ocontents_decl,type,
c_Set_Ocontents: $i > $i > $i ).
thf(class_HOL_Ominus_decl,type,
class_HOL_Ominus: $i > $o ).
thf(c_Complete__Lattice_Ocomplete__lattice_decl,type,
c_Complete__Lattice_Ocomplete__lattice: $i > $i > $i > $i > $i > $i > $i > $i > $i > $o ).
thf(c_Hoare__Mirabelle_Otriple_Otriple__case_decl,type,
c_Hoare__Mirabelle_Otriple_Otriple__case: $i > $i > $i > $i > $i ).
thf(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR_decl,type,
c_Complete__Lattice_Ocomplete__lattice__class_OSUPR: $i > $i > $i > $i > $i ).
thf(c_Map_Orestrict__map_decl,type,
c_Map_Orestrict__map: $i > $i > $i > $i > $i ).
thf(c_Finite__Set_Olinorder__class_OMax_decl,type,
c_Finite__Set_Olinorder__class_OMax: $i > $i > $i ).
thf(class_Lattices_Obounded__lattice_decl,type,
class_Lattices_Obounded__lattice: $i > $o ).
thf(class_Complete__Lattice_Ocomplete__lattice_decl,type,
class_Complete__Lattice_Ocomplete__lattice: $i > $o ).
thf(c_Hoare__Mirabelle_Opeek__and_decl,type,
c_Hoare__Mirabelle_Opeek__and: $i > $i > $i > $i ).
thf(c_Not_decl,type,
c_Not: $i ).
thf(tc_Com_Ostate_decl,type,
tc_Com_Ostate: $i ).
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(c_COMBK_decl,type,
c_COMBK: $i > $i > $i > $i ).
thf(c_SetInterval_Oord__class_OatLeastAtMost_decl,type,
c_SetInterval_Oord__class_OatLeastAtMost: $i > $i > $i > $i ).
thf(class_Orderings_Obot_decl,type,
class_Orderings_Obot: $i > $o ).
thf(c_Option_Ooption_ONone_decl,type,
c_Option_Ooption_ONone: $i > $i ).
thf(c_Complete__Lattice_OInf__class_OInf_decl,type,
c_Complete__Lattice_OInf__class_OInf: $i > $i > $i ).
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(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(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(v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1_decl,type,
v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1: $i > $i > $i > $i > $i ).
thf(c_Complete__Lattice_OSup__class_OSup_decl,type,
c_Complete__Lattice_OSup__class_OSup: $i > $i > $i ).
thf(class_HOL_Oord_decl,type,
class_HOL_Oord: $i > $o ).
thf(class_Lattices_Odistrib__lattice_decl,type,
class_Lattices_Odistrib__lattice: $i > $o ).
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(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_fequal_decl,type,
c_fequal: $i > $i ).
thf(c_COMBC_decl,type,
c_COMBC: $i > $i > $i > $i > $i ).
thf(t_b_decl,type,
t_b: $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_Hoare__Mirabelle_Ohoare__valids_decl,type,
c_Hoare__Mirabelle_Ohoare__valids: $i > $i > $i > $o ).
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(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(c_False_decl,type,
c_False: $i ).
thf(c_Hoare__Mirabelle_Otriple_Otriple__rec_decl,type,
c_Hoare__Mirabelle_Otriple_Otriple__rec: $i > $i > $i > $i > $i ).
thf(158,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/sandbox2/benchmark/theBenchmark.p',cls_sup1CI_0) ).
thf(892,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)],[158]) ).
thf(123,axiom,
! [B: $i,A: $i] :
( ( v_x @ ( B @ ( t_a @ ( tc_bool @ ( t_a @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Map_Orestrict__map ) ) ) @ hAPP ) )
= ( B @ c_Option_Ooption_ONone ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_restrict__map__to__empty_0) ).
thf(809,plain,
! [B: $i,A: $i] :
( ( v_x @ ( B @ ( t_a @ ( tc_bool @ ( t_a @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Map_Orestrict__map ) ) ) @ hAPP ) )
= ( B @ c_Option_Ooption_ONone ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(359,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_Complete__Lattice_OSup__class_OSup ) )
= ( A @ ( C @ c_Complete__Lattice_OSup__class_OSup ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sup__insert_0) ).
thf(1337,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_Complete__Lattice_OSup__class_OSup ) )
= ( A @ ( C @ c_Complete__Lattice_OSup__class_OSup ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(101,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/sandbox2/benchmark/theBenchmark.p',cls_UN__constant_1) ).
thf(760,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)],[101]) ).
thf(412,axiom,
! [B: $i,A: $i] :
( ~ ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_lessequals ) ) )
| ( A
= ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__empty_0) ).
thf(1454,plain,
! [B: $i,A: $i] :
( ~ ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_lessequals ) ) )
| ( A
= ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(458,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
| ~ ( A @ ( B @ ( C @ c_in ) ) @ hBOOL )
| ( A @ ( C @ ( A @ ( B @ c_Finite__Set_Olinorder__class_OMin ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Min__le_0) ).
thf(1559,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
| ~ ( A @ ( B @ ( C @ c_in ) ) @ hBOOL )
| ( A @ ( C @ ( A @ ( B @ c_Finite__Set_Olinorder__class_OMin ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).
thf(48,axiom,
! [A: $i] :
( ( A @ ( A @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ c_Finite__Set_Ofun__left__comm__idem ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__left__comm__idem__sup_0) ).
thf(628,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ c_Finite__Set_Ofun__left__comm__idem ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(350,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/sandbox2/benchmark/theBenchmark.p',cls_Int__left__absorb_0) ).
thf(1315,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)],[350]) ).
thf(190,axiom,
tc_bool @ class_Lattices_Odistrib__lattice,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Odistrib__lattice) ).
thf(962,plain,
tc_bool @ class_Lattices_Odistrib__lattice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(181,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( A @ c_in ) ) @ hBOOL )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
| ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__rev__mp_0) ).
thf(941,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( A @ c_in ) ) @ hBOOL )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
| ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(108,axiom,
! [B: $i,A: $i] :
( ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__empty_0) ).
thf(777,plain,
! [B: $i,A: $i] :
( ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(60,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/sandbox2/benchmark/theBenchmark.p',cls_Int__iff_2) ).
thf(666,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)],[60]) ).
thf(456,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/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_1) ).
thf(1554,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)],[456]) ).
thf(259,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/sandbox2/benchmark/theBenchmark.p',cls_finite__Int_1) ).
thf(1110,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)],[259]) ).
thf(68,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/sandbox2/benchmark/theBenchmark.p',cls_inf__fun__eq_0) ).
thf(683,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)],[68]) ).
thf(340,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/sandbox2/benchmark/theBenchmark.p',cls_inj__on__contraD_0) ).
thf(1290,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)],[340]) ).
thf(240,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_in ) ) @ hBOOL )
| ~ ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ c_lessequals ) ) )
| ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__subset_2) ).
thf(1068,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_in ) ) @ hBOOL )
| ~ ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ c_lessequals ) ) )
| ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(441,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/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Finite__Set_Ofinite_Ofinite) ).
thf(1522,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)],[441]) ).
thf(485,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/sandbox2/benchmark/theBenchmark.p',cls_UN__extend__simps_I2_J_0) ).
thf(1618,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)],[485]) ).
thf(6,axiom,
! [B: $i,A: $i] :
( c_Com_Ocom_OSKIP
!= ( B @ ( A @ c_Com_Ocom_OSemi ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I12_J_0) ).
thf(511,plain,
! [B: $i,A: $i] :
( c_Com_Ocom_OSKIP
!= ( B @ ( A @ c_Com_Ocom_OSemi ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(65,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/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OSup__upper_0) ).
thf(677,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)],[65]) ).
thf(228,axiom,
tc_bool @ class_Lattices_Olattice,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olattice) ).
thf(1041,plain,
tc_bool @ class_Lattices_Olattice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(285,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( tc_bool @ ( A @ tc_fun ) @ ( E @ ( C @ c_lessequals ) ) )
| ( tc_bool @ ( A @ tc_fun ) @ ( 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 ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__mono_0) ).
thf(1173,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( tc_bool @ ( A @ tc_fun ) @ ( E @ ( C @ c_lessequals ) ) )
| ( tc_bool @ ( A @ tc_fun ) @ ( 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 ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(398,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( F @ ( A @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ c_lessequals ) ) )
| ~ ( F @ ( E @ ( B @ c_in ) ) @ hBOOL )
| ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ ( A @ hAPP ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UN__subset__iff_0) ).
thf(1422,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( F @ ( A @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ c_lessequals ) ) )
| ~ ( F @ ( E @ ( B @ c_in ) ) @ hBOOL )
| ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ ( A @ hAPP ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(463,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/sandbox2/benchmark/theBenchmark.p',cls_SUP__const_0) ).
thf(1569,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)],[463]) ).
thf(346,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/sandbox2/benchmark/theBenchmark.p',cls_cut_0) ).
thf(1305,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)],[346]) ).
thf(36,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = F )
| ( ( E @ ( D @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Fun_Ofun__upd ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ ( E @ ( D @ ( G @ ( F @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Fun_Ofun__upd ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__twist_0) ).
thf(597,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = F )
| ( ( E @ ( D @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Fun_Ofun__upd ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ ( E @ ( D @ ( G @ ( F @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Fun_Ofun__upd ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(400,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( B @ c_lessequals ) ) )
| ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__absorb1_0) ).
thf(1426,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( B @ c_lessequals ) ) )
| ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(2,negated_conjecture,
! [B: $i,A: $i] :
~ ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( B @ ( v_c @ ( A @ 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/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(500,plain,
! [B: $i,A: $i] :
~ ( t_a @ ( tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( t_a @ ( B @ ( v_c @ ( A @ 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)],[2]) ).
thf(16,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).
thf(538,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(62,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Lattices_Olattice )
| ( B @ ( A @ tc_fun ) @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Oupper__semilattice) ).
thf(670,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)],[62]) ).
thf(282,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/sandbox2/benchmark/theBenchmark.p',cls_sup__bot__right_0) ).
thf(1164,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)],[282]) ).
thf(117,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ c_Finite__Set_Ofinite ) )
| ~ ( B @ ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Finite__Set_Ofinite ) )
| ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__Diff2_0) ).
thf(797,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ c_Finite__Set_Ofinite ) )
| ~ ( B @ ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Finite__Set_Ofinite ) )
| ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(125,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/sandbox2/benchmark/theBenchmark.p',cls_UN__Un_0) ).
thf(814,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)],[125]) ).
thf(355,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/sandbox2/benchmark/theBenchmark.p',cls_sup__assoc_0) ).
thf(1327,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)],[355]) ).
thf(361,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/sandbox2/benchmark/theBenchmark.p',cls_Un__commute_0) ).
thf(1342,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)],[361]) ).
thf(96,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
| ~ ( B @ ( A @ ( C @ c_in ) ) @ hBOOL )
| ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert__iff_3) ).
thf(747,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
| ~ ( B @ ( A @ ( C @ c_in ) ) @ hBOOL )
| ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(168,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_in ) ) @ hBOOL )
| ( A @ ( A @ ( C @ c_Complete__Lattice_OSup__class_OSup ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sup__upper_0) ).
thf(913,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_in ) ) @ hBOOL )
| ( A @ ( A @ ( C @ c_Complete__Lattice_OSup__class_OSup ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(434,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/sandbox2/benchmark/theBenchmark.p',cls_sup__left__idem_0) ).
thf(1507,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)],[434]) ).
thf(176,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_HOL_Oord )
| ( B @ ( A @ tc_fun ) @ class_HOL_Oord ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__HOL_Oord) ).
thf(930,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_HOL_Oord )
| ( B @ ( A @ tc_fun ) @ class_HOL_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(252,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__le2_0) ).
thf(1095,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(295,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/sandbox2/benchmark/theBenchmark.p',cls_inj__on__Un_1) ).
thf(1196,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)],[295]) ).
thf(161,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( 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 ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distrib__inf__le_0) ).
thf(898,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( 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 ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(209,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/sandbox2/benchmark/theBenchmark.p',cls_Nitpick_OEx1__def_2) ).
thf(1001,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)],[209]) ).
thf(79,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/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I8_J_0) ).
thf(709,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)],[79]) ).
thf(137,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__Un_0) ).
thf(841,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(381,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Map_Orestrict__map ) ) ) @ c_Map_Orestrict__map ) ) ) )
= ( D @ ( C @ ( E @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_Map_Orestrict__map ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_restrict__restrict_0) ).
thf(1386,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Map_Orestrict__map ) ) ) @ c_Map_Orestrict__map ) ) ) )
= ( D @ ( C @ ( E @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_Map_Orestrict__map ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(424,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__subset_0) ).
thf(1482,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(54,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__antisym_0) ).
thf(651,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(383,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/sandbox2/benchmark/theBenchmark.p',cls_Int__insert__right_1) ).
thf(1391,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)],[383]) ).
thf(466,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/sandbox2/benchmark/theBenchmark.p',cls_conseq12_1) ).
thf(1576,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)],[466]) ).
thf(110,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ hAPP ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__triv_0) ).
thf(782,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ hAPP ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(407,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_in ) ) @ hBOOL )
| ( ( tc_bool @ ( A @ tc_fun ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__Diff_0) ).
thf(1441,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_in ) ) @ hBOOL )
| ( ( tc_bool @ ( A @ tc_fun ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(196,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
!= B )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__inf_1) ).
thf(973,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( ( 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)],[196]) ).
thf(231,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/sandbox2/benchmark/theBenchmark.p',cls_Int__Collect_1) ).
thf(1046,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)],[231]) ).
thf(439,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( E @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( A @ ( D @ ( C @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastatMost__subset__iff_0) ).
thf(1518,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( E @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( A @ ( D @ ( C @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(329,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( B @ c_in ) ) @ hBOOL )
| ( tc_bool @ ( E @ tc_fun ) @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ ( A @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( B @ ( A @ hAPP ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UN__upper_0) ).
thf(1265,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( B @ c_in ) ) @ hBOOL )
| ( tc_bool @ ( E @ tc_fun ) @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ ( A @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( B @ ( A @ hAPP ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(490,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/sandbox2/benchmark/theBenchmark.p',cls_singletonE_0) ).
thf(1628,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)],[490]) ).
thf(392,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/sandbox2/benchmark/theBenchmark.p',cls_inj__on__def_0) ).
thf(1409,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)],[392]) ).
thf(339,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/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OInf__empty_0) ).
thf(1287,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)],[339]) ).
thf(343,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( E @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( D @ hAPP ) @ ( C @ ( B @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_HOL_Oord ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__funD_0) ).
thf(1298,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( E @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( D @ hAPP ) @ ( C @ ( B @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_HOL_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(83,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/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OSup__binary_0) ).
thf(719,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)],[83]) ).
thf(356,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F = B )
| ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
= ( F @ ( A @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__other_0) ).
thf(1330,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F = B )
| ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
= ( F @ ( A @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(353,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( D @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__inf__iff_2) ).
thf(1323,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( D @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(178,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/sandbox2/benchmark/theBenchmark.p',cls_sup__inf__distrib2_0) ).
thf(934,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)],[178]) ).
thf(236,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
| ~ ( B @ ( C @ c_Finite__Set_Ofinite ) )
| ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__subset_0) ).
thf(1059,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
| ~ ( B @ ( C @ c_Finite__Set_Ofinite ) )
| ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(184,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/sandbox2/benchmark/theBenchmark.p',cls_insert__absorb2_0) ).
thf(949,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)],[184]) ).
thf(170,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__subset__iff_1) ).
thf(917,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(98,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
| ~ ( C @ ( D @ ( A @ c_in ) ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__mp_0) ).
thf(751,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
| ~ ( C @ ( D @ ( A @ c_in ) ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(24,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OWhile ) )
!= ( D @ ( C @ c_Com_Ocom_OSemi ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I47_J_0) ).
thf(559,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)],[24]) ).
thf(51,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/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I4_J_2) ).
thf(638,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)],[51]) ).
thf(249,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/sandbox2/benchmark/theBenchmark.p',cls_UNION__empty__conv_I2_J_0) ).
thf(1087,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)],[249]) ).
thf(261,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_Complete__Lattice_OInf__class_OInf ) )
= B )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Inf__singleton_0) ).
thf(1115,plain,
! [B: $i,A: $i] :
( ( ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_Complete__Lattice_OInf__class_OInf ) )
= B )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(495,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ hAPP ) @ hBOOL )
| ( C @ ( C @ ( B @ c_Collect ) @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CollectI_0) ).
thf(1641,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)],[495]) ).
thf(254,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/sandbox2/benchmark/theBenchmark.p',cls_conseq1_1) ).
thf(1100,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)],[254]) ).
thf(194,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/sandbox2/benchmark/theBenchmark.p',cls_BodyN_0) ).
thf(969,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)],[194]) ).
thf(40,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( F @ ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Fun_Ofun__upd ) ) ) ) )
= ( E @ ( D @ ( F @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__upd_0) ).
thf(606,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( F @ ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Fun_Ofun__upd ) ) ) ) )
= ( E @ ( D @ ( F @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(464,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( E @ ( D @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( A @ c_Hoare__Mirabelle_Otriple_Otriple__rec ) ) ) )
= ( D @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_triple_Orecs_0) ).
thf(1572,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( E @ ( D @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( A @ c_Hoare__Mirabelle_Otriple_Otriple__rec ) ) ) )
= ( D @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(386,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ c_COMBI @ hAPP ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBI__def_0) ).
thf(1398,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_COMBI @ hAPP ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(154,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/sandbox2/benchmark/theBenchmark.p',cls_triple_Oinject_2) ).
thf(881,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)],[154]) ).
thf(173,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/sandbox2/benchmark/theBenchmark.p',cls_singleton__iff_1) ).
thf(924,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)],[173]) ).
thf(417,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/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OSup__singleton_0) ).
thf(1465,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)],[417]) ).
thf(345,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/sandbox2/benchmark/theBenchmark.p',cls_comp__cong_0) ).
thf(1302,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)],[345]) ).
thf(375,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( ( 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/sandbox2/benchmark/theBenchmark.p',cls_atLeastatMost__empty__iff_0) ).
thf(1373,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( ( 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)],[375]) ).
thf(46,axiom,
! [A: $i] :
( ( A @ c_Com_Ocom_OBODY )
!= c_Com_Ocom_OSKIP ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I19_J_0) ).
thf(623,plain,
! [A: $i] :
( ( A @ c_Com_Ocom_OBODY )
!= c_Com_Ocom_OSKIP ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(7,axiom,
! [A: $i] :
( ( A @ ( A @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ c_Finite__Set_Ofun__left__comm__idem ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__left__comm__idem__inf_0) ).
thf(514,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ c_Finite__Set_Ofun__left__comm__idem ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(337,axiom,
tc_bool @ class_HOL_Ominus,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__HOL_Ominus) ).
thf(1283,plain,
tc_bool @ class_HOL_Ominus,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(233,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/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OInf__insert_0) ).
thf(1051,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)],[233]) ).
thf(164,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( D @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__infI1_0) ).
thf(905,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( D @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(276,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/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I2_J_0) ).
thf(1151,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)],[276]) ).
thf(179,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/sandbox2/benchmark/theBenchmark.p',cls_fold1Set__sing_1) ).
thf(937,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)],[179]) ).
thf(379,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/sandbox2/benchmark/theBenchmark.p',cls_ball__empty_0) ).
thf(1383,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)],[379]) ).
thf(29,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__eqI_0) ).
thf(574,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(89,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/sandbox2/benchmark/theBenchmark.p',cls_finite__UN_0) ).
thf(734,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)],[89]) ).
thf(409,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/sandbox2/benchmark/theBenchmark.p',cls_hoare__derivs_Ointros_I6_J_0) ).
thf(1447,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)],[409]) ).
thf(242,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__supI1_0) ).
thf(1072,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(384,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/sandbox2/benchmark/theBenchmark.p',cls_inf1E_1) ).
thf(1394,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)],[384]) ).
thf(443,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ tc_Option_Ooption @ ( C @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Map_Orestrict__map ) ) ) @ c_Fun_Ofun__upd ) ) ) ) )
= ( D @ tc_Option_Ooption @ ( C @ ( F @ ( E @ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Map_Orestrict__map ) ) ) @ c_Fun_Ofun__upd ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__restrict_0) ).
thf(1526,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ tc_Option_Ooption @ ( C @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Map_Orestrict__map ) ) ) @ c_Fun_Ofun__upd ) ) ) ) )
= ( D @ tc_Option_Ooption @ ( C @ ( F @ ( E @ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Map_Orestrict__map ) ) ) @ c_Fun_Ofun__upd ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(365,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/sandbox2/benchmark/theBenchmark.p',cls_UN__insert_0) ).
thf(1351,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)],[365]) ).
thf(207,axiom,
! [A: $i] : ( tc_bool @ ( A @ tc_fun ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__empty_1) ).
thf(998,plain,
! [A: $i] : ( tc_bool @ ( A @ tc_fun ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(202,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/sandbox2/benchmark/theBenchmark.p',cls_Nitpick_OEx1__def_3) ).
thf(988,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)],[202]) ).
thf(390,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/sandbox2/benchmark/theBenchmark.p',cls_fold1__singleton_0) ).
thf(1405,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)],[390]) ).
thf(199,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/sandbox2/benchmark/theBenchmark.p',cls_IntE_0) ).
thf(981,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)],[199]) ).
thf(104,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/sandbox2/benchmark/theBenchmark.p',cls_o__eq__dest_0) ).
thf(766,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)],[104]) ).
thf(487,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/sandbox2/benchmark/theBenchmark.p',cls_sup__eq__bot__eq2_0) ).
thf(1622,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)],[487]) ).
thf(107,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( E @ c_in ) ) @ hBOOL )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Map_Orestrict__map ) ) ) @ hAPP ) )
= ( E @ ( A @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_restrict__in_0) ).
thf(774,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( E @ c_in ) ) @ hBOOL )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Map_Orestrict__map ) ) ) @ hAPP ) )
= ( E @ ( A @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(256,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/sandbox2/benchmark/theBenchmark.p',cls_inf1E_0) ).
thf(1104,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)],[256]) ).
thf(317,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__valids ) ) )
| ( 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__valids ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Loop__sound__lemma_0) ).
thf(1242,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__valids ) ) )
| ( 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__valids ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(243,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/sandbox2/benchmark/theBenchmark.p',cls_UN__extend__simps_I1_J_0) ).
thf(1074,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)],[243]) ).
thf(19,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__antisym__conv_0) ).
thf(546,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(174,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/sandbox2/benchmark/theBenchmark.p',cls_Int__assoc_0) ).
thf(925,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)],[174]) ).
thf(297,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/sandbox2/benchmark/theBenchmark.p',cls_inj__on__iff_0) ).
thf(1199,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)],[297]) ).
thf(14,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( A @ ( B @ ( A @ c_Fun_Oid @ c_Fun_Ocomp ) ) ) ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_id__o_0) ).
thf(534,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( A @ ( B @ ( A @ c_Fun_Oid @ c_Fun_Ocomp ) ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(81,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( E @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__mono_0) ).
thf(714,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( E @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(405,axiom,
tc_bool @ class_HOL_Oord,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__HOL_Oord) ).
thf(1438,plain,
tc_bool @ class_HOL_Oord,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(58,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Com_Ocom_OCond ) ) )
!= ( D @ c_Com_Ocom_OBODY ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I54_J_0) ).
thf(661,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)],[58]) ).
thf(333,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
= C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__same_0) ).
thf(1274,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(167,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/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I6_J_0) ).
thf(910,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)],[167]) ).
thf(95,axiom,
! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__subset_0) ).
thf(746,plain,
! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(130,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/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_3) ).
thf(825,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)],[130]) ).
thf(219,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofcomp ) ) ) ) @ hAPP ) )
= ( F @ ( A @ hAPP ) @ ( B @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fcomp__apply_0) ).
thf(1021,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofcomp ) ) ) ) @ hAPP ) )
= ( F @ ( A @ hAPP ) @ ( B @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(229,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__infE_0) ).
thf(1042,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(324,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_bool @ ( A @ tc_fun ) @ ( 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 ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__Int__distrib_0) ).
thf(1255,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_bool @ ( A @ tc_fun ) @ ( 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 ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(264,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/sandbox2/benchmark/theBenchmark.p',cls_escape_0) ).
thf(1123,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)],[264]) ).
thf(426,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_Complete__Lattice_OInf__class_OInf ) )
= ( A @ ( C @ c_Complete__Lattice_OInf__class_OInf ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Inf__insert_0) ).
thf(1487,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_Complete__Lattice_OInf__class_OInf ) )
= ( A @ ( C @ c_Complete__Lattice_OInf__class_OInf ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(374,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( E @ c_in ) ) @ hBOOL )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Map_Orestrict__map ) ) ) @ hAPP ) )
= ( D @ c_Option_Ooption_ONone ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_restrict__out_0) ).
thf(1370,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( E @ c_in ) ) @ hBOOL )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Map_Orestrict__map ) ) ) @ hAPP ) )
= ( D @ c_Option_Ooption_ONone ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(87,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( C @ c_in ) ) @ hBOOL )
| ( A @ ( A @ ( E @ ( B @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( C @ ( B @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__SUPI_0) ).
thf(729,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( C @ c_in ) ) @ hBOOL )
| ( A @ ( A @ ( E @ ( B @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( C @ ( B @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(315,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( E @ ( A @ c_Fun_Oinj__on ) ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_lessequals ) ) )
| ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__inj__on_0) ).
thf(1238,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( E @ ( A @ c_Fun_Oinj__on ) ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_lessequals ) ) )
| ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(188,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Orderings_Obot )
| ( B @ ( A @ tc_fun ) @ class_Orderings_Obot ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Obot) ).
thf(957,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Orderings_Obot )
| ( B @ ( A @ tc_fun ) @ class_Orderings_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(308,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/sandbox2/benchmark/theBenchmark.p',cls_bot__empty__eq_0) ).
thf(1223,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)],[308]) ).
thf(159,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ( A @ ( D @ ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__sup__iff_2) ).
thf(894,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ( A @ ( D @ ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(367,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__greatest_0) ).
thf(1355,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(468,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( E @ ( D @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastatMost__subset__iff_2) ).
thf(1580,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( E @ ( D @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
thf(432,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/sandbox2/benchmark/theBenchmark.p',cls_finite__Un_0) ).
thf(1502,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)],[432]) ).
thf(128,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( B @ c_lessequals ) ) )
| ( ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__partition_0) ).
thf(820,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( B @ c_lessequals ) ) )
| ( ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(72,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/sandbox2/benchmark/theBenchmark.p',cls_UNION__empty__conv_I1_J_0) ).
thf(693,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)],[72]) ).
thf(49,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/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I5_J_1) ).
thf(630,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)],[49]) ).
thf(478,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/sandbox2/benchmark/theBenchmark.p',cls_empty__Collect__eq_0) ).
thf(1602,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)],[478]) ).
thf(372,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/sandbox2/benchmark/theBenchmark.p',cls_insert__commute_0) ).
thf(1365,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)],[372]) ).
thf(153,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_INT__extend__simps_I4_J_0) ).
thf(879,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(142,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/sandbox2/benchmark/theBenchmark.p',cls_empty__fold1SetE_0) ).
thf(852,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)],[142]) ).
thf(342,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__subset__conv_1) ).
thf(1296,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(413,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/sandbox2/benchmark/theBenchmark.p',cls_IntE_1) ).
thf(1457,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)],[413]) ).
thf(156,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/sandbox2/benchmark/theBenchmark.p',cls_conseq_0) ).
thf(889,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)],[156]) ).
thf(280,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/sandbox2/benchmark/theBenchmark.p',cls_Int__insert__left_0) ).
thf(1159,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)],[280]) ).
thf(302,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( 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 ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distrib__sup__le_0) ).
thf(1210,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( 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 ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(246,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/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OSup__insert_0) ).
thf(1079,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)],[246]) ).
thf(391,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__supI2_0) ).
thf(1407,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(266,axiom,
! [B: $i,A: $i] :
~ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_in ) ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_emptyE_0) ).
thf(1128,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)],[266]) ).
thf(492,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/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OInf__binary_0) ).
thf(1634,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)],[492]) ).
thf(215,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/sandbox2/benchmark/theBenchmark.p',cls_SUP1__iff_2) ).
thf(1012,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)],[215]) ).
thf(257,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__inf__iff_0) ).
thf(1106,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(140,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/sandbox2/benchmark/theBenchmark.p',cls_sup__left__commute_0) ).
thf(847,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)],[140]) ).
thf(27,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/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I3_J_0) ).
thf(566,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)],[27]) ).
thf(388,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/sandbox2/benchmark/theBenchmark.p',cls_empty_0) ).
thf(1402,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)],[388]) ).
thf(369,axiom,
! [B: $i,A: $i] : ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equalityE_0) ).
thf(1360,plain,
! [B: $i,A: $i] : ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(272,axiom,
! [C: $i,B: $i,A: $i] : ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insertI_0) ).
thf(1143,plain,
! [C: $i,B: $i,A: $i] : ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(447,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ c_in ) ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mem__def_0) ).
thf(1534,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)],[447]) ).
thf(43,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( E @ c_lessequals ) ) )
| ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__eqI_1) ).
thf(615,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( E @ c_lessequals ) ) )
| ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(238,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_in ) ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_DiffE_0) ).
thf(1064,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_in ) ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(310,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ ( A @ ( B @ c_lessequals ) ) )
| ( C @ ( B @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_asm_0) ).
thf(1227,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ ( A @ ( B @ c_lessequals ) ) )
| ( C @ ( B @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(85,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/sandbox2/benchmark/theBenchmark.p',cls_insert__inter__insert_0) ).
thf(725,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)],[85]) ).
thf(212,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/sandbox2/benchmark/theBenchmark.p',cls_K__record__comp_0) ).
thf(1006,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)],[212]) ).
thf(270,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/sandbox2/benchmark/theBenchmark.p',cls_singleton__conv_0) ).
thf(1138,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)],[270]) ).
thf(34,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G @ ( E @ ( C @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofcomp ) ) ) ) @ c_Fun_Ofcomp ) ) ) ) )
= ( G @ ( D @ ( C @ ( G @ ( E @ ( D @ ( F @ ( B @ c_Fun_Ofcomp ) ) ) ) @ ( A @ c_Fun_Ofcomp ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fcomp__assoc_0) ).
thf(593,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G @ ( E @ ( C @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofcomp ) ) ) ) @ c_Fun_Ofcomp ) ) ) ) )
= ( G @ ( D @ ( C @ ( G @ ( E @ ( D @ ( F @ ( B @ c_Fun_Ofcomp ) ) ) ) @ ( A @ c_Fun_Ofcomp ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(150,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__Int_0) ).
thf(869,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(42,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/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I4_J_1) ).
thf(610,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)],[42]) ).
thf(262,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Lattices_Odistrib__lattice )
| ( B @ ( A @ tc_fun ) @ class_Lattices_Odistrib__lattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Odistrib__lattice) ).
thf(1118,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)],[262]) ).
thf(1,negated_conjecture,
v_xa @ ( v_x @ ( v_P @ hAPP ) @ hAPP ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(499,plain,
v_xa @ ( v_x @ ( v_P @ hAPP ) @ hAPP ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(9,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( A @ ( B @ ( A @ c_Fun_Oid @ c_Fun_Ofcomp ) ) ) ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_id__fcomp_0) ).
thf(519,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( A @ ( B @ ( A @ c_Fun_Oid @ c_Fun_Ofcomp ) ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(93,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ ( D @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__sup__iff_1) ).
thf(742,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ ( D @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(313,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/sandbox2/benchmark/theBenchmark.p',cls_Un__empty__right_0) ).
thf(1234,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)],[313]) ).
thf(450,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/sandbox2/benchmark/theBenchmark.p',cls_UnCI_0) ).
thf(1541,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)],[450]) ).
thf(331,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__absorb_0) ).
thf(1270,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)],[331]) ).
thf(326,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/sandbox2/benchmark/theBenchmark.p',cls_inj__on__Un_0) ).
thf(1259,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)],[326]) ).
thf(462,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_Un__Diff__cancel2_0) ).
thf(1567,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( 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)],[462]) ).
thf(370,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Complete__Lattice_Ocomplete__lattice )
| ( B @ ( A @ tc_fun ) @ class_Complete__Lattice_Ocomplete__lattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Complete__Lattice_Ocomplete__lattice) ).
thf(1361,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)],[370]) ).
thf(289,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_lessequals ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__eq__subset_2) ).
thf(1182,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_lessequals ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(415,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/sandbox2/benchmark/theBenchmark.p',cls_sup1E_0) ).
thf(1461,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)],[415]) ).
thf(69,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/sandbox2/benchmark/theBenchmark.p',cls_Un__empty_1) ).
thf(686,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)],[69]) ).
thf(399,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Finite__Set_Ofinite ) )
| ( B @ ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__Diff__insert_1) ).
thf(1424,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Finite__Set_Ofinite ) )
| ( B @ ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Finite__Set_Ofinite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(470,axiom,
! [C: $i,B: $i,A: $i] : ( B @ ( C @ ( A @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_in ) ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insertI1_0) ).
thf(1584,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)],[470]) ).
thf(304,axiom,
( ( v_x @ ( t_a @ c_Fun_Oid @ hAPP ) )
= v_x ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_id__def_0) ).
thf(1214,plain,
( ( v_x @ ( t_a @ c_Fun_Oid @ hAPP ) )
= v_x ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(278,axiom,
! [C: $i,B: $i,A: $i] : ( B @ ( C @ ( A @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_in ) ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insertCI_1) ).
thf(1155,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)],[278]) ).
thf(77,axiom,
! [C: $i,B: $i,A: $i] : ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( A @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__upper1_0) ).
thf(706,plain,
! [C: $i,B: $i,A: $i] : ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( A @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(222,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/sandbox2/benchmark/theBenchmark.p',cls_conseq12_2) ).
thf(1028,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)],[222]) ).
thf(247,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_a @ ( t_b @ ( t_b @ ( E @ ( D @ ( C @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple__case ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_triple_Osplit_0) ).
thf(1082,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_a @ ( t_b @ ( t_b @ ( E @ ( D @ ( C @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple__case ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(22,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Com_Ocom_OBODY )
!= ( C @ ( B @ c_Com_Ocom_OSemi ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I49_J_0) ).
thf(554,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)],[22]) ).
thf(99,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__sup__iff_0) ).
thf(753,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(394,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insertI2_0) ).
thf(1414,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(12,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/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I5_J_0) ).
thf(526,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)],[12]) ).
thf(217,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_Complete__Lattice_OSup__class_OSup ) )
= ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sup__binary_0) ).
thf(1016,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_Complete__Lattice_OSup__class_OSup ) )
= ( 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)],[217]) ).
thf(300,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__supE_0) ).
thf(1207,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(33,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/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I44_J_0) ).
thf(590,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)],[33]) ).
thf(482,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( G @ ( F @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Fun_Ofun__upd ) ) ) ) @ ( A @ c_Fun_Ocomp ) ) ) ) )
= ( G @ ( E @ ( D @ ( A @ hAPP ) @ ( C @ ( E @ ( G @ ( F @ ( B @ ( A @ c_Fun_Ocomp ) ) ) ) @ c_Fun_Ofun__upd ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__comp_0) ).
thf(1612,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( G @ ( F @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Fun_Ofun__upd ) ) ) ) @ ( A @ c_Fun_Ocomp ) ) ) ) )
= ( G @ ( E @ ( D @ ( A @ hAPP ) @ ( C @ ( E @ ( G @ ( F @ ( B @ ( A @ c_Fun_Ocomp ) ) ) ) @ c_Fun_Ofun__upd ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).
thf(66,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( E @ ( D @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( A @ c_Hoare__Mirabelle_Otriple_Otriple__case ) ) ) )
= ( D @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_triple_Ocases_0) ).
thf(679,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( E @ ( D @ ( C @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( A @ c_Hoare__Mirabelle_Otriple_Otriple__case ) ) ) )
= ( D @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(227,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/sandbox2/benchmark/theBenchmark.p',cls_Int__Un__distrib_0) ).
thf(1039,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)],[227]) ).
thf(135,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ c_Finite__Set_Ofinite ) )
| ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__Diff_0) ).
thf(837,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ c_Finite__Set_Ofinite ) )
| ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Finite__Set_Ofinite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(472,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ c_fequal @ hAPP ) @ c_The ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_the__sym__eq__trivial_0) ).
thf(1588,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ c_fequal @ hAPP ) @ c_The ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).
thf(75,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( C @ c_lessequals ) ) )
| ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__absorb1_0) ).
thf(701,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( C @ c_lessequals ) ) )
| ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(312,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/sandbox2/benchmark/theBenchmark.p',cls_Un__empty_0) ).
thf(1231,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)],[312]) ).
thf(55,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ c_Finite__Set_Ofinite ) )
| ~ ( A @ class_Finite__Set_Ofinite_Ofinite ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite_0) ).
thf(654,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)],[55]) ).
thf(293,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ ( C @ ( 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 @ ( C @ ( B @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_derivs__insertD_0) ).
thf(1192,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ ( C @ ( 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 @ ( 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)],[293]) ).
thf(210,axiom,
! [B: $i,A: $i] :
~ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bot1E_0) ).
thf(1002,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)],[210]) ).
thf(401,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/sandbox2/benchmark/theBenchmark.p',cls_bot__fun__eq_0) ).
thf(1429,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)],[401]) ).
thf(477,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/sandbox2/benchmark/theBenchmark.p',cls_sup__eq__bot__eq1_0) ).
thf(1599,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)],[477]) ).
thf(109,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_in ) ) @ hBOOL )
| ( ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__Diff1_0) ).
thf(779,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_in ) ) @ hBOOL )
| ( ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(39,axiom,
! [B: $i,A: $i] : ( A @ ( A @ ( B @ ( A @ c_Fun_Oid @ c_Fun_Oinj__on ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__id_0) ).
thf(605,plain,
! [B: $i,A: $i] : ( A @ ( A @ ( B @ ( A @ c_Fun_Oid @ c_Fun_Oinj__on ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(328,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ ( D @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__subset_1) ).
thf(1263,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ ( D @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(206,axiom,
! [C: $i,B: $i,A: $i] : ( B @ ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__code_1) ).
thf(997,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)],[206]) ).
thf(422,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/sandbox2/benchmark/theBenchmark.p',cls_escape_1) ).
thf(1478,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)],[422]) ).
thf(321,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/sandbox2/benchmark/theBenchmark.p',cls_Un__empty_2) ).
thf(1249,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)],[321]) ).
thf(411,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/sandbox2/benchmark/theBenchmark.p',cls_sup__fun__eq_0) ).
thf(1451,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)],[411]) ).
thf(91,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/sandbox2/benchmark/theBenchmark.p',cls_Loop_0) ).
thf(738,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)],[91]) ).
thf(445,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/sandbox2/benchmark/theBenchmark.p',cls_hoare__derivs_Ointros_I6_J_2) ).
thf(1530,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)],[445]) ).
thf(449,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/sandbox2/benchmark/theBenchmark.p',cls_Int__Un__distrib2_0) ).
thf(1539,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)],[449]) ).
thf(357,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ hAPP ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__idem_0) ).
thf(1333,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ hAPP ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(403,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/sandbox2/benchmark/theBenchmark.p',cls_Un__assoc_0) ).
thf(1434,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)],[403]) ).
thf(180,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/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I5_J_0) ).
thf(938,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)],[180]) ).
thf(121,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__idemp_0) ).
thf(805,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(5,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ c_Com_Ocom_OBODY )
!= ( C @ ( B @ c_Com_Ocom_OWhile ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I59_J_0) ).
thf(508,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)],[5]) ).
thf(460,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
| ( ( 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/sandbox2/benchmark/theBenchmark.p',cls_Un__Int__assoc__eq_1) ).
thf(1563,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
| ( ( 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)],[460]) ).
thf(234,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/sandbox2/benchmark/theBenchmark.p',cls_UN__I_0) ).
thf(1054,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)],[234]) ).
thf(284,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/sandbox2/benchmark/theBenchmark.p',cls_Min__singleton_0) ).
thf(1170,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)],[284]) ).
thf(225,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_Complete__Lattice_OSup__class_OSup ) )
= B )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sup__singleton_0) ).
thf(1035,plain,
! [B: $i,A: $i] :
( ( ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_Complete__Lattice_OSup__class_OSup ) )
= B )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(438,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/sandbox2/benchmark/theBenchmark.p',cls_empty__not__insert_0) ).
thf(1515,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)],[438]) ).
thf(283,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/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I4_J_0) ).
thf(1167,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)],[283]) ).
thf(484,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/sandbox2/benchmark/theBenchmark.p',cls_insertCI_0) ).
thf(1616,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)],[484]) ).
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/sandbox2/benchmark/theBenchmark.p',cls_ex__in__conv_0) ).
thf(1202,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(115,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( E @ c_in ) ) @ hBOOL )
| ( ( D @ tc_Option_Ooption @ ( C @ ( D @ c_Option_Ooption_ONone @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Map_Orestrict__map ) ) ) @ c_Fun_Ofun__upd ) ) ) ) )
= ( D @ ( C @ ( B @ ( A @ c_Map_Orestrict__map ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__None__restrict_1) ).
thf(792,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( E @ c_in ) ) @ hBOOL )
| ( ( D @ tc_Option_Ooption @ ( C @ ( D @ c_Option_Ooption_ONone @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Map_Orestrict__map ) ) ) @ c_Fun_Ofun__upd ) ) ) ) )
= ( D @ ( C @ ( B @ ( A @ c_Map_Orestrict__map ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(291,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/sandbox2/benchmark/theBenchmark.p',cls_finite__insert_0) ).
thf(1187,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)],[291]) ).
thf(64,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( v_x @ ( A @ ( t_a @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ hAPP ) )
= ( A @ ( v_x @ ( C @ hAPP ) @ ( v_x @ ( B @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_HOL_Ominus ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__diff__def_0) ).
thf(674,plain,
! [C: $i,B: $i,A: $i] :
( ( ( v_x @ ( A @ ( t_a @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ hAPP ) )
= ( A @ ( v_x @ ( C @ hAPP ) @ ( v_x @ ( B @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_HOL_Ominus ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(186,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( D @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( tc_bool @ ( C @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ ( A @ ( D @ c_lessequals ) ) )
| ( C @ ( B @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_thin_0) ).
thf(953,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( D @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( tc_bool @ ( C @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ ( A @ ( D @ c_lessequals ) ) )
| ( C @ ( B @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(290,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( v_x @ ( D @ ( C @ ( t_a @ ( B @ ( A @ c_Fun_Ofcomp ) ) ) ) @ hAPP ) )
= ( v_x @ ( A @ hAPP ) @ ( B @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fcomp__def_0) ).
thf(1185,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( v_x @ ( D @ ( C @ ( t_a @ ( B @ ( A @ c_Fun_Ofcomp ) ) ) ) @ hAPP ) )
= ( v_x @ ( A @ hAPP ) @ ( B @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(335,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ( C @ ( B @ ( A @ c_Hoare__Mirabelle_Ohoare__valids ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hoare__sound_0) ).
thf(1278,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ( C @ ( B @ ( A @ c_Hoare__Mirabelle_Ohoare__valids ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(435,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/sandbox2/benchmark/theBenchmark.p',cls_Un__insert__left_0) ).
thf(1510,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)],[435]) ).
thf(274,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( F @ ( B @ c_in ) ) @ hBOOL )
| ( ( E @ ( D @ ( F @ ( E @ tc_Option_Ooption @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Map_Orestrict__map ) ) ) )
= ( E @ ( D @ ( F @ ( A @ c_Map_Orestrict__map ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_restrict__fun__upd_1) ).
thf(1146,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( F @ ( B @ c_in ) ) @ hBOOL )
| ( ( E @ ( D @ ( F @ ( E @ tc_Option_Ooption @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Map_Orestrict__map ) ) ) )
= ( E @ ( D @ ( F @ ( A @ c_Map_Orestrict__map ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(453,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/sandbox2/benchmark/theBenchmark.p',cls_empty__def_0) ).
thf(1548,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)],[453]) ).
thf(475,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/sandbox2/benchmark/theBenchmark.p',cls_SUP1__I_0) ).
thf(1595,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)],[475]) ).
thf(70,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/sandbox2/benchmark/theBenchmark.p',cls_Nitpick_OThe__psimp_0) ).
thf(689,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)],[70]) ).
thf(491,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( B @ c_lessequals ) ) )
| ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__absorb2_0) ).
thf(1631,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( B @ c_lessequals ) ) )
| ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).
thf(269,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
| ( ( 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/sandbox2/benchmark/theBenchmark.p',cls_Un__Int__assoc__eq_0) ).
thf(1135,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
| ( ( 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)],[269]) ).
thf(498,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
= 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/sandbox2/benchmark/theBenchmark.p',cls_Diff__triv_0) ).
thf(1648,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
= 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)],[498]) ).
thf(322,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/sandbox2/benchmark/theBenchmark.p',cls_conseq2_1) ).
thf(1251,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)],[322]) ).
thf(44,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__linear_0) ).
thf(618,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(277,axiom,
! [A: $i] : ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Finite__Set_Ofinite ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite_OemptyI_0) ).
thf(1154,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)],[277]) ).
thf(25,axiom,
! [B: $i,A: $i] : ( A @ ( A @ ( B @ ( A @ c_COMBI @ c_Fun_Oinj__on ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__id2_0) ).
thf(562,plain,
! [B: $i,A: $i] : ( A @ ( A @ ( B @ ( A @ c_COMBI @ c_Fun_Oinj__on ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(106,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/sandbox2/benchmark/theBenchmark.p',cls_Un__Int__distrib2_0) ).
thf(772,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)],[106]) ).
thf(486,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
| ~ ( A @ ( B @ ( C @ c_in ) ) @ hBOOL )
| ( A @ ( C @ ( A @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ c_Finite__Set_Ofold1 ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fold1__belowI_0) ).
thf(1620,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
| ~ ( A @ ( B @ ( C @ c_in ) ) @ hBOOL )
| ( A @ ( C @ ( A @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ c_Finite__Set_Ofold1 ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).
thf(382,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/sandbox2/benchmark/theBenchmark.p',cls_Max__singleton_0) ).
thf(1388,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)],[382]) ).
thf(30,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/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I53_J_0) ).
thf(577,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)],[30]) ).
thf(389,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/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_4) ).
thf(1403,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)],[389]) ).
thf(440,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( D @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__greatest_0) ).
thf(1520,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( D @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).
thf(138,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/sandbox2/benchmark/theBenchmark.p',cls_finite__Int_0) ).
thf(843,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)],[138]) ).
thf(265,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ hAPP ) )
= C )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) )
!= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__idem__iff_0) ).
thf(1125,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ hAPP ) )
= C )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) )
!= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(349,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/sandbox2/benchmark/theBenchmark.p',cls_sup__inf__absorb_0) ).
thf(1312,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)],[349]) ).
thf(113,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( G @ ( B @ hAPP ) @ ( A @ hAPP ) )
= ( G @ ( F @ hAPP ) ) )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ocomp ) ) ) ) )
!= ( E @ ( D @ ( D @ ( F @ ( D @ c_Fun_Oid @ c_Fun_Ocomp ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_o__eq__id__dest_0) ).
thf(787,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( G @ ( B @ hAPP ) @ ( A @ hAPP ) )
= ( G @ ( F @ hAPP ) ) )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ocomp ) ) ) ) )
!= ( E @ ( D @ ( D @ ( F @ ( D @ c_Fun_Oid @ c_Fun_Ocomp ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(250,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__inf_0) ).
thf(1090,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( ( 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)],[250]) ).
thf(171,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/sandbox2/benchmark/theBenchmark.p',cls_sup__commute_0) ).
thf(919,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)],[171]) ).
thf(76,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Lattices_Obounded__lattice )
| ( B @ ( A @ tc_fun ) @ class_Lattices_Obounded__lattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Obounded__lattice) ).
thf(704,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)],[76]) ).
thf(17,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/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I45_J_0) ).
thf(540,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)],[17]) ).
thf(63,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/sandbox2/benchmark/theBenchmark.p',cls_contents__eq_0) ).
thf(672,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)],[63]) ).
thf(294,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_bool @ ( A @ tc_fun ) @ ( 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 ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__Int__distrib2_0) ).
thf(1194,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_bool @ ( A @ tc_fun ) @ ( 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 ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(301,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/sandbox2/benchmark/theBenchmark.p',cls_inj__on__empty_0) ).
thf(1209,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)],[301]) ).
thf(162,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/sandbox2/benchmark/theBenchmark.p',cls_Int__insert__right_0) ).
thf(900,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)],[162]) ).
thf(132,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/sandbox2/benchmark/theBenchmark.p',cls_UN__empty2_0) ).
thf(831,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)],[132]) ).
thf(67,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/sandbox2/benchmark/theBenchmark.p',cls_insert__code_2) ).
thf(681,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)],[67]) ).
thf(111,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ c_Orderings_Obot__class_Obot @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Obot ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bot__least_0) ).
thf(784,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ c_Orderings_Obot__class_Obot @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(465,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( tc_bool @ ( A @ ( A @ ( A @ c_fequal @ c_COMBC ) ) ) @ hAPP ) @ c_The ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_the__eq__trivial_0) ).
thf(1574,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)],[465]) ).
thf(442,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/sandbox2/benchmark/theBenchmark.p',cls_Int__Collect_0) ).
thf(1524,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)],[442]) ).
thf(428,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( B @ c_in ) ) @ hBOOL )
| ( ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__Diff__if_1) ).
thf(1492,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( B @ c_in ) ) @ hBOOL )
| ( ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(273,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__ge1_0) ).
thf(1144,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(347,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
| ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__subset__conv_0) ).
thf(1307,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
| ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(103,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( C @ ( E @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( A @ ( B @ ( D @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( D @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastatMost__subset__iff_1) ).
thf(764,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( C @ ( E @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( A @ ( B @ ( D @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( D @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(198,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__insert_0) ).
thf(979,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(232,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/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I3_J_0) ).
thf(1048,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)],[232]) ).
thf(90,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/sandbox2/benchmark/theBenchmark.p',cls_insert__is__Un_0) ).
thf(736,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)],[90]) ).
thf(376,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ c_lessequals ) ) )
| ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__subset__iff_2) ).
thf(1376,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ c_lessequals ) ) )
| ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(406,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( D @ c_in ) ) @ hBOOL )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert_0) ).
thf(1439,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( D @ c_in ) ) @ hBOOL )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(147,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ hAPP ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__idem__iff_1) ).
thf(863,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ hAPP ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(286,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/sandbox2/benchmark/theBenchmark.p',cls_Int__left__commute_0) ).
thf(1175,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)],[286]) ).
thf(124,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_Complete__Lattice_OInf__class_OInf ) )
= ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Inf__binary_0) ).
thf(811,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_Complete__Lattice_OInf__class_OInf ) )
= ( 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)],[124]) ).
thf(419,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ ( A @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__subset__iff_0) ).
thf(1471,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ ( A @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(126,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/sandbox2/benchmark/theBenchmark.p',cls_conseq12_0) ).
thf(816,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)],[126]) ).
thf(354,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/sandbox2/benchmark/theBenchmark.p',cls_conseq_2) ).
thf(1325,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)],[354]) ).
thf(362,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ( A @ ( D @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__infI2_0) ).
thf(1344,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ( A @ ( D @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(105,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/sandbox2/benchmark/theBenchmark.p',cls_inj__onD_0) ).
thf(769,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)],[105]) ).
thf(182,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/sandbox2/benchmark/theBenchmark.p',cls_insert__ident_0) ).
thf(943,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)],[182]) ).
thf(287,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__absorb1_0) ).
thf(1177,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( ( 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)],[287]) ).
thf(260,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/sandbox2/benchmark/theBenchmark.p',cls_insert__not__empty_0) ).
thf(1112,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)],[260]) ).
thf(145,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/sandbox2/benchmark/theBenchmark.p',cls_conseq2_0) ).
thf(858,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)],[145]) ).
thf(457,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__trans_0) ).
thf(1557,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(21,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/sandbox2/benchmark/theBenchmark.p',cls_o__assoc_0) ).
thf(552,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)],[21]) ).
thf(118,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_in ) ) @ hBOOL )
| ( A @ ( C @ ( A @ ( B @ c_Complete__Lattice_OInf__class_OInf ) @ c_lessequals ) ) )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Inf__lower_0) ).
thf(799,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_in ) ) @ hBOOL )
| ( A @ ( C @ ( A @ ( B @ c_Complete__Lattice_OInf__class_OInf ) @ c_lessequals ) ) )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(281,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/sandbox2/benchmark/theBenchmark.p',cls_insert__iff_2) ).
thf(1162,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)],[281]) ).
thf(275,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ c_in ) ) @ hBOOL )
| ~ ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert__iff_2) ).
thf(1149,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ c_in ) ) @ hBOOL )
| ~ ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(192,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( A @ c_Finite__Set_Ofun__left__comm__idem ) ) )
| ( ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__left__comm__idem_Ofun__left__idem_0) ).
thf(964,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( A @ c_Finite__Set_Ofun__left__comm__idem ) ) )
| ( ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(47,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/sandbox2/benchmark/theBenchmark.p',cls_fold1__def_0) ).
thf(626,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)],[47]) ).
thf(169,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/sandbox2/benchmark/theBenchmark.p',cls_hoare__derivs_OIf_0) ).
thf(915,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)],[169]) ).
thf(341,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( E @ c_in ) ) @ hBOOL )
| ( ( D @ tc_Option_Ooption @ ( C @ ( D @ c_Option_Ooption_ONone @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Map_Orestrict__map ) ) ) @ c_Fun_Ofun__upd ) ) ) ) )
= ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Map_Orestrict__map ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__None__restrict_0) ).
thf(1293,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( E @ c_in ) ) @ hBOOL )
| ( ( D @ tc_Option_Ooption @ ( C @ ( D @ c_Option_Ooption_ONone @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Map_Orestrict__map ) ) ) @ c_Fun_Ofun__upd ) ) ) ) )
= ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Map_Orestrict__map ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(61,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/sandbox2/benchmark/theBenchmark.p',cls_finite__Un_1) ).
thf(668,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)],[61]) ).
thf(177,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( B @ ( D @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Map_Orestrict__map ) ) ) )
= ( E @ tc_Option_Ooption @ ( B @ ( C @ ( A @ hAPP ) @ ( C @ ( E @ ( B @ ( D @ ( A @ c_Map_Orestrict__map ) ) ) @ c_Fun_Ofun__upd ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_restrict__map__insert_0) ).
thf(932,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( B @ ( D @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Map_Orestrict__map ) ) ) )
= ( E @ tc_Option_Ooption @ ( B @ ( C @ ( A @ hAPP ) @ ( C @ ( E @ ( B @ ( D @ ( A @ c_Map_Orestrict__map ) ) ) @ c_Fun_Ofun__upd ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(237,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/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__distrib1_0) ).
thf(1061,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)],[237]) ).
thf(10,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/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I52_J_0) ).
thf(521,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)],[10]) ).
thf(200,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( F @ ( B @ c_in ) ) @ hBOOL )
| ( ( E @ ( D @ ( F @ ( E @ tc_Option_Ooption @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Map_Orestrict__map ) ) ) )
= ( E @ tc_Option_Ooption @ ( D @ ( C @ ( B @ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( F @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Map_Orestrict__map ) ) ) @ c_Fun_Ofun__upd ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_restrict__fun__upd_0) ).
thf(983,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( F @ ( B @ c_in ) ) @ hBOOL )
| ( ( E @ ( D @ ( F @ ( E @ tc_Option_Ooption @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Map_Orestrict__map ) ) ) )
= ( E @ tc_Option_Ooption @ ( D @ ( C @ ( B @ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( F @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Map_Orestrict__map ) ) ) @ c_Fun_Ofun__upd ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(189,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/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__absorb_0) ).
thf(959,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)],[189]) ).
thf(496,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/sandbox2/benchmark/theBenchmark.p',cls_disjoint__iff__not__equal_0) ).
thf(1643,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)],[496]) ).
thf(41,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).
thf(608,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(201,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
= C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__apply_0) ).
thf(986,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(26,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__iff_2) ).
thf(563,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(430,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/sandbox2/benchmark/theBenchmark.p',cls_Collect__empty__eq_0) ).
thf(1496,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)],[430]) ).
thf(255,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_a @ ( t_b @ ( t_b @ ( E @ ( D @ ( C @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple__case ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_triple_Osplit__asm_0) ).
thf(1102,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( C @ ( B @ hAPP ) @ hAPP ) @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ~ ( t_a @ ( t_b @ ( t_b @ ( E @ ( D @ ( C @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( B @ c_Hoare__Mirabelle_Otriple_Otriple__case ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OSemi ) )
!= c_Com_Ocom_OSKIP ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I13_J_0) ).
thf(505,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OSemi ) )
!= c_Com_Ocom_OSKIP ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(172,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/sandbox2/benchmark/theBenchmark.p',cls_Un__left__commute_0) ).
thf(922,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)],[172]) ).
thf(296,axiom,
tc_bool @ class_Lattices_Olower__semilattice,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olower__semilattice) ).
thf(1198,plain,
tc_bool @ class_Lattices_Olower__semilattice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(385,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Fun_Oid @ hAPP ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_id__apply_0) ).
thf(1396,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Fun_Oid @ hAPP ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(230,axiom,
! [B: $i,A: $i] :
~ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_in ) ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__iff_0) ).
thf(1044,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)],[230]) ).
thf(319,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_lessequals ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equalityI_0) ).
thf(1245,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_lessequals ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(239,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_in ) ) @ hBOOL )
| ~ ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_DiffE_1) ).
thf(1066,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_in ) ) @ hBOOL )
| ~ ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(444,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mem__def_1) ).
thf(1528,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)],[444]) ).
thf(244,axiom,
tc_bool @ class_Orderings_Opreorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Opreorder) ).
thf(1076,plain,
tc_bool @ class_Orderings_Opreorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(489,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/sandbox2/benchmark/theBenchmark.p',cls_singleton__conv2_0) ).
thf(1626,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)],[489]) ).
thf(84,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/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OSup__empty_0) ).
thf(722,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)],[84]) ).
thf(13,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ c_Com_Ocom_OBODY )
!= ( D @ ( C @ ( B @ c_Com_Ocom_OCond ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I55_J_0) ).
thf(531,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)],[13]) ).
thf(116,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/sandbox2/benchmark/theBenchmark.p',cls_IntI_0) ).
thf(795,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)],[116]) ).
thf(397,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/sandbox2/benchmark/theBenchmark.p',cls_Int__empty__left_0) ).
thf(1420,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)],[397]) ).
thf(175,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/sandbox2/benchmark/theBenchmark.p',cls_inf__left__commute_0) ).
thf(927,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)],[175]) ).
thf(53,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Com_Ocom_OCond ) ) )
!= c_Com_Ocom_OSKIP ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I15_J_0) ).
thf(648,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)],[53]) ).
thf(97,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Orderings_Opreorder )
| ( B @ ( A @ tc_fun ) @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Opreorder) ).
thf(749,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Orderings_Opreorder )
| ( B @ ( A @ tc_fun ) @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(8,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OSemi ) )
!= ( D @ ( C @ c_Com_Ocom_OWhile ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I46_J_0) ).
thf(516,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)],[8]) ).
thf(360,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Orderings_Oorder )
| ( B @ ( A @ tc_fun ) @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Oorder) ).
thf(1340,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Orderings_Oorder )
| ( B @ ( A @ tc_fun ) @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(129,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/sandbox2/benchmark/theBenchmark.p',cls_finite__UnI_0) ).
thf(823,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)],[129]) ).
thf(455,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
!= C )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__sup_1) ).
thf(1551,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( ( 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)],[455]) ).
thf(221,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/sandbox2/benchmark/theBenchmark.p',cls_insert__code_0) ).
thf(1025,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)],[221]) ).
thf(241,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/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_Odual__complete__lattice_0) ).
thf(1070,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)],[241]) ).
thf(279,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( ( 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/sandbox2/benchmark/theBenchmark.p',cls_atLeastatMost__empty__iff2_0) ).
thf(1156,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( ( 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)],[279]) ).
thf(195,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( D @ ( C @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ( C @ ( B @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_derivs__insertD_1) ).
thf(971,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( D @ ( C @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ( C @ ( B @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(461,axiom,
tc_bool @ class_Finite__Set_Ofinite_Ofinite,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Finite__Set_Ofinite_Ofinite) ).
thf(1566,plain,
tc_bool @ class_Finite__Set_Ofinite_Ofinite,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(479,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Diff__Int_0) ).
thf(1605,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).
thf(330,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/sandbox2/benchmark/theBenchmark.p',cls_sup__idem_0) ).
thf(1267,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)],[330]) ).
thf(425,axiom,
! [A: $i] :
( ( ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Complete__Lattice_OSup__class_OSup ) )
= ( A @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sup__empty_0) ).
thf(1484,plain,
! [A: $i] :
( ( ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Complete__Lattice_OSup__class_OSup ) )
= ( A @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(204,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ c_lessequals ) ) )
| ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__mono_0) ).
thf(993,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ c_lessequals ) ) )
| ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(80,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__absorb_0) ).
thf(712,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)],[80]) ).
thf(23,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I6_J_0) ).
thf(557,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(31,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/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I4_J_0) ).
thf(580,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)],[31]) ).
thf(144,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/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I7_J_0) ).
thf(855,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)],[144]) ).
thf(309,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/sandbox2/benchmark/theBenchmark.p',cls_hoare__derivs_Oinsert_0) ).
thf(1225,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)],[309]) ).
thf(387,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/sandbox2/benchmark/theBenchmark.p',cls_COMBC__def_0) ).
thf(1400,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)],[387]) ).
thf(78,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Diff_0) ).
thf(707,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(431,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/sandbox2/benchmark/theBenchmark.p',cls_insert__absorb_0) ).
thf(1499,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)],[431]) ).
thf(402,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__insert2_0) ).
thf(1432,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(3,axiom,
! [B: $i,A: $i] :
( c_Com_Ocom_OSKIP
!= ( B @ ( A @ c_Com_Ocom_OWhile ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I16_J_0) ).
thf(502,plain,
! [B: $i,A: $i] :
( c_Com_Ocom_OSKIP
!= ( B @ ( A @ c_Com_Ocom_OWhile ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(351,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/sandbox2/benchmark/theBenchmark.p',cls_atLeastAtMost__singleton_0) ).
thf(1317,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)],[351]) ).
thf(185,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__Diff__single_0) ).
thf(951,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(267,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/sandbox2/benchmark/theBenchmark.p',cls_inf__left__idem_0) ).
thf(1130,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)],[267]) ).
thf(306,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/sandbox2/benchmark/theBenchmark.p',cls_insertE_0) ).
thf(1218,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)],[306]) ).
thf(52,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Com_Ocom_OBODY )
!= ( B @ c_Com_Ocom_OBODY ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I6_J_0) ).
thf(643,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)],[52]) ).
thf(165,axiom,
! [C: $i,B: $i,A: $i] : ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__lower2_0) ).
thf(907,plain,
! [C: $i,B: $i,A: $i] : ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(344,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_lessequals ) ) )
| ~ ( B @ ( C @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_predicate1D_0) ).
thf(1300,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_lessequals ) ) )
| ~ ( B @ ( C @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(493,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ c_in ) ) @ hBOOL )
| ~ ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert_1) ).
thf(1637,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ c_in ) ) @ hBOOL )
| ~ ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).
thf(226,axiom,
! [B: $i,A: $i] : ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__subsetI_0) ).
thf(1038,plain,
! [B: $i,A: $i] : ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(32,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/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I3_J_1) ).
thf(585,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)],[32]) ).
thf(94,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/sandbox2/benchmark/theBenchmark.p',cls_conseq_1) ).
thf(744,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)],[94]) ).
thf(451,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/sandbox2/benchmark/theBenchmark.p',cls_inf__assoc_0) ).
thf(1543,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)],[451]) ).
thf(325,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/sandbox2/benchmark/theBenchmark.p',cls_Int__empty__right_0) ).
thf(1257,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)],[325]) ).
thf(448,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( ( 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/sandbox2/benchmark/theBenchmark.p',cls_atLeastatMost__empty__iff2_1) ).
thf(1536,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( ( 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)],[448]) ).
thf(213,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/sandbox2/benchmark/theBenchmark.p',cls_UN__iff_2) ).
thf(1008,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)],[213]) ).
thf(28,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OWhile ) )
!= ( C @ c_Com_Ocom_OBODY ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I58_J_0) ).
thf(571,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)],[28]) ).
thf(35,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( C @ ( B @ c_Fun_Oid @ ( A @ c_Fun_Ofcomp ) ) ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fcomp__id_0) ).
thf(595,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( C @ ( B @ c_Fun_Oid @ ( A @ c_Fun_Ofcomp ) ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(332,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/sandbox2/benchmark/theBenchmark.p',cls_hoare__derivs_Ointros_I6_J_1) ).
thf(1272,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)],[332]) ).
thf(152,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( C @ c_lessequals ) ) )
| ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__absorb2_0) ).
thf(876,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( C @ c_lessequals ) ) )
| ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(56,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OWhile ) )
!= c_Com_Ocom_OSKIP ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I17_J_0) ).
thf(656,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OWhile ) )
!= c_Com_Ocom_OSKIP ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(220,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ( A @ ( D @ ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__supI_0) ).
thf(1023,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ( A @ ( D @ ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(307,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Lattices_Olattice )
| ( B @ ( A @ tc_fun ) @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olattice) ).
thf(1221,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Lattices_Olattice )
| ( B @ ( A @ tc_fun ) @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(338,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/sandbox2/benchmark/theBenchmark.p',cls_sup__bot__left_0) ).
thf(1284,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)],[338]) ).
thf(366,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( E @ ( C @ c_lessequals ) ) )
| ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( E @ ( D @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastatMost__subset__iff_3) ).
thf(1353,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( E @ ( C @ c_lessequals ) ) )
| ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( E @ ( D @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(37,axiom,
! [C: $i,B: $i,A: $i] :
( c_Com_Ocom_OSKIP
!= ( C @ ( B @ ( A @ c_Com_Ocom_OCond ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I14_J_0) ).
thf(600,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)],[37]) ).
thf(433,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( C @ c_lessequals ) ) )
| ( C
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
| ( A @ ( A @ ( C @ c_Finite__Set_Olinorder__class_OMin ) @ ( A @ ( B @ c_Finite__Set_Olinorder__class_OMin ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Min__antimono_0) ).
thf(1504,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( C @ c_lessequals ) ) )
| ( C
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
| ( A @ ( A @ ( C @ c_Finite__Set_Olinorder__class_OMin ) @ ( A @ ( B @ c_Finite__Set_Olinorder__class_OMin ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(86,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/sandbox2/benchmark/theBenchmark.p',cls_finite__insert_1) ).
thf(727,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)],[86]) ).
thf(471,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_lessequals ) ) )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__diff_0) ).
thf(1585,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_lessequals ) ) )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
thf(271,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/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I1_J_0) ).
thf(1140,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)],[271]) ).
thf(316,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ c_Finite__Set_Ofinite ) )
| ~ ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
| ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__finite__subset_0) ).
thf(1240,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ c_Finite__Set_Ofinite ) )
| ~ ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
| ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(203,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/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OInf__lower_0) ).
thf(991,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)],[203]) ).
thf(139,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__subset__iff_2) ).
thf(845,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(248,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= C )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__absorb2_0) ).
thf(1084,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( ( 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)],[248]) ).
thf(414,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Finite__Set_Ofinite ) )
| ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__Diff__insert_0) ).
thf(1459,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Finite__Set_Ofinite ) )
| ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Finite__Set_Ofinite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(288,axiom,
( ( v_P @ ( t_a @ c_COMBI @ hAPP ) )
= v_P ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBI__def__raw_0) ).
thf(1180,plain,
( ( v_P @ ( t_a @ c_COMBI @ hAPP ) )
= v_P ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(11,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Collect ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Collect__def_0) ).
thf(524,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Collect ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(393,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_in ) ) @ hBOOL )
| ( D @ ( C @ ( A @ c_in ) ) @ hBOOL )
| ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_DiffI_0) ).
thf(1412,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_in ) ) @ hBOOL )
| ( D @ ( C @ ( A @ c_in ) ) @ hBOOL )
| ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(292,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/sandbox2/benchmark/theBenchmark.p',cls_Min__in_0) ).
thf(1189,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)],[292]) ).
thf(214,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) )
| ~ ( B @ ( A @ ( C @ c_in ) ) @ hBOOL )
| ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert__iff_0) ).
thf(1010,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) )
| ~ ( B @ ( A @ ( C @ c_in ) ) @ hBOOL )
| ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(258,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_COMBK ) ) @ hAPP ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBK__def_0) ).
thf(1108,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)],[258]) ).
thf(197,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/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_0) ).
thf(976,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)],[197]) ).
thf(163,axiom,
! [B: $i,A: $i] :
( ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__cancel_0) ).
thf(903,plain,
! [B: $i,A: $i] :
( ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(305,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_in ) ) @ hBOOL )
| ( D @ ( C @ ( A @ c_in ) ) @ hBOOL )
| ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__iff_2) ).
thf(1216,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_in ) ) @ hBOOL )
| ( D @ ( C @ ( A @ c_in ) ) @ hBOOL )
| ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(157,axiom,
! [C: $i,B: $i,A: $i] : ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__lower1_0) ).
thf(891,plain,
! [C: $i,B: $i,A: $i] : ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(497,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__subset__iff_0) ).
thf(1646,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).
thf(380,axiom,
! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_fequal @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ATP__Linkup_Oequal__imp__fequal_0) ).
thf(1385,plain,
! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_fequal @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(191,axiom,
tc_bool @ class_Orderings_Obot,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Obot) ).
thf(963,plain,
tc_bool @ class_Orderings_Obot,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(421,axiom,
! [B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__Diff_0) ).
thf(1476,plain,
! [B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(160,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/sandbox2/benchmark/theBenchmark.p',cls_Un__empty__left_0) ).
thf(896,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)],[160]) ).
thf(494,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
| ~ ( B @ ( A @ ( C @ c_in ) ) @ hBOOL )
| ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__single__insert_0) ).
thf(1639,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
| ~ ( B @ ( A @ ( C @ c_in ) ) @ hBOOL )
| ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).
thf(183,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/sandbox2/benchmark/theBenchmark.p',cls_Max__in_0) ).
thf(946,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)],[183]) ).
thf(318,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/sandbox2/benchmark/theBenchmark.p',cls_hoare__derivs_OSkip_0) ).
thf(1244,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)],[318]) ).
thf(205,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/sandbox2/benchmark/theBenchmark.p',cls_UnCI_1) ).
thf(995,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)],[205]) ).
thf(334,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__inf__iff_1) ).
thf(1276,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(473,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/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OInf__singleton_0) ).
thf(1590,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)],[473]) ).
thf(323,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__subset__iff_1) ).
thf(1253,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(74,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
| ~ ( A @ ( C @ ( B @ c_in ) ) @ hBOOL )
| ( A @ ( A @ ( C @ c_Finite__Set_Olinorder__class_OMax ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Max__ge_0) ).
thf(699,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
| ~ ( A @ ( C @ ( B @ c_in ) ) @ hBOOL )
| ( A @ ( A @ ( C @ c_Finite__Set_Olinorder__class_OMax ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(88,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) )
| ( 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/sandbox2/benchmark/theBenchmark.p',cls_subset__singletonD_0) ).
thf(731,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) )
| ( 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)],[88]) ).
thf(112,axiom,
! [C: $i,B: $i,A: $i] : ( B @ ( C @ ( A @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_in ) ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__iff_1) ).
thf(786,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)],[112]) ).
thf(223,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_fequal @ hAPP ) @ hAPP ) @ hBOOL )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ATP__Linkup_Ofequal__imp__equal_0) ).
thf(1030,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)],[223]) ).
thf(245,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/sandbox2/benchmark/theBenchmark.p',cls_UN__extend__simps_I3_J_0) ).
thf(1077,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)],[245]) ).
thf(303,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/sandbox2/benchmark/theBenchmark.p',cls_o__def_0) ).
thf(1212,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)],[303]) ).
thf(437,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__ord_I2_J_0) ).
thf(1513,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(348,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/sandbox2/benchmark/theBenchmark.p',cls_Int__insert__left_1) ).
thf(1309,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)],[348]) ).
thf(15,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( B @ ( B @ c_Fun_Oid @ ( A @ c_Fun_Ocomp ) ) ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_o__id_0) ).
thf(536,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( B @ ( B @ c_Fun_Oid @ ( A @ c_Fun_Ocomp ) ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(480,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/sandbox2/benchmark/theBenchmark.p',cls_singleton__inject_0) ).
thf(1607,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)],[480]) ).
thf(102,axiom,
! [A: $i] : ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( A @ c_Set_Oinsert @ c_Finite__Set_Ofun__left__comm__idem ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__left__comm__idem__insert_0) ).
thf(763,plain,
! [A: $i] : ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( A @ c_Set_Oinsert @ c_Finite__Set_Ofun__left__comm__idem ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(20,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( D @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__eqI_1) ).
thf(549,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( D @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(408,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( A @ c_Finite__Set_Ofun__left__comm__idem ) ) )
| ( ( C @ ( C @ ( C @ ( B @ ( A @ hAPP ) @ ( B @ ( A @ hAPP ) @ c_Fun_Ocomp ) ) ) ) )
= ( B @ ( A @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__left__comm__idem_Ofun__comp__idem_0) ).
thf(1444,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( A @ c_Finite__Set_Ofun__left__comm__idem ) ) )
| ( ( C @ ( C @ ( C @ ( B @ ( A @ hAPP ) @ ( B @ ( A @ hAPP ) @ c_Fun_Ocomp ) ) ) ) )
= ( B @ ( A @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(82,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/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_2) ).
thf(716,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)],[82]) ).
thf(483,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
| ~ ( C @ ( A @ c_Finite__Set_Ofinite ) )
| ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__Diff2_1) ).
thf(1614,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
| ~ ( C @ ( A @ c_Finite__Set_Ofinite ) )
| ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Finite__Set_Ofinite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).
thf(268,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__diff_0) ).
thf(1133,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(364,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/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Ononempty__iff_2) ).
thf(1348,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)],[364]) ).
thf(436,axiom,
tc_bool @ class_Lattices_Oupper__semilattice,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oupper__semilattice) ).
thf(1512,plain,
tc_bool @ class_Lattices_Oupper__semilattice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(336,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/sandbox2/benchmark/theBenchmark.p',cls_sup__inf__distrib1_0) ).
thf(1280,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)],[336]) ).
thf(467,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
| ~ ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert__iff_4) ).
thf(1578,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
| ~ ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).
thf(311,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
| ~ ( C @ ( D @ ( A @ c_in ) ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__iff_0) ).
thf(1229,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
| ~ ( C @ ( D @ ( A @ c_in ) ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(452,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/sandbox2/benchmark/theBenchmark.p',cls_Un__Int__distrib_0) ).
thf(1546,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)],[452]) ).
thf(488,axiom,
tc_bool @ class_Orderings_Oorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Oorder) ).
thf(1625,plain,
tc_bool @ class_Orderings_Oorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).
thf(127,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) )
| ( C @ ( A @ ( D @ c_in ) ) @ hBOOL )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert__iff_1) ).
thf(818,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) )
| ( C @ ( A @ ( D @ c_in ) ) @ hBOOL )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(143,axiom,
tc_bool @ class_Lattices_Obounded__lattice,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Obounded__lattice) ).
thf(854,plain,
tc_bool @ class_Lattices_Obounded__lattice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(149,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/sandbox2/benchmark/theBenchmark.p',cls_Un__left__absorb_0) ).
thf(867,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)],[149]) ).
thf(38,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__trans_0) ).
thf(603,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(208,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__ord_I4_J_0) ).
thf(999,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(45,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ c_Com_Ocom_OSemi ) )
!= ( C @ c_Com_Ocom_OBODY ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I48_J_0) ).
thf(620,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)],[45]) ).
thf(133,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 @ 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/sandbox2/benchmark/theBenchmark.p',cls_weak__Body_0) ).
thf(833,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 @ 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)],[133]) ).
thf(193,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/sandbox2/benchmark/theBenchmark.p',cls_conseq1_0) ).
thf(967,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)],[193]) ).
thf(253,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( ( 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/sandbox2/benchmark/theBenchmark.p',cls_atLeastatMost__empty__iff_1) ).
thf(1097,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( ( 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)],[253]) ).
thf(134,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ c_lessequals ) ) )
| ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__least_0) ).
thf(835,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ c_lessequals ) ) )
| ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(474,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( tc_bool @ ( A @ tc_fun ) @ ( E @ ( C @ c_lessequals ) ) )
| ( tc_bool @ ( A @ tc_fun ) @ ( 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 ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__mono_0) ).
thf(1593,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( tc_bool @ ( A @ tc_fun ) @ ( E @ ( C @ c_lessequals ) ) )
| ( tc_bool @ ( A @ tc_fun ) @ ( 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 ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(378,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= C )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__sup_0) ).
thf(1380,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( ( 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)],[378]) ).
thf(320,axiom,
tc_bool @ class_Complete__Lattice_Ocomplete__lattice,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Complete__Lattice_Ocomplete__lattice) ).
thf(1248,plain,
tc_bool @ class_Complete__Lattice_Ocomplete__lattice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(114,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_HOL_Ominus )
| ( B @ ( A @ tc_fun ) @ class_HOL_Ominus ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__HOL_Ominus) ).
thf(790,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_HOL_Ominus )
| ( B @ ( A @ tc_fun ) @ class_HOL_Ominus ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(148,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__le1_0) ).
thf(865,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(423,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_Un__Diff__cancel_0) ).
thf(1480,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( 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)],[423]) ).
thf(404,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ ( 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 ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__Int2_0) ).
thf(1436,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ ( 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 ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(119,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/sandbox2/benchmark/theBenchmark.p',cls_inf1I_0) ).
thf(801,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)],[119]) ).
thf(371,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/sandbox2/benchmark/theBenchmark.p',cls_insert__def_0) ).
thf(1363,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)],[371]) ).
thf(429,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( B @ ( tc_bool @ ( B @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( D @ ( C @ ( B @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( tc_Com_Ostate @ ( tc_bool @ ( c_False @ c_COMBK ) ) @ c_COMBK ) ) @ c_Hoare__Mirabelle_Otriple_Otriple ) ) ) @ ( B @ tc_Hoare__Mirabelle_Otriple @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_falseE_0) ).
thf(1495,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( B @ ( tc_bool @ ( B @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( D @ ( C @ ( B @ ( tc_bool @ ( tc_Com_Ostate @ tc_fun ) @ ( tc_Com_Ostate @ ( tc_bool @ ( c_False @ c_COMBK ) ) @ c_COMBK ) ) @ 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)],[429]) ).
thf(122,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( tc_bool @ ( C @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
| ( C @ ( B @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_weaken_0) ).
thf(807,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( tc_bool @ ( C @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
| ( C @ ( B @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(358,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Lattices_Olattice )
| ( B @ ( A @ tc_fun ) @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olower__semilattice) ).
thf(1335,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)],[358]) ).
thf(459,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/sandbox2/benchmark/theBenchmark.p',cls_Un__Int__crazy_0) ).
thf(1561,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)],[459]) ).
thf(224,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__Diff_0) ).
thf(1033,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(131,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 @ ( A @ ( D @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ c_Finite__Set_Ofold1 ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( C @ c_in ) ) @ hBOOL )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_below__fold1__iff_0) ).
thf(828,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 @ ( A @ ( D @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ c_Finite__Set_Ofold1 ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( C @ c_in ) ) @ hBOOL )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(73,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( E @ c_in ) ) @ hBOOL )
| ( ( D @ tc_Option_Ooption @ ( C @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Map_Orestrict__map ) ) ) @ c_Fun_Ofun__upd ) ) ) ) )
= ( D @ tc_Option_Ooption @ ( C @ ( F @ ( E @ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Map_Orestrict__map ) ) ) @ c_Fun_Ofun__upd ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__restrict__conv_0) ).
thf(696,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( E @ c_in ) ) @ hBOOL )
| ( ( D @ tc_Option_Ooption @ ( C @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Map_Orestrict__map ) ) ) @ c_Fun_Ofun__upd ) ) ) ) )
= ( D @ tc_Option_Ooption @ ( C @ ( F @ ( E @ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Map_Orestrict__map ) ) ) @ c_Fun_Ofun__upd ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(187,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/sandbox2/benchmark/theBenchmark.p',cls_Comp_0) ).
thf(955,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)],[187]) ).
thf(155,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/sandbox2/benchmark/theBenchmark.p',cls_inf__commute_0) ).
thf(886,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)],[155]) ).
thf(235,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/sandbox2/benchmark/theBenchmark.p',cls_fold1Set__sing_0) ).
thf(1056,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)],[235]) ).
thf(59,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__ge2_0) ).
thf(664,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(50,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( D @ ( E @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__eqI_0) ).
thf(635,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( D @ ( E @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(420,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F = B )
| ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
= ( F @ ( A @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__apply_1) ).
thf(1473,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F = B )
| ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
= ( F @ ( A @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(363,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_Diff__disjoint_0) ).
thf(1346,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( 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)],[363]) ).
thf(481,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/sandbox2/benchmark/theBenchmark.p',cls_o__eq__dest__lhs_0) ).
thf(1610,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)],[481]) ).
thf(92,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/sandbox2/benchmark/theBenchmark.p',cls_UnE_0) ).
thf(740,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)],[92]) ).
thf(314,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/sandbox2/benchmark/theBenchmark.p',cls_finite__Un_2) ).
thf(1236,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)],[314]) ).
thf(327,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/sandbox2/benchmark/theBenchmark.p',cls_bex__empty_0) ).
thf(1261,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)],[327]) ).
thf(377,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/sandbox2/benchmark/theBenchmark.p',cls_Int__Collect_2) ).
thf(1378,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)],[377]) ).
thf(454,axiom,
! [B: $i,A: $i] : ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__refl_0) ).
thf(1550,plain,
! [B: $i,A: $i] : ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).
thf(368,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/sandbox2/benchmark/theBenchmark.p',cls_inf__bot__left_0) ).
thf(1357,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)],[368]) ).
thf(166,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/sandbox2/benchmark/theBenchmark.p',cls_Int__commute_0) ).
thf(908,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)],[166]) ).
thf(141,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/sandbox2/benchmark/theBenchmark.p',cls_inj__on__insert_0) ).
thf(850,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)],[141]) ).
thf(71,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ hAPP ) @ hBOOL )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_lessequals ) ) )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__predicate1D_0) ).
thf(691,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ hAPP ) @ hBOOL )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_lessequals ) ) )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(151,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/sandbox2/benchmark/theBenchmark.p',cls_triple_Oinject_0) ).
thf(871,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)],[151]) ).
thf(263,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/sandbox2/benchmark/theBenchmark.p',cls_inf__bot__right_0) ).
thf(1120,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)],[263]) ).
thf(251,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( A @ c_Collect ) @ ( B @ c_in ) ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CollectD_0) ).
thf(1093,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)],[251]) ).
thf(136,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/sandbox2/benchmark/theBenchmark.p',cls_sup1CI_1) ).
thf(839,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)],[136]) ).
thf(446,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/sandbox2/benchmark/theBenchmark.p',cls_o__apply_0) ).
thf(1532,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)],[446]) ).
thf(146,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( B @ c_lessequals ) ) )
| ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
!= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__Un__eq_1) ).
thf(860,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( B @ c_lessequals ) ) )
| ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
!= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(469,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__ord_I3_J_0) ).
thf(1582,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).
thf(218,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
| ~ ( C @ ( D @ ( A @ c_in ) ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subsetD_0) ).
thf(1019,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
| ~ ( C @ ( D @ ( A @ c_in ) ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(476,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__infE_1) ).
thf(1597,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).
thf(211,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/sandbox2/benchmark/theBenchmark.p',cls_UN__constant_0) ).
thf(1004,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)],[211]) ).
thf(120,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ( A @ ( D @ ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__least_0) ).
thf(803,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ( A @ ( D @ ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(352,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_in ) ) @ hBOOL )
| ( ( tc_bool @ ( A @ tc_fun ) @ ( 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 ) @ c_HOL_Ominus__class_Ominus ) ) )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__insert__absorb_0) ).
thf(1320,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_in ) ) @ hBOOL )
| ( ( tc_bool @ ( A @ tc_fun ) @ ( 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 ) @ c_HOL_Ominus__class_Ominus ) ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(373,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/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__distrib2_0) ).
thf(1367,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)],[373]) ).
thf(18,axiom,
! [A: $i] :
( c_Com_Ocom_OSKIP
!= ( A @ c_Com_Ocom_OBODY ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I18_J_0) ).
thf(543,plain,
! [A: $i] :
( c_Com_Ocom_OSKIP
!= ( A @ c_Com_Ocom_OBODY ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(427,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/sandbox2/benchmark/theBenchmark.p',cls_Un__insert__right_0) ).
thf(1490,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)],[427]) ).
thf(395,axiom,
! [C: $i,B: $i,A: $i] : ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__upper2_0) ).
thf(1416,plain,
! [C: $i,B: $i,A: $i] : ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(100,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/sandbox2/benchmark/theBenchmark.p',cls_triple_Oinject_1) ).
thf(755,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)],[100]) ).
thf(418,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/sandbox2/benchmark/theBenchmark.p',cls_inf__idem_0) ).
thf(1468,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)],[418]) ).
thf(416,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( D @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__infI_0) ).
thf(1463,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( D @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(57,axiom,
! [A: $i] :
( ~ ( A @ class_Finite__Set_Ofinite_Ofinite )
| ( A @ tc_Option_Ooption @ class_Finite__Set_Ofinite_Ofinite ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_Option__Ooption__Finite__Set_Ofinite_Ofinite) ).
thf(659,plain,
! [A: $i] :
( ~ ( A @ class_Finite__Set_Ofinite_Ofinite )
| ( A @ tc_Option_Ooption @ class_Finite__Set_Ofinite_Ofinite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(299,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/sandbox2/benchmark/theBenchmark.p',cls_UN__absorb_0) ).
thf(1204,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)],[299]) ).
thf(410,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ ( D @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__supE_1) ).
thf(1449,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ ( D @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(216,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__ord_I1_J_0) ).
thf(1014,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(396,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( B @ c_lessequals ) ) )
| ( B
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
| ( A @ ( A @ ( C @ c_Finite__Set_Olinorder__class_OMax ) @ ( A @ ( B @ c_Finite__Set_Olinorder__class_OMax ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Max__mono_0) ).
thf(1417,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( B @ c_lessequals ) ) )
| ( B
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ ( C @ c_Finite__Set_Ofinite ) )
| ( A @ ( A @ ( C @ c_Finite__Set_Olinorder__class_OMax ) @ ( A @ ( B @ c_Finite__Set_Olinorder__class_OMax ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(1685,plain,
$false,
inference(e,[status(thm)],[892,809,1337,760,1454,1559,628,1315,962,941,777,666,1554,1110,683,1290,1068,1522,1618,511,677,1041,1173,1422,1569,1305,597,1426,500,538,670,1164,797,814,1327,1342,747,913,1507,930,1095,1196,898,1001,709,841,1386,1482,651,1391,1576,782,1441,973,1046,1518,1265,1628,1409,1287,1298,719,1330,1323,934,1059,949,917,751,559,638,1087,1115,1641,1100,969,606,1572,1398,881,924,1465,1302,1373,623,514,1283,1051,905,1151,937,1383,574,734,1447,1072,1394,1526,1351,998,988,1405,981,766,1622,774,1104,1242,1074,546,925,1199,534,714,1438,661,1274,910,746,825,1021,1042,1255,1123,1487,1370,729,1238,957,1223,894,1355,1580,1502,820,693,630,1602,1365,879,852,1296,1457,889,1159,1210,1079,1407,1128,1634,1012,1106,847,566,1402,1360,1143,1534,615,1064,1227,725,1006,1138,593,869,610,1118,499,519,742,1234,1541,1270,1259,1567,1361,1182,1461,686,1424,1584,1214,1155,706,1028,1082,554,753,1414,526,1016,1207,590,1612,679,1039,837,1588,701,1231,654,1192,1002,1429,1599,779,605,1263,997,1478,1249,1451,738,1530,1539,1333,1434,938,805,508,1563,1054,1170,1035,1515,1167,1616,1202,792,1187,674,953,1185,1278,1510,1146,1548,1595,689,1631,1135,1648,1251,618,1154,562,772,1620,1388,577,1403,1520,843,1125,1312,787,1090,919,704,540,672,1194,1209,900,831,681,784,1574,1524,1492,1144,1307,764,979,1048,736,1376,1439,863,1175,811,1471,816,1325,1344,769,943,1177,1112,858,1557,552,799,1162,1149,964,626,915,1293,668,932,1061,521,983,959,1643,608,986,563,1496,1102,505,922,1198,1396,1044,1245,1066,1528,1076,1626,722,531,795,1420,927,648,749,516,1340,823,1551,1025,1070,1156,971,1566,1605,1267,1484,993,712,557,580,855,1225,1400,707,1499,1432,502,1317,951,1130,1218,643,907,1300,1637,1038,585,744,1543,1257,1536,1008,571,595,1272,876,656,1023,1221,1284,1353,600,1504,727,1585,1140,1240,991,845,1084,1459,1180,524,1412,1189,1010,1108,976,903,1216,891,1646,1385,963,1476,896,1639,946,1244,995,1276,1590,1253,699,731,786,1030,1077,1212,1513,1309,536,1607,763,549,1444,716,1614,1133,1348,1512,1280,1578,1229,1546,1625,818,854,867,603,999,620,833,967,1097,835,1593,1380,1248,790,865,1480,1436,801,1363,1495,807,1335,1561,1033,828,696,955,886,1056,664,635,1473,1346,1610,740,1236,1261,1378,1550,1357,908,850,691,871,1120,1093,839,1532,860,1582,1019,1597,1004,803,1320,1367,543,1490,1416,755,1468,1463,659,1204,1449,1014,1417]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV910-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.12/0.39 % Computer : n006.cluster.edu
% 0.12/0.39 % Model : x86_64 x86_64
% 0.12/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.39 % Memory : 8046.5625MB
% 0.12/0.39 % OS : Linux 6.8.0-71-generic
% 0.12/0.39 % CPULimit : 300
% 0.12/0.39 % WCLimit : 300
% 0.12/0.39 % DateTime : Sat Sep 26 15:09:10 UTC 2026
% 0.12/0.39 % CPUTime :
% 0.12/0.39 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.89/0.99 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.96/1.37 % [INFO] Parsing done (375ms).
% 1.96/1.38 % [INFO] Running in sequential loop mode.
% 3.13/1.77 % [INFO] eprover registered as external prover.
% 3.13/1.78 % [INFO] Scanning for conjecture ...
% 3.62/2.00 % [INFO] Found a conjecture (or negated_conjecture) and 496 axioms. Running axiom selection ...
% 4.92/2.25 % [INFO] Axiom selection finished. Selected 496 axioms (removed 0 axioms).
% 6.10/2.57 % [INFO] Problem is propositional (TPTP CNF).
% 6.10/2.58 % [INFO] Type checking passed.
% 6.10/2.59 % [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 ...
% 16.31/4.93 % External prover 'e' found a proof!
% 16.31/4.93 % [INFO] Killing All external provers ...
% 16.31/4.93 % Time passed: 4393ms (effective reasoning time: 3539ms)
% 16.31/4.93 % Axioms used in derivation (496): cls_inf__sup__absorb_0, cls_inf__sup__aci_I2_J_0, cls_atLeastatMost__subset__iff_2, cls_the__sym__eq__trivial_0, cls_Diff__iff_2, cls_restrict__map__to__empty_0, cls_bot__fun__eq_0, cls_Int__Un__distrib_0, cls_com_Osimps_I55_J_0, clsarity_fun__Lattices_Olower__semilattice, cls_Diff__cancel_0, cls_INT__extend__simps_I4_J_0, cls_Int__absorb2_0, cls_com_Osimps_I18_J_0, cls_asm_0, cls_subset__insert_1, cls_sup__ge1_0, clsarity_Option__Ooption__Finite__Set_Ofinite_Ofinite, cls_insertE_0, cls_Un__Diff_0, cls_com_Osimps_I3_J_0, cls_Un__subset__iff_0, cls_equalityI_0, cls_insert__inter__insert_0, cls_order__eq__iff_0, cls_com_Osimps_I5_J_0, cls_id__o_0, cls_weak__Body_0, cls_COMBC__def_0, cls_subset__empty_1, cls_finite__insert_0, cls_com_Osimps_I44_J_0, cls_com_Osimps_I14_J_0, cls_Un__empty__left_0, cls_fun__upd__apply_1, cls_le__funD_0, cls_sup__bot__right_0, cls_insert__code_1, cls_Loop__sound__lemma_0, clsarity_bool__Lattices_Olower__semilattice, cls_le__SUPI_0, cls_Un__upper1_0, cls_fold1Set__sing_1, cls_Un__commute_0, cls_COMBK__def_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_inf__sup__aci_I6_J_0, cls_restrict__fun__upd_0, clsarity_fun__Orderings_Oorder, cls_finite__Un_2, cls_Diff__Un_0, cls_Int__insert__left_0, cls_triple_Oinject_1, cls_Int__subset__iff_2, cls_le__inf__iff_1, clsarity_bool__HOL_Ominus, cls_o__eq__id__dest_0, cls_Diff__subset__conv_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_Int__Un__distrib2_0, cls_restrict__map__insert_0, cls_derivs__insertD_1, cls_inf1E_1, cls_com_Osimps_I5_J_1, cls_Diff__triv_0, cls_insert__iff_1, cls_inf__sup__distrib1_0, cls_sup__inf__distrib2_0, cls_fun__upd__None__restrict_0, cls_K__record__comp_0, clsarity_fun__Lattices_Oupper__semilattice, cls_com_Osimps_I4_J_2, cls_le__sup__iff_0, cls_COMBI__def__raw_0, cls_insert__subset_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_CollectI_0, cls_subset__insert__iff_2, cls_com_Osimps_I54_J_0, 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, clsarity_bool__HOL_Oord, cls_set__mp_0, cls_Un__Int__distrib2_0, cls_BodyN_0, cls_finite__Int_1, cls_Int__empty__right_0, cls_fold1__def_0, cls_com_Osimps_I45_J_0, cls_Collect__empty__eq_0, cls_inf__fun__eq_0, cls_Inf__singleton_0, cls_le__supI_0, cls_UN__extend__simps_I1_J_0, cls_CollectD_0, cls_Un__empty_2, cls_le__iff__sup_1, cls_triple_Ocases_0, cls_Un__subset__iff_1, cls_Inf__binary_0, cls_SUP__const_0, cls_inj__on__insert_0, cls_SUP1__I_0, cls_triple_Oinject_2, cls_UN__iff_2, cls_le__iff__sup_0, cls_UN__extend__simps_I3_J_0, cls_order__eq__refl_0, cls_UN__absorb_0, clsarity_fun__Orderings_Obot, cls_le__supE_1, cls_fun__upd__other_0, cls_finite__Int_0, cls_Un__absorb2_0, cls_atLeastatMost__subset__iff_3, cls_inf__sup__aci_I8_J_0, cls_Un__empty__right_0, cls_insert__ident_0, cls_conseq1_1, cls_id__apply_0, clsarity_bool__Orderings_Oorder, cls_bot__least_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_triple_Orecs_0, cls_UN__Un_0, cls_Max__mono_0, cls_Sup__singleton_0, cls_UN__constant_0, cls_com_Osimps_I6_J_0, cls_UnCI_0, cls_escape_0, cls_subset__iff_0, cls_insert__code_2, cls_com_Osimps_I58_J_0, clsarity_fun__HOL_Oord, cls_Diff__idemp_0, cls_subset__empty_0, cls_rev__predicate1D_0, cls_insert__Diff__single_0, cls_singleton__iff_1, cls_atLeastatMost__empty__iff_1, cls_finite_0, cls_complete__lattice_OInf__empty_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_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_Inf__insert_0, cls_fun__upd__triv_0, cls_falseE_0, cls_id__fcomp_0, cls_finite__UnI_0, cls_inf__sup__aci_I3_J_0, cls_set__eq__subset_2, cls_Un__mono_0, cls_Int__insert__left_1, cls_insert__subset_1, cls_Int__empty__left_0, cls_ATP__Linkup_Ofequal__imp__equal_0, cls_ex__in__conv_0, cls_sup__commute_0, cls_le__inf__iff_0, cls_Int__subset__iff_1, cls_fun__upd__restrict__conv_0, cls_Un__subset__iff_2, clsarity_fun__Lattices_Olattice, cls_linorder__linear_0, cls_Un__empty_0, cls_Int__assoc_0, cls_conseq12_2, cls_order__antisym_0, cls_com_Osimps_I46_J_0, cls_inf__le2_0, cls_insert__is__Un_0, cls_com_Osimps_I19_J_0, cls_order__trans_0, cls_subset__trans_0, cls_atLeastAtMost__singleton_0, cls_double__diff_0, cls_com_Osimps_I3_J_1, cls_insertI1_0, cls_DiffI_0, cls_le__supE_0, cls_empty__not__insert_0, cls_sup__assoc_0, cls_insert__Diff1_0, cls_Diff__Int__distrib2_0, cls_the__eq__trivial_0, cls_le__sup__iff_1, clsarity_bool__Orderings_Obot, cls_mem__def_0, cls_inf__sup__aci_I7_J_0, cls_Un__Int__crazy_0, clsarity_bool__Orderings_Opreorder, cls_singleton__conv_0, cls_Nitpick_OEx1__def_2, cls_fun__left__comm__idem__sup_0, cls_hoare__derivs_Oinsert_0, cls_empty__subsetI_0, cls_fun__upd__twist_0, cls_atLeastatMost__subset__iff_0, cls_Un__absorb1_0, cls_hoare__derivs_OIf_0, cls_Diff__insert2_0, cls_Int__commute_0, cls_Sup__upper_0, cls_sup__least_0, cls_com_Osimps_I17_J_0, cls_doubleton__eq__iff_0, cls_inf__sup__aci_I1_J_0, cls_sup1E_0, cls_distrib__inf__le_0, cls_subset__refl_0, cls_Max__singleton_0, cls_singletonE_0, cls_inj__on__iff_0, cls_fun__left__comm__idem_Ofun__left__idem_0, cls_inj__on__empty_0, cls_DiffE_0, cls_Int__Diff_0, cls_conseq2_1, cls_insertCI_0, cls_le__inf__iff_2, cls_Un__Diff__cancel_0, cls_complete__lattice_OInf__insert_0, cls_insert__Diff_0, cls_sup1CI_1, cls_complete__lattice_OInf__binary_0, cls_below__fold1__iff_0, cls_le__infE_0, cls_fun__upd__apply_0, cls_complete__lattice_OSup__binary_0, cls_restrict__in_0, cls_order__eq__iff_2, cls_le__infI1_0, cls_bot1E_0, cls_weaken_0, cls_Int__absorb_0, cls_inf__assoc_0, cls_insert__mono_0, cls_hoare__derivs_Ointros_I6_J_2, cls_le__supI2_0, cls_fold1__singleton_0, cls_Collect__def_0, cls_Int__lower2_0, cls_UN__constant_1, cls_o__eq__dest_0, cls_Un__assoc_0, cls_Un__Diff__cancel2_0, cls_Max__ge_0, cls_empty__fold1SetE_0, cls_bex__empty_0, cls_Int__left__absorb_0, cls_Diff__disjoint_0, cls_inf__sup__ord_I4_J_0, cls_fcomp__id_0, cls_o__eq__dest__lhs_0, cls_Diff__mono_0, cls_order__antisym__conv_0, cls_UnE_0, cls_inj__on__Un_0, cls_restrict__restrict_0, cls_subset__insertI2_0, cls_conseq_1, cls_id__def_0, cls_doubleton__eq__iff_3, cls_atLeastatMost__empty__iff_0, cls_finite__Diff__insert_1, cls_complete__lattice_Odual__complete__lattice_0, cls_Diff__Int__distrib_0, cls_finite__Diff2_1, cls_Un__absorb_0, cls_com_Osimps_I13_J_0, cls_inj__on__def_0, cls_Int__lower1_0, clsarity_bool__Lattices_Olattice, cls_fun__upd__restrict_0, cls_com_Osimps_I49_J_0, cls_Un__Int__distrib_0, clsarity_bool__Lattices_Obounded__lattice, cls_inf__sup__ord_I1_J_0, cls_le__infI_0, cls_subset__insert__iff_4, cls_Int__subset__iff_0, cls_bot__empty__eq_0, cls_eq__eqI_0, cls_complete__lattice_OInf__lower_0, cls_fun__left__comm__idem_Ofun__comp__idem_0, cls_insert__subset_2, cls_le__supI1_0, cls_le__eqI_0, cls_sup__left__idem_0, cls_complete__lattice_OSup__insert_0, cls_o__id_0, cls_thin_0, cls_subsetD_0, cls_insert__not__empty_0, cls_finite__Un_0, cls_inf__idem_0, clsarity_fun__Lattices_Obounded__lattice, cls_com_Osimps_I12_J_0, cls_finite__subset_0, cls_inf__bot__left_0, cls_inf1I_0, cls_Int__left__commute_0, cls_le__sup__iff_2, cls_o__def_0, clsarity_fun__Complete__Lattice_Ocomplete__lattice, cls_restrict__out_0, cls_insert__absorb2_0, cls_sup__fun__eq_0, cls_UNION__empty__conv_I1_J_0, cls_fun__upd__idem_0, cls_finite__Diff__insert_0, cls_inf__sup__aci_I4_J_0, cls_inj__on__id_0, cls_sup__inf__absorb_0, cls_subset__singletonD_0, cls_UN__I_0, cls_Un__Int__assoc__eq_1, cls_doubleton__eq__iff_1, cls_UN__extend__simps_I2_J_0, cls_fun__upd__idem__iff_0, cls_fun__diff__def_0, cls_Sup__insert_0, cls_xt1_I6_J_0, cls_subset__insert__iff_0, cls_empty_0, cls_com_Osimps_I52_J_0, cls_Int__iff_2, cls_complete__lattice_OInf__singleton_0, cls_Nitpick_OEx1__def_3, clsarity_bool__Complete__Lattice_Ocomplete__lattice, cls_Diff__empty_0, cls_fold1__belowI_0, cls_Un__left__absorb_0, cls_IntI_0, cls_inf__greatest_0, cls_Sup__empty_0, cls_empty__Collect__eq_0, cls_atLeastatMost__subset__iff_1, cls_emptyE_0, cls_ATP__Linkup_Oequal__imp__fequal_0, cls_inf__sup__aci_I5_J_0, cls_Diff__Int_0, cls_triple_Oinject_0, cls_Un__empty_1, cls_comp__cong_0, cls_le__iff__inf_0, cls_subset__insert_0, cls_sup__idem_0, cls_inf__sup__ord_I3_J_0, cls_fun__upd__same_0, cls_eq__eqI_1, cls_com_Osimps_I4_J_1, cls_insert__def_0, cls_sup__eq__bot__eq1_0, cls_fun__left__comm__idem__inf_0, cls_comm__monoid__add_Ononempty__iff_2, cls_subset__inj__on_0, cls_singleton__inject_0, cls_UN__upper_0, cls_fun__upd__None__restrict_1, cls_IntE_0, cls_Un__least_0, cls_inj__on__contraD_0, cls_sup1CI_0, cls_Int__greatest_0, cls_Loop_0, cls_inj__onD_0, cls_hoare__derivs_Ointros_I6_J_1, cls_sup__ge2_0, clsarity_fun__Orderings_Opreorder, cls_atLeastatMost__empty__iff2_1, cls_triple_Osplit_0, cls_IntE_1, cls_subset__Un__eq_1, cls_sup__left__commute_0, cls_conseq2_0, cls_restrict__fun__upd_1, clsarity_bool__Lattices_Odistrib__lattice, cls_fold1Set__sing_0, cls_finite__UN_0, cls_le__infE_1, cls_finite_OemptyI_0, cls_Nitpick_OThe__psimp_0, cls_inj__on__diff_0, cls_fcomp__apply_0, cls_inf__le1_0, cls_insertCI_1, cls_inf__left__idem_0, cls_doubleton__eq__iff_4, cls_Max__in_0, cls_complete__lattice_OSup__upper_0, cls_insert__code_0, cls_le__eqI_1, cls_inj__on__id2_0, cls_fcomp__def_0, cls_DiffE_1, cls_complete__lattice_OSup__empty_0, cls_Diff__subset__conv_1, cls_conseq12_0, cls_Un__Diff__Int_0, cls_subset__insertI_0, cls_triple_Osplit__asm_0, cls_Diff__Int2_0, cls_Diff__insert__absorb_0, cls_Diff__partition_0, cls_sup__bot__left_0, cls_rev__finite__subset_0, cls_finite__Un_1, cls_fun__upd__upd_0, cls_disjoint__iff__not__equal_0, cls_inj__on__Un_1, cls_com_Osimps_I16_J_0, cls_fcomp__assoc_0, cls_com_Osimps_I15_J_0, cls_Un__Int__assoc__eq_0, cls_COMBI__def_0, cls_insert__commute_0, cls_insert__iff_2, cls_le__infI2_0, cls_UNION__empty__conv_I2_J_0, cls_sup__inf__distrib1_0, cls_hoare__sound_0, cls_finite__Diff2_0, cls_UN__insert_0, cls_Min__in_0, cls_Un__insert__right_0, cls_equalityE_0, cls_inf__sup__distrib2_0, cls_cut_0, clsarity_fun__Lattices_Odistrib__lattice, clsarity_fun__HOL_Ominus, cls_com_Osimps_I4_J_0, cls_empty__def_0, cls_o__apply_0, cls_inf__bot__right_0, cls_sup__absorb1_0, cls_fun__left__comm__idem__insert_0, cls_com_Osimps_I53_J_0, cls_ball__empty_0, cls_Int__insert__right_0, cls_fun__upd__comp_0, cls_UN__empty2_0, cls_Min__antimono_0, cls_o__assoc_0, cls_subset__insert__iff_1, cls_escape_1, cls_singleton__conv2_0, cls_Diff__subset_0, cls_derivs__insertD_0, cls_conseq1_0, cls_predicate1D_0, cls_inf1E_0, cls_empty__Diff_0, cls_Int__Collect_2, cls_fun__upd__idem__iff_1
% 16.31/4.93 % No. of inferences in proof: 997
% 16.31/4.93 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 4393 ms resp. 3539 ms w/o parsing
% 17.33/5.19 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 17.66/5.20 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------