TSTP Solution File: SWV827-1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SWV827-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 12:18:46 EDT 2023
% Result : Unsatisfiable 54.37s 11.55s
% Output : Refutation 54.71s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 567
% Syntax : Number of formulae : 1051 ( 287 unt; 84 typ; 0 def)
% Number of atoms : 2037 ( 582 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 17022 (1046 ~;1070 |; 0 &;14906 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 184 ( 184 >; 0 *; 0 +; 0 <<)
% Number of symbols : 86 ( 84 usr; 15 con; 0-9 aty)
% Number of variables : 3572 ( 0 ^;3572 !; 0 ?;3572 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_Hoare__Mirabelle_Ohoare__derivs_type,type,
c_Hoare__Mirabelle_Ohoare__derivs: $i > $i > $i > $o ).
thf(v_G_type,type,
v_G: $i ).
thf(hAPP_type,type,
hAPP: $i > $i > $i ).
thf(c_Set_Oinsert_type,type,
c_Set_Oinsert: $i > $i ).
thf(tc_Hoare__Mirabelle_Otriple_type,type,
tc_Hoare__Mirabelle_Otriple: $i > $i ).
thf(t_a_type,type,
t_a: $i ).
thf(c_Hoare__Mirabelle_Otriple_Otriple_type,type,
c_Hoare__Mirabelle_Otriple_Otriple: $i > $i > $i > $i > $i ).
thf(v_P_type,type,
v_P: $i ).
thf(v_c_type,type,
v_c: $i ).
thf(v_Q_H_type,type,
v_Q_H: $i ).
thf(c_Orderings_Obot__class_Obot_type,type,
c_Orderings_Obot__class_Obot: $i > $i ).
thf(tc_fun_type,type,
tc_fun: $i > $i > $i ).
thf(tc_bool_type,type,
tc_bool: $i ).
thf(v_Q_type,type,
v_Q: $i ).
thf(hBOOL_type,type,
hBOOL: $i > $o ).
thf(c_Com_Ocom_OSKIP_type,type,
c_Com_Ocom_OSKIP: $i ).
thf(c_Com_Ocom_OWhile_type,type,
c_Com_Ocom_OWhile: $i > $i > $i ).
thf(c_Com_Ocom_OSemi_type,type,
c_Com_Ocom_OSemi: $i > $i > $i ).
thf(class_Lattices_Olower__semilattice_type,type,
class_Lattices_Olower__semilattice: $i > $o ).
thf(c_Finite__Set_Ofun__left__comm__idem_type,type,
c_Finite__Set_Ofun__left__comm__idem: $i > $i > $i > $o ).
thf(c_Lattices_Olower__semilattice__class_Oinf_type,type,
c_Lattices_Olower__semilattice__class_Oinf: $i > $i ).
thf(c_Com_Ocom_OCond_type,type,
c_Com_Ocom_OCond: $i > $i > $i > $i ).
thf(c_Collect_type,type,
c_Collect: $i > $i > $i ).
thf(c_The_type,type,
c_The: $i > $i > $i ).
thf(c_fequal_type,type,
c_fequal: $i > $i > $i ).
thf(c_Fun_Oinj__on_type,type,
c_Fun_Oinj__on: $i > $i > $i > $i > $o ).
thf(c_Set_Oimage_type,type,
c_Set_Oimage: $i > $i > $i > $i > $i ).
thf(c_Fun_Ocomp_type,type,
c_Fun_Ocomp: $i > $i > $i > $i > $i > $i ).
thf(class_Orderings_Opreorder_type,type,
class_Orderings_Opreorder: $i > $o ).
thf(c_lessequals_type,type,
c_lessequals: $i > $i > $i > $o ).
thf(class_OrderedGroup_Oab__group__add_type,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
thf(c_HOL_Ominus__class_Ominus_type,type,
c_HOL_Ominus__class_Ominus: $i > $i > $i > $i ).
thf(c_COMBI_type,type,
c_COMBI: $i > $i ).
thf(class_Orderings_Oorder_type,type,
class_Orderings_Oorder: $i > $o ).
thf(c_COMBB_type,type,
c_COMBB: $i > $i > $i > $i > $i > $i ).
thf(class_Orderings_Olinorder_type,type,
class_Orderings_Olinorder: $i > $o ).
thf(c_SetInterval_Oord__class_OlessThan_type,type,
c_SetInterval_Oord__class_OlessThan: $i > $i > $i ).
thf(class_OrderedGroup_Opordered__ab__group__add_type,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
thf(c_Finite__Set_Ofold1_type,type,
c_Finite__Set_Ofold1: $i > $i > $i > $i ).
thf(c_Finite__Set_Ofold1Set_type,type,
c_Finite__Set_Ofold1Set: $i > $i > $i > $i ).
thf(class_Lattices_Oupper__semilattice_type,type,
class_Lattices_Oupper__semilattice: $i > $o ).
thf(c_Lattices_Oupper__semilattice__class_Osup_type,type,
c_Lattices_Oupper__semilattice__class_Osup: $i > $i ).
thf(c_Finite__Set_Ofinite_type,type,
c_Finite__Set_Ofinite: $i > $i > $o ).
thf(class_Finite__Set_Ofinite_Ofinite_type,type,
class_Finite__Set_Ofinite_Ofinite: $i > $o ).
thf(c_in_type,type,
c_in: $i > $i > $i > $i ).
thf(class_Lattices_Olattice_type,type,
class_Lattices_Olattice: $i > $o ).
thf(c_Set_Ocontents_type,type,
c_Set_Ocontents: $i > $i > $i ).
thf(class_HOL_Ominus_type,type,
class_HOL_Ominus: $i > $o ).
thf(v_x_type,type,
v_x: $i ).
thf(c_Complete__Lattice_Ocomplete__lattice_type,type,
c_Complete__Lattice_Ocomplete__lattice: $i > $i > $i > $i > $i > $i > $i > $i > $i > $o ).
thf(c_Hoare__Mirabelle_Otriple_Otriple__case_type,type,
c_Hoare__Mirabelle_Otriple_Otriple__case: $i > $i > $i > $i > $i ).
thf(c_Finite__Set_Olinorder__class_OMax_type,type,
c_Finite__Set_Olinorder__class_OMax: $i > $i > $i ).
thf(class_Lattices_Obounded__lattice_type,type,
class_Lattices_Obounded__lattice: $i > $o ).
thf(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR_type,type,
c_Complete__Lattice_Ocomplete__lattice__class_OSUPR: $i > $i > $i > $i > $i ).
thf(class_Complete__Lattice_Ocomplete__lattice_type,type,
class_Complete__Lattice_Ocomplete__lattice: $i > $o ).
thf(c_Hoare__Mirabelle_Opeek__and_type,type,
c_Hoare__Mirabelle_Opeek__and: $i > $i > $i > $i ).
thf(c_Not_type,type,
c_Not: $i ).
thf(tc_Com_Ostate_type,type,
tc_Com_Ostate: $i ).
thf(v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3_type,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_type,type,
v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2: $i > $i > $i > $i > $i ).
thf(c_SetInterval_Oord__class_OatLeastAtMost_type,type,
c_SetInterval_Oord__class_OatLeastAtMost: $i > $i > $i > $i ).
thf(class_Orderings_Obot_type,type,
class_Orderings_Obot: $i > $o ).
thf(c_COMBS_type,type,
c_COMBS: $i > $i > $i > $i > $i > $i > $i ).
thf(c_COMBK_type,type,
c_COMBK: $i > $i > $i > $i ).
thf(c_COMBC_type,type,
c_COMBC: $i > $i > $i > $i > $i > $i > $i ).
thf(c_Complete__Lattice_OInf__class_OInf_type,type,
c_Complete__Lattice_OInf__class_OInf: $i > $i > $i ).
thf(v_sko__Hoare__Mirabelle__Xconseq12__1_type,type,
v_sko__Hoare__Mirabelle__Xconseq12__1: $i > $i > $i > $i > $i ).
thf(v_sko__Hoare__Mirabelle__Xconseq12__2_type,type,
v_sko__Hoare__Mirabelle__Xconseq12__2: $i > $i > $i > $i > $i ).
thf(v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1_type,type,
v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1: $i > $i > $i > $i > $i ).
thf(c_Complete__Lattice_OSup__class_OSup_type,type,
c_Complete__Lattice_OSup__class_OSup: $i > $i > $i ).
thf(class_HOL_Oord_type,type,
class_HOL_Oord: $i > $o ).
thf(class_Lattices_Odistrib__lattice_type,type,
class_Lattices_Odistrib__lattice: $i > $o ).
thf(t_b_type,type,
t_b: $i ).
thf(v_sko__Hoare__Mirabelle__Xconseq1__1_type,type,
v_sko__Hoare__Mirabelle__Xconseq1__1: $i > $i > $i ).
thf(v_sko__Hoare__Mirabelle__Xconseq1__2_type,type,
v_sko__Hoare__Mirabelle__Xconseq1__2: $i > $i > $i ).
thf(c_Nitpick_Osko__Nitpick__XEx1__def__1__3_type,type,
c_Nitpick_Osko__Nitpick__XEx1__def__1__3: $i > $i > $i ).
thf(v_sko__Hoare__Mirabelle__Xconseq12__3_type,type,
v_sko__Hoare__Mirabelle__Xconseq12__3: $i > $i > $i > $i > $i ).
thf(v_R_type,type,
v_R: $i ).
thf(t_c_type,type,
t_c: $i ).
thf(c_Finite__Set_Olinorder__class_OMin_type,type,
c_Finite__Set_Olinorder__class_OMin: $i > $i > $i ).
thf(v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3_type,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_type,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_type,type,
v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1: $i > $i > $i > $i > $i ).
thf(c_Hoare__Mirabelle_Otriple_Otriple__rec_type,type,
c_Hoare__Mirabelle_Otriple_Otriple__rec: $i > $i > $i > $i > $i ).
thf(64,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ ( c_Finite__Set_Olinorder__class_OMax @ C @ A ) @ A )
| ~ ( hBOOL @ ( c_in @ B @ C @ A ) )
| ~ ( c_Finite__Set_Ofinite @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Max__ge_0) ).
thf(645,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ ( c_Finite__Set_Olinorder__class_OMax @ C @ A ) @ A )
| ~ ( hBOOL @ ( c_in @ B @ C @ A ) )
| ~ ( c_Finite__Set_Ofinite @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(138,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D ) @ ( tc_fun @ B @ tc_bool ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ B @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ A @ C @ ( tc_fun @ B @ tc_bool ) ) ) @ ( c_HOL_Ominus__class_Ominus @ A @ D @ ( tc_fun @ B @ tc_bool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__Int_0) ).
thf(809,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D ) @ ( tc_fun @ B @ tc_bool ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ B @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ A @ C @ ( tc_fun @ B @ tc_bool ) ) ) @ ( c_HOL_Ominus__class_Ominus @ A @ D @ ( tc_fun @ B @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(375,axiom,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ A ) @ ( tc_fun @ B @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__upper2_0) ).
thf(1337,plain,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ A ) @ ( tc_fun @ B @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(57,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ ( hAPP @ C @ D ) ) )
| ~ ( hBOOL @ ( c_in @ B @ D @ E ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ F @ C @ A @ G @ H @ I @ J @ K @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OSup__upper_0) ).
thf(629,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ ( hAPP @ C @ D ) ) )
| ~ ( hBOOL @ ( c_in @ B @ D @ E ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ F @ C @ A @ G @ H @ I @ J @ K @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(237,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ ( c_Hoare__Mirabelle_Otriple_Otriple__case @ B @ ( c_Hoare__Mirabelle_Otriple_Otriple @ C @ D @ E @ t_b ) @ t_b @ t_a ) ) )
| ( hBOOL @ ( hAPP @ A @ ( hAPP @ ( hAPP @ ( hAPP @ B @ C ) @ D ) @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_triple_Osplit_0) ).
thf(1024,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ ( c_Hoare__Mirabelle_Otriple_Otriple__case @ B @ ( c_Hoare__Mirabelle_Otriple_Otriple @ C @ D @ E @ t_b ) @ t_b @ t_a ) ) )
| ( hBOOL @ ( hAPP @ A @ ( hAPP @ ( hAPP @ ( hAPP @ B @ C ) @ D ) @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(117,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ( hBOOL @ ( c_in @ D @ A @ C ) )
| ~ ( c_lessequals @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ D ) @ B ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert__iff_1) ).
thf(760,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ( hBOOL @ ( c_in @ D @ A @ C ) )
| ~ ( c_lessequals @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ D ) @ B ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(176,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( c_in @ ( c_Finite__Set_Olinorder__class_OMax @ B @ A ) @ B @ A ) )
| ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Max__in_0) ).
thf(893,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( c_in @ ( c_Finite__Set_Olinorder__class_OMax @ B @ A ) @ B @ A ) )
| ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(15,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
!= ( c_HOL_Ominus__class_Ominus @ D @ D @ A ) )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__eqI_1) ).
thf(518,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
!= ( c_HOL_Ominus__class_Ominus @ D @ D @ A ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(470,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C )
!= ( c_Orderings_Obot__class_Obot @ A ) )
| ( C
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__eq__bot__eq2_0) ).
thf(1554,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C )
!= ( c_Orderings_Obot__class_Obot @ A ) )
| ( C
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(261,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I1_J_0) ).
thf(1083,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(208,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C ) @ D @ A )
| ~ ( c_lessequals @ C @ D @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__supI_0) ).
thf(962,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C ) @ D @ A )
| ~ ( c_lessequals @ C @ D @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(215,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_HOL_Ominus__class_Ominus @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_DiffE_0) ).
thf(977,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_HOL_Ominus__class_Ominus @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(405,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Set_Oimage @ B @ ( c_HOL_Ominus__class_Ominus @ C @ D @ ( tc_fun @ E @ tc_bool ) ) @ E @ A ) ) @ ( c_Set_Oimage @ B @ ( c_HOL_Ominus__class_Ominus @ D @ C @ ( tc_fun @ E @ tc_bool ) ) @ E @ A ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( c_Fun_Oinj__on @ B @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ E @ tc_bool ) ) @ C ) @ D ) @ E @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__Un_2) ).
thf(1406,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Set_Oimage @ B @ ( c_HOL_Ominus__class_Ominus @ C @ D @ ( tc_fun @ E @ tc_bool ) ) @ E @ A ) ) @ ( c_Set_Oimage @ B @ ( c_HOL_Ominus__class_Ominus @ D @ C @ ( tc_fun @ E @ tc_bool ) ) @ E @ A ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( c_Fun_Oinj__on @ B @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ E @ tc_bool ) ) @ C ) @ D ) @ E @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(80,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) )
| ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
| ~ ( c_lessequals @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__singletonD_0) ).
thf(683,plain,
! [C: $i,B: $i,A: $i] :
( ( A
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) )
| ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
| ~ ( c_lessequals @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(354,axiom,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ ( c_Orderings_Obot__class_Obot @ A ) ) @ B )
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__bot__left_0) ).
thf(1290,plain,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ ( c_Orderings_Obot__class_Obot @ A ) ) @ B )
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(255,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( c_in @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ ( c_HOL_Ominus__class_Ominus @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) ) @ ( tc_fun @ D @ tc_bool ) ) @ D @ E ) @ E ) )
| ~ ( c_Fun_Oinj__on @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ C ) @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__insert_1) ).
thf(1068,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( c_in @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ ( c_HOL_Ominus__class_Ominus @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) ) @ ( tc_fun @ D @ tc_bool ) ) @ D @ E ) @ E ) )
| ~ ( c_Fun_Oinj__on @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ C ) @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(456,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) )
= C )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ A @ D @ E @ F @ G @ H @ I @ J @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OInf__singleton_0) ).
thf(1522,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) )
= C )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ A @ D @ E @ F @ G @ H @ I @ J @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).
thf(403,axiom,
! [A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A )
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sup__empty_0) ).
thf(1401,plain,
! [A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A )
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(476,axiom,
( ( hAPP @ ( c_COMBB @ v_P @ v_Q @ t_a @ t_b @ t_c ) @ v_R )
= ( hAPP @ v_P @ ( hAPP @ v_Q @ v_R ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBB__def__raw_0) ).
thf(1569,plain,
( ( hAPP @ ( c_COMBB @ v_P @ v_Q @ t_a @ t_b @ t_c ) @ v_R )
= ( hAPP @ v_P @ ( hAPP @ v_Q @ v_R ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).
thf(257,axiom,
! [B: $i,A: $i] :
~ ( hBOOL @ ( c_in @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_emptyE_0) ).
thf(1073,plain,
! [B: $i,A: $i] :
~ ( hBOOL @ ( c_in @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(465,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ A @ ( hAPP @ B @ C ) )
= ( hAPP @ ( c_Fun_Ocomp @ A @ B @ D @ E @ F ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_o__eq__dest__lhs_0) ).
thf(1544,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ A @ ( hAPP @ B @ C ) )
= ( hAPP @ ( c_Fun_Ocomp @ A @ B @ D @ E @ F ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(287,axiom,
! [B: $i,A: $i] :
~ ( hBOOL @ ( c_in @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ex__in__conv_0) ).
thf(1142,plain,
! [B: $i,A: $i] :
~ ( hBOOL @ ( c_in @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(461,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
!= ( c_Collect @ B @ A ) )
| ~ ( hBOOL @ ( hAPP @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__Collect__eq_0) ).
thf(1533,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
!= ( c_Collect @ B @ A ) )
| ~ ( hBOOL @ ( hAPP @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(161,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Set_Oimage @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D ) @ B @ E ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ E @ tc_bool ) ) @ ( c_Set_Oimage @ A @ C @ B @ E ) ) @ ( c_Set_Oimage @ A @ D @ B @ E ) ) @ ( tc_fun @ E @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__Int__subset_0) ).
thf(861,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Set_Oimage @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D ) @ B @ E ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ E @ tc_bool ) ) @ ( c_Set_Oimage @ A @ C @ B @ E ) ) @ ( c_Set_Oimage @ A @ D @ B @ E ) ) @ ( tc_fun @ E @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(440,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ A @ B @ C @ D )
!= ( c_Set_Oimage @ A @ E @ C @ D ) )
| ~ ( c_Fun_Oinj__on @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ C @ tc_bool ) ) @ B ) @ E ) @ C @ D )
| ( B = E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__Un__image__eq__iff_0) ).
thf(1486,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ A @ B @ C @ D )
!= ( c_Set_Oimage @ A @ E @ C @ D ) )
| ~ ( c_Fun_Oinj__on @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ C @ tc_bool ) ) @ B ) @ E ) @ C @ D )
| ( B = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).
thf(17,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OWhile @ A @ B )
!= ( c_Com_Ocom_OSemi @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I47_J_0) ).
thf(523,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OWhile @ A @ B )
!= ( c_Com_Ocom_OSemi @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(118,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_HOL_Ominus__class_Ominus @ C @ B @ ( tc_fun @ A @ tc_bool ) ) )
= C )
| ~ ( c_lessequals @ B @ C @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__partition_0) ).
thf(762,plain,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_HOL_Ominus__class_Ominus @ C @ B @ ( tc_fun @ A @ tc_bool ) ) )
= C )
| ~ ( c_lessequals @ B @ C @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(167,axiom,
! [B: $i,A: $i] :
( ( class_HOL_Oord @ ( tc_fun @ A @ B ) )
| ~ ( class_HOL_Oord @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__HOL_Oord) ).
thf(873,plain,
! [B: $i,A: $i] :
( ( class_HOL_Oord @ ( tc_fun @ A @ B ) )
| ~ ( class_HOL_Oord @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(318,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( hAPP @ A @ B ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ A @ D @ ( tc_fun @ E @ tc_bool ) ) @ ( tc_fun @ E @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ B @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UN__upper_0) ).
thf(1205,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( hAPP @ A @ B ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ A @ D @ ( tc_fun @ E @ tc_bool ) ) @ ( tc_fun @ E @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(68,axiom,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ B @ tc_bool ) ) @ A ) @ C ) @ ( tc_fun @ B @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__upper1_0) ).
thf(655,plain,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ B @ tc_bool ) ) @ A ) @ C ) @ ( tc_fun @ B @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(12,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Oinj__on @ A @ ( c_Set_Oimage @ B @ C @ D @ E ) @ E @ F )
| ~ ( c_Fun_Oinj__on @ ( c_Fun_Ocomp @ A @ B @ E @ F @ D ) @ C @ D @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__imageI_0) ).
thf(511,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Oinj__on @ A @ ( c_Set_Oimage @ B @ C @ D @ E ) @ E @ F )
| ~ ( c_Fun_Oinj__on @ ( c_Fun_Ocomp @ A @ B @ E @ F @ D ) @ C @ D @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(50,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oimage @ ( c_Fun_Ocomp @ A @ B @ C @ D @ E ) @ F @ E @ D )
= ( c_Set_Oimage @ A @ ( c_Set_Oimage @ B @ F @ E @ C ) @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__compose_0) ).
thf(614,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oimage @ ( c_Fun_Ocomp @ A @ B @ C @ D @ E ) @ F @ E @ D )
= ( c_Set_Oimage @ A @ ( c_Set_Oimage @ B @ F @ E @ C ) @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(77,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__inter__insert_0) ).
thf(677,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(445,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ ( c_COMBK @ A @ B @ C ) @ D @ C @ B )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) )
| ( D
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__constant__conv_1) ).
thf(1497,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ ( c_COMBK @ A @ B @ C ) @ D @ C @ B )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) )
| ( D
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(259,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Oinj__on @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E )
| ~ ( c_Fun_Oinj__on @ A @ B @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__diff_0) ).
thf(1078,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Oinj__on @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E )
| ~ ( c_Fun_Oinj__on @ A @ B @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(8,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OCond @ A @ B @ C )
!= ( c_Com_Ocom_OWhile @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I52_J_0) ).
thf(500,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OCond @ A @ B @ C )
!= ( c_Com_Ocom_OWhile @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(133,axiom,
! [C: $i,B: $i,A: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__fold1SetE_0) ).
thf(797,plain,
! [C: $i,B: $i,A: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(347,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) @ D @ A )
| ~ ( c_lessequals @ C @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__infI2_0) ).
thf(1275,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) @ D @ A )
| ~ ( c_lessequals @ C @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(330,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ C @ B ) )
| ~ ( c_lessequals @ C @ A @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_predicate1D_0) ).
thf(1233,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ C @ B ) )
| ~ ( c_lessequals @ C @ A @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(87,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ D ) @ B ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__sup__iff_1) ).
thf(698,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ D ) @ B ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(199,axiom,
! [A: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ A @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__empty_1) ).
thf(945,plain,
! [A: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ A @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(253,axiom,
! [B: $i,A: $i] :
( ( class_Lattices_Odistrib__lattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Odistrib__lattice @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Odistrib__lattice) ).
thf(1063,plain,
! [B: $i,A: $i] :
( ( class_Lattices_Odistrib__lattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Odistrib__lattice @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(449,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ D ) @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) @ ( tc_fun @ B @ tc_bool ) ) @ D @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert__iff_4) ).
thf(1507,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ D ) @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) @ ( tc_fun @ B @ tc_bool ) ) @ D @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).
thf(192,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ D ) @ ( tc_fun @ B @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ D @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__insert_0) ).
thf(930,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ D ) @ ( tc_fun @ B @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ D @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(145,axiom,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) @ B @ ( tc_fun @ A @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__lower1_0) ).
thf(829,plain,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) @ B @ ( tc_fun @ A @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(178,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ C @ D @ t_a ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) ) @ t_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ B @ ( v_sko__Hoare__Mirabelle__Xconseq1__1 @ B @ E ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq1__2 @ B @ E ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ E @ C @ D @ t_a ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) ) @ t_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conseq1_0) ).
thf(898,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ C @ D @ t_a ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) ) @ t_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ B @ ( v_sko__Hoare__Mirabelle__Xconseq1__1 @ B @ E ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq1__2 @ B @ E ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ E @ C @ D @ t_a ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) ) @ t_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(226,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_Finite__Set_Ofinite @ C @ B )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__subset_0) ).
thf(1001,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_Finite__Set_Ofinite @ C @ B )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(419,axiom,
class_Lattices_Oupper__semilattice @ tc_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oupper__semilattice) ).
thf(1441,plain,
class_Lattices_Oupper__semilattice @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(151,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_lessequals @ A @ ( c_Set_Oimage @ C @ D @ E @ B ) @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__surj_0) ).
thf(841,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_lessequals @ A @ ( c_Set_Oimage @ C @ D @ E @ B ) @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(435,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Oinj__on @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ D ) @ B @ E )
| ( hBOOL @ ( c_in @ ( hAPP @ A @ C ) @ ( c_Set_Oimage @ A @ ( c_HOL_Ominus__class_Ominus @ D @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) @ ( tc_fun @ B @ tc_bool ) ) @ B @ E ) @ E ) )
| ~ ( c_Fun_Oinj__on @ A @ D @ B @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__insert_2) ).
thf(1475,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Oinj__on @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ D ) @ B @ E )
| ( hBOOL @ ( c_in @ ( hAPP @ A @ C ) @ ( c_Set_Oimage @ A @ ( c_HOL_Ominus__class_Ominus @ D @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) @ ( tc_fun @ B @ tc_bool ) ) @ B @ E ) @ E ) )
| ~ ( c_Fun_Oinj__on @ A @ D @ B @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(388,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ D ) @ B ) @ ( tc_fun @ C @ tc_bool ) )
| ( hBOOL @ ( c_in @ D @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert_0) ).
thf(1366,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ D ) @ B ) @ ( tc_fun @ C @ tc_bool ) )
| ( hBOOL @ ( c_in @ D @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(459,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ B @ F ) @ E ) )
| ~ ( hBOOL @ ( c_in @ F @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SUP1__I_0) ).
thf(1529,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ B @ F ) @ E ) )
| ~ ( hBOOL @ ( c_in @ F @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(454,axiom,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ A ) @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insertI1_0) ).
thf(1518,plain,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ A ) @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).
thf(399,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ D ) @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__infI_0) ).
thf(1391,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ D ) @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(479,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Collect @ B @ C ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CollectI_0) ).
thf(1576,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Collect @ B @ C ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).
thf(213,axiom,
! [B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( c_Complete__Lattice_OSup__class_OSup @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sup__singleton_0) ).
thf(973,plain,
! [B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( c_Complete__Lattice_OSup__class_OSup @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(173,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I5_J_0) ).
thf(885,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(33,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
!= ( c_HOL_Ominus__class_Ominus @ D @ E @ A ) )
| ( c_lessequals @ C @ B @ A )
| ~ ( c_lessequals @ E @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__eqI_1) ).
thf(570,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
!= ( c_HOL_Ominus__class_Ominus @ D @ E @ A ) )
| ( c_lessequals @ C @ B @ A )
| ~ ( c_lessequals @ E @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(98,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ D @ B @ A )
| ~ ( c_lessequals @ ( c_SetInterval_Oord__class_OatLeastAtMost @ D @ B @ A ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ E @ C @ A ) @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastatMost__subset__iff_1) ).
thf(719,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ D @ B @ A )
| ~ ( c_lessequals @ ( c_SetInterval_Oord__class_OatLeastAtMost @ D @ B @ A ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ E @ C @ A ) @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(372,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
!= ( hAPP @ A @ C ) )
| ~ ( hBOOL @ ( c_in @ C @ D @ E ) )
| ~ ( hBOOL @ ( c_in @ B @ D @ E ) )
| ~ ( c_Fun_Oinj__on @ A @ D @ E @ F )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__def_0) ).
thf(1330,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
!= ( hAPP @ A @ C ) )
| ~ ( hBOOL @ ( c_in @ C @ D @ E ) )
| ~ ( hBOOL @ ( c_in @ B @ D @ E ) )
| ~ ( c_Fun_Oinj__on @ A @ D @ E @ F )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(135,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C )
!= C )
| ( c_lessequals @ B @ C @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__Un__eq_1) ).
thf(802,plain,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C )
!= C )
| ( c_lessequals @ B @ C @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(426,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( hAPP @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mem__def_1) ).
thf(1455,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( hAPP @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(311,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ A ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__subset__iff_1) ).
thf(1191,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ A ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(202,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ ( c_COMBK @ A @ B @ C ) @ D @ C @ B @ t_a ) @ v_x )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_K__record__comp_0) ).
thf(949,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ ( c_COMBK @ A @ B @ C ) @ D @ C @ B @ t_a ) @ v_x )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(24,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OWhile @ A @ B )
!= ( c_Com_Ocom_OCond @ C @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I53_J_0) ).
thf(542,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OWhile @ A @ B )
!= ( c_Com_Ocom_OCond @ C @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(100,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
!= ( hAPP @ A @ C ) )
| ~ ( c_Fun_Oinj__on @ A @ D @ E @ F )
| ( B = C )
| ~ ( hBOOL @ ( c_in @ C @ D @ E ) )
| ~ ( hBOOL @ ( c_in @ B @ D @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__onD_0) ).
thf(724,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
!= ( hAPP @ A @ C ) )
| ~ ( c_Fun_Oinj__on @ A @ D @ E @ F )
| ( B = C )
| ~ ( hBOOL @ ( c_in @ C @ D @ E ) )
| ~ ( hBOOL @ ( c_in @ B @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(250,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) @ A )
| ~ ( c_Finite__Set_Ofinite @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__Int_1) ).
thf(1055,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) @ A )
| ~ ( c_Finite__Set_Ofinite @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(406,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( c_Complete__Lattice_OInf__class_OInf @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ ( c_Complete__Lattice_OInf__class_OInf @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Inf__insert_0) ).
thf(1409,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( c_Complete__Lattice_OInf__class_OInf @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ ( c_Complete__Lattice_OInf__class_OInf @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(368,axiom,
! [B: $i,A: $i] : ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ B ) @ tc_bool ) ) @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty_0) ).
thf(1323,plain,
! [B: $i,A: $i] : ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ B ) @ tc_bool ) ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(150,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) ) )
| ~ ( hBOOL @ ( c_in @ C @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__insert__right_0) ).
thf(838,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) ) )
| ~ ( hBOOL @ ( c_in @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(187,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ C @ tc_bool ) ) @ B ) @ D ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntE_0) ).
thf(917,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ C @ tc_bool ) ) @ B ) @ D ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(89,axiom,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ A ) @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__iff_1) ).
thf(702,plain,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ A ) @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(364,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Finite__Set_Olinorder__class_OMax @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Max__singleton_0) ).
thf(1313,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Finite__Set_Olinorder__class_OMax @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(349,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_HOL_Ominus__class_Ominus @ C @ B @ ( tc_fun @ A @ tc_bool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__disjoint_0) ).
thf(1279,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_HOL_Ominus__class_Ominus @ C @ B @ ( tc_fun @ A @ tc_bool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(29,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_SetInterval_Oord__class_OlessThan @ B @ A )
!= ( c_SetInterval_Oord__class_OlessThan @ C @ A ) )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lessThan__eq__iff_0) ).
thf(559,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_SetInterval_Oord__class_OlessThan @ B @ A )
!= ( c_SetInterval_Oord__class_OlessThan @ C @ A ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(452,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_lessequals @ ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ D @ E @ A ) @ ( tc_fun @ A @ tc_bool ) )
| ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastatMost__subset__iff_2) ).
thf(1514,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_lessequals @ ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ D @ E @ A ) @ ( tc_fun @ A @ tc_bool ) )
| ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(289,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ D ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__supE_0) ).
thf(1147,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ D ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(121,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( hBOOL @ ( c_in @ C @ D @ A ) )
| ~ ( c_lessequals @ B @ ( c_Finite__Set_Ofold1 @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ D @ A ) @ A )
| ( D
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_below__fold1__iff_0) ).
thf(770,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( hBOOL @ ( c_in @ C @ D @ A ) )
| ~ ( c_lessequals @ B @ ( c_Finite__Set_Ofold1 @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ D @ A ) @ A )
| ( D
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(402,axiom,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__idem_0) ).
thf(1398,plain,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(269,axiom,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ A ) @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insertCI_1) ).
thf(1100,plain,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ A ) @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(61,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__empty_1) ).
thf(638,plain,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(157,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( c_lessequals @ B @ ( c_Complete__Lattice_OSup__class_OSup @ C @ A ) @ A )
| ~ ( hBOOL @ ( c_in @ B @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sup__upper_0) ).
thf(853,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( c_lessequals @ B @ ( c_Complete__Lattice_OSup__class_OSup @ C @ A ) @ A )
| ~ ( hBOOL @ ( c_in @ B @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(366,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf1E_1) ).
thf(1319,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(166,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__left__commute_0) ).
thf(870,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(211,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) @ D @ ( tc_fun @ A @ tc_bool ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_HOL_Ominus__class_Ominus @ C @ D @ ( tc_fun @ A @ tc_bool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__Diff_0) ).
thf(969,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) @ D @ ( tc_fun @ A @ tc_bool ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_HOL_Ominus__class_Ominus @ C @ D @ ( tc_fun @ A @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(380,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C )
= C )
| ~ ( c_lessequals @ B @ C @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__absorb1_0) ).
thf(1347,plain,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C )
= C )
| ~ ( c_lessequals @ B @ C @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(441,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ ( c_Finite__Set_Olinorder__class_OMin @ B @ A ) @ C @ A )
| ~ ( hBOOL @ ( c_in @ C @ B @ A ) )
| ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Min__le_0) ).
thf(1489,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ ( c_Finite__Set_Olinorder__class_OMin @ B @ A ) @ C @ A )
| ~ ( hBOOL @ ( c_in @ C @ B @ A ) )
| ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ( c_Com_Ocom_OSemi @ A @ B )
!= c_Com_Ocom_OSKIP ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I13_J_0) ).
thf(492,plain,
! [B: $i,A: $i] :
( ( c_Com_Ocom_OSemi @ A @ B )
!= c_Com_Ocom_OSKIP ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(41,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Com_Ocom_OCond @ A @ B @ C )
!= ( c_Com_Ocom_OCond @ D @ E @ F ) )
| ( C = F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I4_J_2) ).
thf(591,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Com_Ocom_OCond @ A @ B @ C )
!= ( c_Com_Ocom_OCond @ D @ E @ F ) )
| ( C = F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(410,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) @ D @ ( tc_fun @ A @ tc_bool ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_HOL_Ominus__class_Ominus @ C @ D @ ( tc_fun @ A @ tc_bool ) ) ) )
| ( hBOOL @ ( c_in @ B @ D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__Diff__if_1) ).
thf(1418,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) @ D @ ( tc_fun @ A @ tc_bool ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_HOL_Ominus__class_Ominus @ C @ D @ ( tc_fun @ A @ tc_bool ) ) ) )
| ( hBOOL @ ( c_in @ B @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(195,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ D ) @ ( tc_fun @ A @ tc_bool ) )
| ~ ( c_lessequals @ C @ D @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__mono_0) ).
thf(937,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ D ) @ ( tc_fun @ A @ tc_bool ) )
| ~ ( c_lessequals @ C @ D @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(481,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ C @ tc_bool ) ) @ B ) @ D ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__subset__iff_0) ).
thf(1581,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ C @ tc_bool ) ) @ B ) @ D ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).
thf(307,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( c_lessequals @ B @ A @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equalityI_0) ).
thf(1183,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( c_lessequals @ B @ A @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(248,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ D ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__inf__iff_0) ).
thf(1051,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ D ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(181,axiom,
! [B: $i,A: $i] :
( ( class_Orderings_Obot @ ( tc_fun @ A @ B ) )
| ~ ( class_Orderings_Obot @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Obot) ).
thf(905,plain,
! [B: $i,A: $i] :
( ( class_Orderings_Obot @ ( tc_fun @ A @ B ) )
| ~ ( class_Orderings_Obot @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(359,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) @ D @ ( tc_fun @ A @ tc_bool ) )
| ~ ( c_lessequals @ C @ D @ ( tc_fun @ A @ tc_bool ) )
| ~ ( c_lessequals @ B @ D @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__subset__iff_2) ).
thf(1302,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) @ D @ ( tc_fun @ A @ tc_bool ) )
| ~ ( c_lessequals @ C @ D @ ( tc_fun @ A @ tc_bool ) )
| ~ ( c_lessequals @ B @ D @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(115,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) @ D @ A @ ( tc_fun @ E @ tc_bool ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ E @ tc_bool ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ B @ D @ A @ ( tc_fun @ E @ tc_bool ) ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ D @ A @ ( tc_fun @ E @ tc_bool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UN__Un_0) ).
thf(756,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) @ D @ A @ ( tc_fun @ E @ tc_bool ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ E @ tc_bool ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ B @ D @ A @ ( tc_fun @ E @ tc_bool ) ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ D @ A @ ( tc_fun @ E @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(2,negated_conjecture,
~ ( c_Hoare__Mirabelle_Ohoare__derivs @ v_G @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ v_P @ v_c @ v_Q @ t_a ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) ) @ t_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(485,plain,
~ ( c_Hoare__Mirabelle_Ohoare__derivs @ v_G @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ v_P @ v_c @ v_Q @ t_a ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) ) @ t_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(284,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Oinj__on @ A @ B @ C @ D )
| ~ ( c_Fun_Oinj__on @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ C @ tc_bool ) ) @ E ) @ B ) @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__Un_1) ).
thf(1136,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Oinj__on @ A @ B @ C @ D )
| ~ ( c_Fun_Oinj__on @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ C @ tc_bool ) ) @ E ) @ B ) @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(148,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ B )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__empty__left_0) ).
thf(834,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(300,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
= ( c_Set_Oimage @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__is__image_1) ).
thf(1169,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
= ( c_Set_Oimage @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(104,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_COMBS @ A @ B @ C @ D @ E @ F )
= ( hAPP @ ( hAPP @ A @ C ) @ ( hAPP @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBS__def_0) ).
thf(734,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_COMBS @ A @ B @ C @ D @ E @ F )
= ( hAPP @ ( hAPP @ A @ C ) @ ( hAPP @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(422,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ C @ D @ A )
| ~ ( c_lessequals @ ( c_SetInterval_Oord__class_OatLeastAtMost @ C @ D @ A ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ E @ A ) @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastatMost__subset__iff_0) ).
thf(1447,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ C @ D @ A )
| ~ ( c_lessequals @ ( c_SetInterval_Oord__class_OatLeastAtMost @ C @ D @ A ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ E @ A ) @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(277,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__left__commute_0) ).
thf(1119,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(225,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) ) @ D ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fold1Set__sing_0) ).
thf(998,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) ) @ D ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(416,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ ( c_Finite__Set_Olinorder__class_OMin @ B @ A ) @ ( c_Finite__Set_Olinorder__class_OMin @ C @ A ) @ A )
| ~ ( c_Finite__Set_Ofinite @ B @ A )
| ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( c_lessequals @ C @ B @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Min__antimono_0) ).
thf(1433,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ ( c_Finite__Set_Olinorder__class_OMin @ B @ A ) @ ( c_Finite__Set_Olinorder__class_OMin @ C @ A ) @ A )
| ~ ( c_Finite__Set_Ofinite @ B @ A )
| ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( c_lessequals @ C @ B @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(316,axiom,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__empty_2) ).
thf(1201,plain,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(19,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( B = C )
| ~ ( c_lessequals @ C @ B @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__iff_2) ).
thf(527,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( B = C )
| ~ ( c_lessequals @ C @ B @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(474,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ D ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) ) )
= ( hAPP @ ( hAPP @ E @ C ) @ D ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ A @ F @ G @ H @ E @ I @ J @ K @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OInf__binary_0) ).
thf(1564,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ D ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) ) )
= ( hAPP @ ( hAPP @ E @ C ) @ D ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ A @ F @ G @ H @ E @ I @ J @ K @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(45,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OCond @ A @ B @ C )
!= c_Com_Ocom_OSKIP ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I15_J_0) ).
thf(602,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OCond @ A @ B @ C )
!= c_Com_Ocom_OSKIP ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(217,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__Un__distrib_0) ).
thf(981,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(169,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__inf__distrib2_0) ).
thf(877,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(84,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__is__Un_0) ).
thf(692,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(379,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ D ) @ ( tc_fun @ B @ tc_bool ) ) @ B )
| ~ ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ A @ D @ ( tc_fun @ B @ tc_bool ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__Diff__insert_1) ).
thf(1345,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ D ) @ ( tc_fun @ B @ tc_bool ) ) @ B )
| ~ ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ A @ D @ ( tc_fun @ B @ tc_bool ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(221,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( c_in @ B @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ ( c_Collect @ A @ C ) ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__Collect_1) ).
thf(988,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( c_in @ B @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ ( c_Collect @ A @ C ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(271,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Set_Oimage @ A @ B @ C @ D ) @ ( c_Set_Oimage @ A @ E @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ B @ E @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__mono_0) ).
thf(1104,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Set_Oimage @ A @ B @ C @ D ) @ ( c_Set_Oimage @ A @ E @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ B @ E @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(334,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) )
| ( hBOOL @ ( c_in @ B @ D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__insert__left_1) ).
thf(1242,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) )
| ( hBOOL @ ( c_in @ B @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(197,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ B @ F ) @ E ) )
| ~ ( hBOOL @ ( c_in @ F @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SUP1__iff_2) ).
thf(942,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ B @ F ) @ E ) )
| ~ ( hBOOL @ ( c_in @ F @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(71,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ B )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__absorb_0) ).
thf(661,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(190,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ ( c_COMBK @ A @ B @ C ) @ D @ C @ B )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( c_in @ E @ D @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__constant_0) ).
thf(925,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ ( c_COMBK @ A @ B @ C ) @ D @ C @ B )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( c_in @ E @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(361,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C )
= C )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__sup_0) ).
thf(1306,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C )
= C )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(315,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( c_in @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bex__empty_0) ).
thf(1199,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( c_in @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(376,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ ( c_Finite__Set_Olinorder__class_OMax @ B @ A ) @ ( c_Finite__Set_Olinorder__class_OMax @ C @ A ) @ A )
| ~ ( c_Finite__Set_Ofinite @ C @ A )
| ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( c_lessequals @ B @ C @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Max__mono_0) ).
thf(1338,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ ( c_Finite__Set_Olinorder__class_OMax @ B @ A ) @ ( c_Finite__Set_Olinorder__class_OMax @ C @ A ) @ A )
| ~ ( c_Finite__Set_Ofinite @ C @ A )
| ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( c_lessequals @ B @ C @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(433,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__assoc_0) ).
thf(1470,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(96,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Hoare__Mirabelle_Otriple_Otriple @ A @ B @ C @ D )
!= ( c_Hoare__Mirabelle_Otriple_Otriple @ E @ F @ G @ D ) )
| ( B = F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_triple_Oinject_1) ).
thf(714,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Hoare__Mirabelle_Otriple_Otriple @ A @ B @ C @ D )
!= ( c_Hoare__Mirabelle_Otriple_Otriple @ E @ F @ G @ D ) )
| ( B = F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(363,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__commute_0) ).
thf(1311,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(21,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( B = C )
| ~ ( c_lessequals @ C @ B @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__antisym_0) ).
thf(534,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( B = C )
| ~ ( c_lessequals @ C @ B @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(246,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ ( c_Hoare__Mirabelle_Otriple_Otriple__case @ B @ ( c_Hoare__Mirabelle_Otriple_Otriple @ C @ D @ E @ t_b ) @ t_b @ t_a ) ) )
| ( hBOOL @ ( hAPP @ A @ ( hAPP @ ( hAPP @ ( hAPP @ B @ C ) @ D ) @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_triple_Osplit__asm_0) ).
thf(1047,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ ( c_Hoare__Mirabelle_Otriple_Otriple__case @ B @ ( c_Hoare__Mirabelle_Otriple_Otriple @ C @ D @ E @ t_b ) @ t_b @ t_a ) ) )
| ( hBOOL @ ( hAPP @ A @ ( hAPP @ ( hAPP @ ( hAPP @ B @ C ) @ D ) @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(251,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__not__empty_0) ).
thf(1057,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(297,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) @ C ) @ D ) @ B )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ D @ B )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ B ) @ tc_bool ) ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hoare__derivs_Oinsert_0) ).
thf(1163,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) @ C ) @ D ) @ B )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ D @ B )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ B ) @ tc_bool ) ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(378,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( hAPP @ A @ B ) @ C @ ( tc_fun @ D @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ B @ E @ F ) )
| ~ ( c_lessequals @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ A @ F @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UN__subset__iff_0) ).
thf(1343,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( hAPP @ A @ B ) @ C @ ( tc_fun @ D @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ B @ E @ F ) )
| ~ ( c_lessequals @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ A @ F @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(244,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( hAPP @ ( c_fequal @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ATP__Linkup_Ofequal__imp__equal_0) ).
thf(1042,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( hAPP @ ( c_fequal @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(455,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
= C )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ C @ A @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__diff_0) ).
thf(1519,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
= C )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ C @ A @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(383,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__assoc_0) ).
thf(1355,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(162,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__commute_0) ).
thf(862,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(302,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__empty__right_0) ).
thf(1174,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(43,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_Fun_Oinj__on @ C @ A @ B @ D )
| ~ ( c_Finite__Set_Ofinite @ ( c_Set_Oimage @ C @ A @ B @ D ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__imageD_0) ).
thf(598,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_Fun_Oinj__on @ C @ A @ B @ D )
| ~ ( c_Finite__Set_Ofinite @ ( c_Set_Oimage @ C @ A @ B @ D ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(129,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) @ A )
| ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__Int_0) ).
thf(788,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) @ A )
| ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(140,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C )
= B )
| ~ ( c_lessequals @ C @ B @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__absorb2_0) ).
thf(815,plain,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C )
= B )
| ~ ( c_lessequals @ C @ B @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(102,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) @ D @ ( tc_fun @ A @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ C @ D @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( hBOOL @ ( c_in @ B @ D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__Diff1_0) ).
thf(729,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) @ D @ ( tc_fun @ A @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ C @ D @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( hBOOL @ ( c_in @ B @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(332,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ B @ C )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ D @ C )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ D @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cut_0) ).
thf(1238,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ B @ C )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ D @ C )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ D @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(397,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ C )
| ~ ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ D ) @ B ) @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__Diff__insert_0) ).
thf(1387,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ C )
| ~ ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ D ) @ B ) @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(183,axiom,
class_Lattices_Odistrib__lattice @ tc_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Odistrib__lattice) ).
thf(910,plain,
class_Lattices_Odistrib__lattice @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(206,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( c_Complete__Lattice_OSup__class_OSup @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sup__binary_0) ).
thf(957,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( c_Complete__Lattice_OSup__class_OSup @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(326,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
= C )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ A @ D @ E @ F @ G @ H @ I @ C @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OInf__empty_0) ).
thf(1223,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
= C )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ A @ D @ E @ F @ G @ H @ I @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(110,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( c_lessequals @ ( c_Complete__Lattice_OInf__class_OInf @ B @ A ) @ C @ A )
| ~ ( hBOOL @ ( c_in @ C @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Inf__lower_0) ).
thf(746,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( c_lessequals @ ( c_Complete__Lattice_OInf__class_OInf @ B @ A ) @ C @ A )
| ~ ( hBOOL @ ( c_in @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(265,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ D ) @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ B @ tc_bool ) )
| ( hBOOL @ ( c_in @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert__iff_2) ).
thf(1091,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ D ) @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ B @ tc_bool ) )
| ( hBOOL @ ( c_in @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(236,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ E @ C ) @ ( hAPP @ A @ D ) ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ F @ A @ G @ H @ I @ E @ J @ K @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OSup__insert_0) ).
thf(1021,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ E @ C ) @ ( hAPP @ A @ D ) ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ F @ A @ G @ H @ I @ E @ J @ K @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(124,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ C )
| ~ ( c_Finite__Set_Ofinite @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__Diff_0) ).
thf(778,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ C )
| ~ ( c_Finite__Set_Ofinite @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(447,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ B @ ( c_COMBK @ C @ A @ D ) @ D @ A )
= C )
| ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SUP__const_0) ).
thf(1502,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ B @ ( c_COMBK @ C @ A @ D ) @ D @ A )
= C )
| ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(142,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Hoare__Mirabelle_Otriple_Otriple @ A @ B @ C @ D )
!= ( c_Hoare__Mirabelle_Otriple_Otriple @ E @ F @ G @ D ) )
| ( C = G ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_triple_Oinject_2) ).
thf(820,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Hoare__Mirabelle_Otriple_Otriple @ A @ B @ C @ D )
!= ( c_Hoare__Mirabelle_Otriple_Otriple @ E @ F @ G @ D ) )
| ( C = G ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(412,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__Diff_0) ).
thf(1423,plain,
! [B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(240,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C )
= B )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__inf_0) ).
thf(1032,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C )
= B )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(387,axiom,
class_HOL_Oord @ tc_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__HOL_Oord) ).
thf(1365,plain,
class_HOL_Oord @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(304,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Oinj__on @ A @ B @ C @ D )
| ~ ( c_lessequals @ B @ E @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ A @ E @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__inj__on_0) ).
thf(1178,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Oinj__on @ A @ B @ C @ D )
| ~ ( c_lessequals @ B @ E @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ A @ E @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(427,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ C @ D @ t_a ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) ) @ t_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ D @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1 @ A @ B @ D @ C ) ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3 @ A @ B @ D @ C @ E @ F ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ E @ C @ F @ t_a ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) ) @ t_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hoare__derivs_Ointros_I6_J_2) ).
thf(1457,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ C @ D @ t_a ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) ) @ t_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ D @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1 @ A @ B @ D @ C ) ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3 @ A @ B @ D @ C @ E @ F ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ E @ C @ F @ t_a ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) ) @ t_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(146,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup1CI_0) ).
thf(830,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(295,axiom,
! [B: $i,A: $i] :
( ( class_Lattices_Olattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Olattice @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olattice) ).
thf(1159,plain,
! [B: $i,A: $i] :
( ( class_Lattices_Olattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Olattice @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(320,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ B )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__absorb_0) ).
thf(1210,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(313,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_HOL_Ominus__class_Ominus @ C @ D @ ( tc_fun @ A @ tc_bool ) ) )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__Int__distrib_0) ).
thf(1195,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_HOL_Ominus__class_Ominus @ C @ D @ ( tc_fun @ A @ tc_bool ) ) )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(350,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ( hBOOL @ ( c_in @ B @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Ononempty__iff_2) ).
thf(1281,plain,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ( hBOOL @ ( c_in @ B @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(94,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ D @ C ) )
| ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__mp_0) ).
thf(710,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ D @ C ) )
| ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(231,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Fun_Oinj__on @ A @ B @ C @ C )
| ~ ( c_lessequals @ B @ ( c_Set_Oimage @ A @ B @ C @ C ) @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__surj__inj_0) ).
thf(1012,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Fun_Oinj__on @ A @ B @ C @ C )
| ~ ( c_lessequals @ B @ ( c_Set_Oimage @ A @ B @ C @ C ) @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(272,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ D ) @ B ) )
| ~ ( hBOOL @ ( c_in @ A @ D @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__iff_2) ).
thf(1106,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ D ) @ B ) )
| ~ ( hBOOL @ ( c_in @ A @ D @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(154,axiom,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) @ C @ ( tc_fun @ A @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__lower2_0) ).
thf(847,plain,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) @ C @ ( tc_fun @ A @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(32,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Com_Ocom_OCond @ A @ B @ C )
!= ( c_Com_Ocom_OCond @ D @ E @ F ) )
| ( B = E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I4_J_1) ).
thf(566,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Com_Ocom_OCond @ A @ B @ C )
!= ( c_Com_Ocom_OCond @ D @ E @ F ) )
| ( B = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(1,negated_conjecture,
c_Hoare__Mirabelle_Ohoare__derivs @ v_G @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ v_P @ v_c @ v_Q_H @ t_a ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) ) @ t_a,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(484,plain,
c_Hoare__Mirabelle_Ohoare__derivs @ v_G @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ v_P @ v_c @ v_Q_H @ t_a ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) ) @ t_a,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(357,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__distrib2_0) ).
thf(1296,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(73,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) )
!= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ E ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ) )
| ( B = E )
| ( C = E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_2) ).
thf(665,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) )
!= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ E ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ) )
| ( B = E )
| ( C = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(108,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_COMBC @ A @ B @ C @ D @ E @ F )
= ( hAPP @ ( hAPP @ A @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBC__def_0) ).
thf(742,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_COMBC @ A @ B @ C @ D @ E @ F )
= ( hAPP @ ( hAPP @ A @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(340,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ D ) @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__inf__iff_2) ).
thf(1259,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ D ) @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(371,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ C ) @ D ) @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__supI2_0) ).
thf(1328,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ C ) @ D ) @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(278,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C )
= B )
| ~ ( c_lessequals @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__absorb1_0) ).
thf(1121,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C )
= B )
| ~ ( c_lessequals @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(274,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I4_J_0) ).
thf(1111,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(413,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Collect @ A @ B )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Collect__empty__eq_0) ).
thf(1425,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Collect @ A @ B )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(228,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_HOL_Ominus__class_Ominus @ D @ B @ ( tc_fun @ C @ tc_bool ) ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_DiffE_1) ).
thf(1006,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_HOL_Ominus__class_Ominus @ D @ B @ ( tc_fun @ C @ tc_bool ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(285,axiom,
class_Lattices_Olower__semilattice @ tc_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olower__semilattice) ).
thf(1138,plain,
class_Lattices_Olower__semilattice @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(126,axiom,
class_Lattices_Obounded__lattice @ tc_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Obounded__lattice) ).
thf(783,plain,
class_Lattices_Obounded__lattice @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(159,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ B ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__subset__iff_1) ).
thf(857,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ B ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(385,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D ) @ B @ E )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ E @ tc_bool ) ) @ ( c_Set_Oimage @ A @ C @ B @ E ) ) @ ( c_Set_Oimage @ A @ D @ B @ E ) ) )
| ~ ( c_lessequals @ D @ F @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_lessequals @ C @ F @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ A @ F @ B @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__image__Int_0) ).
thf(1360,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D ) @ B @ E )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ E @ tc_bool ) ) @ ( c_Set_Oimage @ A @ C @ B @ E ) ) @ ( c_Set_Oimage @ A @ D @ B @ E ) ) )
| ~ ( c_lessequals @ D @ F @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_lessequals @ C @ F @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ A @ F @ B @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(381,axiom,
! [A: $i] :
( ~ ( class_Orderings_Obot @ A )
| ( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ A ) ) @ v_x )
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bot__fun__eq_0) ).
thf(1350,plain,
! [A: $i] :
( ~ ( class_Orderings_Obot @ A )
| ( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ A ) ) @ v_x )
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(264,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__ge1_0) ).
thf(1089,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(464,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
!= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_singleton__inject_0) ).
thf(1541,plain,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
!= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(66,axiom,
! [B: $i,A: $i] :
( ( class_Lattices_Obounded__lattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Obounded__lattice @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Obounded__lattice) ).
thf(650,plain,
! [B: $i,A: $i] :
( ( class_Lattices_Obounded__lattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Obounded__lattice @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(201,axiom,
! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ ( c_Nitpick_Osko__Nitpick__XEx1__def__1__3 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nitpick_OEx1__def_2) ).
thf(948,plain,
! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ ( c_Nitpick_Osko__Nitpick__XEx1__def__1__3 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(475,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ D ) @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ B @ tc_bool ) )
| ( hBOOL @ ( c_in @ C @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert_1) ).
thf(1567,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ D ) @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ B @ tc_bool ) )
| ( hBOOL @ ( c_in @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).
thf(443,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) )
| ~ ( c_lessequals @ D @ B @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Int__assoc__eq_1) ).
thf(1493,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) )
| ~ ( c_lessequals @ D @ B @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(172,axiom,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fold1Set__sing_1) ).
thf(884,plain,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(306,axiom,
! [C: $i,B: $i,A: $i] : ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ C @ c_Com_Ocom_OSKIP @ C @ B ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ B ) @ tc_bool ) ) ) @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hoare__derivs_OSkip_0) ).
thf(1182,plain,
! [C: $i,B: $i,A: $i] : ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ C @ c_Com_Ocom_OSKIP @ C @ B ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ B ) @ tc_bool ) ) ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OWhile @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I16_J_0) ).
thf(489,plain,
! [B: $i,A: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OWhile @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(322,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ D ) @ C ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__inf__iff_1) ).
thf(1214,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ D ) @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(92,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ D ) @ ( tc_fun @ B @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ C @ A @ B ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) @ ( tc_fun @ B @ tc_bool ) ) @ D @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert__iff_3) ).
thf(706,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ D ) @ ( tc_fun @ B @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ C @ A @ B ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) @ ( tc_fun @ B @ tc_bool ) ) @ D @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(429,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( c_in @ B @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mem__def_0) ).
thf(1461,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( c_in @ B @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(22,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oimage @ A @ ( c_Set_Oimage @ B @ C @ D @ E ) @ E @ F )
= ( c_Set_Oimage @ ( c_COMBB @ A @ B @ E @ F @ D ) @ C @ D @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__image_0) ).
thf(537,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oimage @ A @ ( c_Set_Oimage @ B @ C @ D @ E ) @ E @ F )
= ( c_Set_Oimage @ ( c_COMBB @ A @ B @ E @ F @ D ) @ C @ D @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(81,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ A @ B ) @ C )
| ~ ( hBOOL @ ( c_in @ B @ D @ E ) )
| ~ ( c_Finite__Set_Ofinite @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ A @ E @ ( tc_fun @ C @ tc_bool ) ) @ C )
| ~ ( c_Finite__Set_Ofinite @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__UN_0) ).
thf(686,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ A @ B ) @ C )
| ~ ( hBOOL @ ( c_in @ B @ D @ E ) )
| ~ ( c_Finite__Set_Ofinite @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ A @ E @ ( tc_fun @ C @ tc_bool ) ) @ C )
| ~ ( c_Finite__Set_Ofinite @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(258,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__left__idem_0) ).
thf(1075,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(408,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ D ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__subset_0) ).
thf(1414,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ D ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(18,axiom,
! [B: $i,A: $i] : ( c_Fun_Oinj__on @ ( c_COMBI @ A ) @ B @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__id2_0) ).
thf(526,plain,
! [B: $i,A: $i] : ( c_Fun_Oinj__on @ ( c_COMBI @ A ) @ B @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(233,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ D @ C @ ( tc_fun @ A @ tc_bool ) ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UN__extend__simps_I1_J_0) ).
thf(1016,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ D @ C @ ( tc_fun @ A @ tc_bool ) ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(319,axiom,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__idem_0) ).
thf(1207,plain,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(78,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) @ A )
| ~ ( c_Finite__Set_Ofinite @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__insert_1) ).
thf(679,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) @ A )
| ~ ( c_Finite__Set_Ofinite @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(243,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastatMost__empty__iff_1) ).
thf(1039,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(54,axiom,
! [B: $i,A: $i] :
( ( class_Lattices_Oupper__semilattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Olattice @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Oupper__semilattice) ).
thf(622,plain,
! [B: $i,A: $i] :
( ( class_Lattices_Oupper__semilattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Olattice @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(282,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( c_in @ ( c_Finite__Set_Olinorder__class_OMin @ B @ A ) @ B @ A ) )
| ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Min__in_0) ).
thf(1131,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( c_in @ ( c_Finite__Set_Olinorder__class_OMin @ B @ A ) @ B @ A ) )
| ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(469,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ ( c_Finite__Set_Ofold1 @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B @ A ) @ C @ A )
| ~ ( hBOOL @ ( c_in @ C @ B @ A ) )
| ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fold1__belowI_0) ).
thf(1552,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ ( c_Finite__Set_Ofold1 @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B @ A ) @ C @ A )
| ~ ( hBOOL @ ( c_in @ C @ B @ A ) )
| ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).
thf(252,axiom,
! [B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( c_Complete__Lattice_OInf__class_OInf @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Inf__singleton_0) ).
thf(1060,plain,
! [B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( c_Complete__Lattice_OInf__class_OInf @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(99,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Fun_Ocomp @ A @ B @ C @ D @ E )
!= ( c_Fun_Ocomp @ F @ G @ H @ D @ E ) )
| ( ( hAPP @ A @ ( hAPP @ B @ I ) )
= ( hAPP @ F @ ( hAPP @ G @ I ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_o__eq__dest_0) ).
thf(721,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Fun_Ocomp @ A @ B @ C @ D @ E )
!= ( c_Fun_Ocomp @ F @ G @ H @ D @ E ) )
| ( ( hAPP @ A @ ( hAPP @ B @ I ) )
= ( hAPP @ F @ ( hAPP @ G @ I ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(457,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ E ) @ ( tc_fun @ A @ tc_bool ) )
| ~ ( c_lessequals @ C @ E @ ( tc_fun @ A @ tc_bool ) )
| ~ ( c_lessequals @ B @ D @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__mono_0) ).
thf(1525,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ E ) @ ( tc_fun @ A @ tc_bool ) )
| ~ ( c_lessequals @ C @ E @ ( tc_fun @ A @ tc_bool ) )
| ~ ( c_lessequals @ B @ D @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(369,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_4) ).
thf(1324,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(275,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Finite__Set_Olinorder__class_OMin @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Min__singleton_0) ).
thf(1114,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Finite__Set_Olinorder__class_OMin @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(65,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C )
= C )
| ~ ( c_lessequals @ C @ B @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__absorb1_0) ).
thf(647,plain,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C )
= C )
| ~ ( c_lessequals @ C @ B @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(342,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__assoc_0) ).
thf(1263,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(14,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OCond @ A @ B @ C )
!= ( c_Com_Ocom_OSemi @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I45_J_0) ).
thf(515,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OCond @ A @ B @ C )
!= ( c_Com_Ocom_OSemi @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(291,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ D ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distrib__sup__le_0) ).
thf(1150,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ D ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(437,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C )
!= C )
| ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__sup_1) ).
thf(1478,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C )
!= C )
| ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(424,axiom,
! [B: $i,A: $i] :
( ( class_Finite__Set_Ofinite_Ofinite @ ( tc_fun @ A @ B ) )
| ~ ( class_Finite__Set_Ofinite_Ofinite @ B )
| ~ ( class_Finite__Set_Ofinite_Ofinite @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Finite__Set_Ofinite_Ofinite) ).
thf(1451,plain,
! [B: $i,A: $i] :
( ( class_Finite__Set_Ofinite_Ofinite @ ( tc_fun @ A @ B ) )
| ~ ( class_Finite__Set_Ofinite_Ofinite @ B )
| ~ ( class_Finite__Set_Ofinite_Ofinite @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(106,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oimage @ ( c_COMBK @ A @ B @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C @ B )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__constant__conv_0) ).
thf(738,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oimage @ ( c_COMBK @ A @ B @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C @ B )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(343,axiom,
! [B: $i,A: $i] :
( ( class_Lattices_Olower__semilattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Olattice @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olower__semilattice) ).
thf(1266,plain,
! [B: $i,A: $i] :
( ( class_Lattices_Olower__semilattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Olattice @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(329,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Oord @ A )
| ( c_lessequals @ ( hAPP @ B @ C ) @ ( hAPP @ D @ C ) @ A )
| ~ ( c_lessequals @ B @ D @ ( tc_fun @ E @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__funD_0) ).
thf(1231,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Oord @ A )
| ( c_lessequals @ ( hAPP @ B @ C ) @ ( hAPP @ D @ C ) @ A )
| ~ ( c_lessequals @ B @ D @ ( tc_fun @ E @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(219,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ D ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__infE_0) ).
thf(984,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ D ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(184,axiom,
class_Orderings_Obot @ tc_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Obot) ).
thf(911,plain,
class_Orderings_Obot @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(400,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) )
= C )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ D @ A @ E @ F @ G @ H @ I @ J @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OSup__singleton_0) ).
thf(1393,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) )
= C )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ D @ A @ E @ F @ G @ H @ I @ J @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ( c_Collect @ A @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Collect__def_0) ).
thf(503,plain,
! [B: $i,A: $i] :
( ( c_Collect @ A @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(46,axiom,
! [B: $i,A: $i] :
( ~ ( class_Finite__Set_Ofinite_Ofinite @ A )
| ( c_Finite__Set_Ofinite @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite_0) ).
thf(605,plain,
! [B: $i,A: $i] :
( ~ ( class_Finite__Set_Ofinite_Ofinite @ A )
| ( c_Finite__Set_Ofinite @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(373,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D ) )
| ( hBOOL @ ( c_in @ A @ C @ D ) )
| ~ ( hBOOL @ ( c_in @ A @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_DiffI_0) ).
thf(1333,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D ) )
| ( hBOOL @ ( c_in @ A @ C @ D ) )
| ~ ( hBOOL @ ( c_in @ A @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(131,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__left__commute_0) ).
thf(792,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(262,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oimage @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D ) @ B @ E )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ E @ tc_bool ) ) @ ( c_Set_Oimage @ A @ C @ B @ E ) ) @ ( c_Set_Oimage @ A @ D @ B @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__Un_0) ).
thf(1086,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oimage @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D ) @ B @ E )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ E @ tc_bool ) ) @ ( c_Set_Oimage @ A @ C @ B @ E ) ) @ ( c_Set_Oimage @ A @ D @ B @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(59,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__code_2) ).
thf(633,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(136,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__le1_0) ).
thf(805,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(119,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) @ A )
| ~ ( c_Finite__Set_Ofinite @ C @ A )
| ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__UnI_0) ).
thf(765,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) @ A )
| ~ ( c_Finite__Set_Ofinite @ C @ A )
| ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(431,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__Un__distrib2_0) ).
thf(1466,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(20,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Com_Ocom_OSemi @ A @ B )
!= ( c_Com_Ocom_OSemi @ C @ D ) )
| ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I3_J_0) ).
thf(530,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Com_Ocom_OSemi @ A @ B )
!= ( c_Com_Ocom_OSemi @ C @ D ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(204,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) @ ( tc_fun @ B @ tc_bool ) ) @ D @ ( tc_fun @ B @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ C @ A @ B ) )
| ~ ( c_lessequals @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ D ) @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert__iff_0) ).
thf(953,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) @ ( tc_fun @ B @ tc_bool ) ) @ D @ ( tc_fun @ B @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ C @ A @ B ) )
| ~ ( c_lessequals @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ D ) @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(122,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( c_Complete__Lattice_OInf__class_OInf @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Inf__binary_0) ).
thf(773,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( c_Complete__Lattice_OInf__class_OInf @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(352,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_lessequals @ ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ D @ E @ A ) @ ( tc_fun @ A @ tc_bool ) )
| ~ ( c_lessequals @ C @ E @ A )
| ~ ( c_lessequals @ D @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastatMost__subset__iff_3) ).
thf(1286,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_lessequals @ ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ D @ E @ A ) @ ( tc_fun @ A @ tc_bool ) )
| ~ ( c_lessequals @ C @ E @ A )
| ~ ( c_lessequals @ D @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(241,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( c_in @ B @ ( c_Collect @ A @ C ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CollectD_0) ).
thf(1035,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( c_in @ B @ ( c_Collect @ A @ C ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(309,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__empty__right_0) ).
thf(1187,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(76,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
= C )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ D @ A @ E @ F @ G @ H @ C @ I @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OSup__empty_0) ).
thf(674,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
= C )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ D @ A @ E @ F @ G @ H @ C @ I @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(238,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C )
= C )
| ~ ( c_lessequals @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__absorb2_0) ).
thf(1026,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C )
= C )
| ~ ( c_lessequals @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(299,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ D @ C ) )
| ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__iff_0) ).
thf(1167,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ D @ C ) )
| ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(97,axiom,
! [A: $i] : ( c_Finite__Set_Ofun__left__comm__idem @ ( c_Set_Oinsert @ A ) @ A @ ( tc_fun @ A @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__left__comm__idem__insert_0) ).
thf(718,plain,
! [A: $i] : ( c_Finite__Set_Ofun__left__comm__idem @ ( c_Set_Oinsert @ A ) @ A @ ( tc_fun @ A @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(174,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ A @ D @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__rev__mp_0) ).
thf(888,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ A @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(112,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C ) @ D @ A )
| ~ ( c_lessequals @ C @ D @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__least_0) ).
thf(750,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C ) @ D @ A )
| ~ ( c_lessequals @ C @ D @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(52,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D ) @ B ) )
| ~ ( hBOOL @ ( c_in @ A @ D @ B ) )
| ~ ( hBOOL @ ( c_in @ A @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__iff_2) ).
thf(618,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D ) @ B ) )
| ~ ( hBOOL @ ( c_in @ A @ D @ B ) )
| ~ ( hBOOL @ ( c_in @ A @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(13,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( c_lessequals @ B @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).
thf(513,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( c_lessequals @ B @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(346,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__commute_0) ).
thf(1273,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(467,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ D ) @ B ) )
| ~ ( hBOOL @ ( c_in @ A @ D @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insertCI_0) ).
thf(1548,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ D ) @ B ) )
| ~ ( hBOOL @ ( c_in @ A @ D @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).
thf(34,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ C @ A )
| ( c_lessequals @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__linear_0) ).
thf(573,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ C @ A )
| ( c_lessequals @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(391,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ C @ D @ t_a ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) ) @ t_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ B @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1 @ A @ B @ D @ C ) ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2 @ A @ B @ D @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hoare__derivs_Ointros_I6_J_0) ).
thf(1374,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ C @ D @ t_a ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) ) @ t_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ B @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1 @ A @ B @ D @ C ) ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2 @ A @ B @ D @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(324,axiom,
class_HOL_Ominus @ tc_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__HOL_Ominus) ).
thf(1219,plain,
class_HOL_Ominus @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(143,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__commute_0) ).
thf(824,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(293,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D ) )
| ( hBOOL @ ( c_in @ A @ C @ D ) )
| ~ ( hBOOL @ ( c_in @ A @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__iff_2) ).
thf(1154,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D ) )
| ( hBOOL @ ( c_in @ A @ C @ D ) )
| ~ ( hBOOL @ ( c_in @ A @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(30,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_lessequals @ B @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).
thf(562,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_lessequals @ B @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(85,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ C @ ( c_Com_Ocom_OWhile @ D @ E ) @ ( c_Hoare__Mirabelle_Opeek__and @ C @ ( c_Fun_Ocomp @ c_Not @ D @ tc_bool @ tc_bool @ tc_Com_Ostate ) @ B ) @ B ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ B ) @ tc_bool ) ) ) @ B )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ ( c_Hoare__Mirabelle_Opeek__and @ C @ D @ B ) @ E @ C @ B ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ B ) @ tc_bool ) ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Loop_0) ).
thf(694,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ C @ ( c_Com_Ocom_OWhile @ D @ E ) @ ( c_Hoare__Mirabelle_Opeek__and @ C @ ( c_Fun_Ocomp @ c_Not @ D @ tc_bool @ tc_bool @ tc_Com_Ostate ) @ B ) @ B ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ B ) @ tc_bool ) ) ) @ B )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ ( c_Hoare__Mirabelle_Opeek__and @ C @ D @ B ) @ E @ C @ B ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ B ) @ tc_bool ) ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(103,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Obot @ A )
| ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bot__least_0) ).
thf(732,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Obot @ A )
| ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(398,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ C @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ D @ tc_bool ) ) @ C ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup1E_0) ).
thf(1389,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ C @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ D @ tc_bool ) ) @ C ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(152,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ A @ A @ ( tc_fun @ B @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__cancel_0) ).
thf(843,plain,
! [B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ A @ A @ ( tc_fun @ B @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(37,axiom,
! [A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_Finite__Set_Ofun__left__comm__idem @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__left__comm__idem__sup_0) ).
thf(579,plain,
! [A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_Finite__Set_Ofun__left__comm__idem @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(279,axiom,
( ( hAPP @ ( c_COMBI @ t_a ) @ v_P )
= v_P ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBI__def__raw_0) ).
thf(1124,plain,
( ( hAPP @ ( c_COMBI @ t_a ) @ v_P )
= v_P ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(168,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( c_in @ A @ B @ C ) )
| ( hBOOL @ ( c_in @ ( hAPP @ D @ A ) @ ( c_Set_Oimage @ D @ B @ C @ E ) @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__iff_2) ).
thf(875,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( c_in @ A @ B @ C ) )
| ( hBOOL @ ( c_in @ ( hAPP @ D @ A ) @ ( c_Set_Oimage @ D @ B @ C @ E ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(36,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Oinj__on @ ( c_Fun_Ocomp @ A @ B @ C @ D @ E ) @ F @ E @ D )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Set_Oimage @ B @ F @ E @ C ) @ C @ D )
| ~ ( c_Fun_Oinj__on @ B @ F @ E @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comp__inj__on_0) ).
thf(577,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Oinj__on @ ( c_Fun_Ocomp @ A @ B @ C @ D @ E ) @ F @ E @ D )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Set_Oimage @ B @ F @ E @ C ) @ C @ D )
| ~ ( c_Fun_Oinj__on @ B @ F @ E @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(339,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ ( tc_fun @ A @ tc_bool ) )
= C )
| ( hBOOL @ ( c_in @ B @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__insert__absorb_0) ).
thf(1256,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ ( tc_fun @ A @ tc_bool ) )
= C )
| ( hBOOL @ ( c_in @ B @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(327,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
!= ( hAPP @ A @ C ) )
| ~ ( hBOOL @ ( c_in @ C @ D @ E ) )
| ~ ( hBOOL @ ( c_in @ B @ D @ E ) )
| ( B = C )
| ~ ( c_Fun_Oinj__on @ A @ D @ E @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__contraD_0) ).
thf(1226,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
!= ( hAPP @ A @ C ) )
| ~ ( hBOOL @ ( c_in @ C @ D @ E ) )
| ~ ( hBOOL @ ( c_in @ B @ D @ E ) )
| ( B = C )
| ~ ( c_Fun_Oinj__on @ A @ D @ E @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(25,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Com_Ocom_OCond @ A @ B @ C )
!= ( c_Com_Ocom_OCond @ D @ E @ F ) )
| ( A = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I4_J_0) ).
thf(545,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Com_Ocom_OCond @ A @ B @ C )
!= ( c_Com_Ocom_OCond @ D @ E @ F ) )
| ( A = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(286,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
!= ( hAPP @ A @ C ) )
| ~ ( hBOOL @ ( c_in @ C @ D @ E ) )
| ~ ( hBOOL @ ( c_in @ B @ D @ E ) )
| ~ ( c_Fun_Oinj__on @ A @ D @ E @ F )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__iff_0) ).
thf(1139,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
!= ( hAPP @ A @ C ) )
| ~ ( hBOOL @ ( c_in @ C @ D @ E ) )
| ~ ( hBOOL @ ( c_in @ B @ D @ E ) )
| ~ ( c_Fun_Oinj__on @ A @ D @ E @ F )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(188,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C )
!= B )
| ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__inf_1) ).
thf(919,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C )
!= B )
| ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(62,axiom,
! [B: $i,A: $i] :
( ( c_The @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ A )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nitpick_OThe__psimp_0) ).
thf(641,plain,
! [B: $i,A: $i] :
( ( c_The @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(414,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C )
= C )
| ~ ( hBOOL @ ( c_in @ B @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__absorb_0) ).
thf(1428,plain,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C )
= C )
| ~ ( hBOOL @ ( c_in @ B @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(345,axiom,
! [B: $i,A: $i] :
( ( class_Orderings_Oorder @ ( tc_fun @ A @ B ) )
| ~ ( class_Orderings_Oorder @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Oorder) ).
thf(1271,plain,
! [B: $i,A: $i] :
( ( class_Orderings_Oorder @ ( tc_fun @ A @ B ) )
| ~ ( class_Orderings_Oorder @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(390,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Fun_Ocomp @ ( hAPP @ A @ B ) @ ( hAPP @ A @ B ) @ C @ C @ C )
= ( hAPP @ A @ B ) )
| ~ ( c_Finite__Set_Ofun__left__comm__idem @ A @ D @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__left__comm__idem_Ofun__comp__idem_0) ).
thf(1371,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Fun_Ocomp @ ( hAPP @ A @ B ) @ ( hAPP @ A @ B ) @ C @ C @ C )
= ( hAPP @ A @ B ) )
| ~ ( c_Finite__Set_Ofun__left__comm__idem @ A @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(216,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E ) )
| ~ ( hBOOL @ ( c_in @ B @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_imageI_0) ).
thf(979,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E ) )
| ~ ( hBOOL @ ( c_in @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(179,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OlessThan @ B @ A ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ivl__disj__int_I4_J_0) ).
thf(900,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OlessThan @ B @ A ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(79,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( c_lessequals @ ( hAPP @ B @ C ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ B @ E @ A ) @ A )
| ~ ( hBOOL @ ( c_in @ C @ D @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__SUPI_0) ).
thf(681,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( c_lessequals @ ( hAPP @ B @ C ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ B @ E @ A ) @ A )
| ~ ( hBOOL @ ( c_in @ C @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(478,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ D ) @ ( tc_fun @ B @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ C @ A @ B ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) @ ( tc_fun @ B @ tc_bool ) ) @ D @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__single__insert_0) ).
thf(1574,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ D ) @ ( tc_fun @ B @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ C @ A @ B ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) @ ( tc_fun @ B @ tc_bool ) ) @ D @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).
thf(105,axiom,
! [B: $i,A: $i] :
( ( class_HOL_Ominus @ ( tc_fun @ A @ B ) )
| ~ ( class_HOL_Ominus @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__HOL_Ominus) ).
thf(736,plain,
! [B: $i,A: $i] :
( ( class_HOL_Ominus @ ( tc_fun @ A @ B ) )
| ~ ( class_HOL_Ominus @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(288,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ B @ C ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ B @ E @ ( tc_fun @ A @ tc_bool ) ) )
= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ B @ E @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( hBOOL @ ( c_in @ C @ D @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UN__absorb_0) ).
thf(1144,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ B @ C ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ B @ E @ ( tc_fun @ A @ tc_bool ) ) )
= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ B @ E @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( hBOOL @ ( c_in @ C @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(51,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ C ) @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__ge2_0) ).
thf(616,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ C ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(127,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup1CI_1) ).
thf(784,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(276,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ E ) @ ( tc_fun @ A @ tc_bool ) )
| ~ ( c_lessequals @ C @ E @ ( tc_fun @ A @ tc_bool ) )
| ~ ( c_lessequals @ B @ D @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__mono_0) ).
thf(1117,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ E ) @ ( tc_fun @ A @ tc_bool ) )
| ~ ( c_lessequals @ C @ E @ ( tc_fun @ A @ tc_bool ) )
| ~ ( c_lessequals @ B @ D @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(222,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I3_J_0) ).
thf(990,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(224,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ B @ C @ D @ ( tc_fun @ E @ tc_bool ) ) @ E ) )
| ~ ( hBOOL @ ( c_in @ A @ ( hAPP @ C @ F ) @ E ) )
| ~ ( hBOOL @ ( c_in @ F @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UN__I_0) ).
thf(996,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ B @ C @ D @ ( tc_fun @ E @ tc_bool ) ) @ E ) )
| ~ ( hBOOL @ ( c_in @ A @ ( hAPP @ C @ F ) @ E ) )
| ~ ( hBOOL @ ( c_in @ F @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(11,axiom,
! [B: $i,A: $i] :
( ( c_The @ ( c_fequal @ A @ B ) @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_the__sym__eq__trivial_0) ).
thf(509,plain,
! [B: $i,A: $i] :
( ( c_The @ ( c_fequal @ A @ B ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(170,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ C @ ( c_Com_Ocom_OSemi @ D @ E ) @ F @ B ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ B ) @ tc_bool ) ) ) @ B )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ G @ E @ F @ B ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ B ) @ tc_bool ) ) ) @ B )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ C @ D @ G @ B ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ B ) @ tc_bool ) ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Comp_0) ).
thf(880,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ C @ ( c_Com_Ocom_OSemi @ D @ E ) @ F @ B ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ B ) @ tc_bool ) ) ) @ B )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ G @ E @ F @ B ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ B ) @ tc_bool ) ) ) @ B )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ C @ D @ G @ B ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ B ) @ tc_bool ) ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(477,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ A @ tc_bool ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__triv_0) ).
thf(1571,plain,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ A @ tc_bool ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).
thf(392,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ D ) @ B ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__supE_1) ).
thf(1376,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ D ) @ B ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(418,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__insert__left_0) ).
thf(1439,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(175,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C )
!= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ D ) )
| ( hBOOL @ ( c_in @ B @ D @ A ) )
| ( hBOOL @ ( c_in @ B @ C @ A ) )
| ( C = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__ident_0) ).
thf(890,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C )
!= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ D ) )
| ( hBOOL @ ( c_in @ B @ D @ A ) )
| ( hBOOL @ ( c_in @ B @ C @ A ) )
| ( C = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(139,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Hoare__Mirabelle_Otriple_Otriple @ A @ B @ C @ D )
!= ( c_Hoare__Mirabelle_Otriple_Otriple @ E @ F @ G @ D ) )
| ( A = E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_triple_Oinject_0) ).
thf(811,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Hoare__Mirabelle_Otriple_Otriple @ A @ B @ C @ D )
!= ( c_Hoare__Mirabelle_Otriple_Otriple @ E @ F @ G @ D ) )
| ( A = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(260,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) @ D )
!= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) )
| ( c_lessequals @ D @ B @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Int__assoc__eq_0) ).
thf(1080,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) @ D )
!= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) )
| ( c_lessequals @ D @ B @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(58,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Otriple_Otriple__case @ A @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ C @ D @ E ) @ E @ F )
= ( hAPP @ ( hAPP @ ( hAPP @ A @ B ) @ C ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_triple_Ocases_0) ).
thf(631,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Otriple_Otriple__case @ A @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ C @ D @ E ) @ E @ F )
= ( hAPP @ ( hAPP @ ( hAPP @ A @ B ) @ C ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(116,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ C @ D @ t_a ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) ) @ t_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ B @ ( v_sko__Hoare__Mirabelle__Xconseq12__1 @ B @ E @ D @ F ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__2 @ B @ E @ D @ F ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ E @ C @ F @ t_a ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) ) @ t_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conseq12_0) ).
thf(758,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ C @ D @ t_a ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) ) @ t_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ B @ ( v_sko__Hoare__Mirabelle__Xconseq12__1 @ B @ E @ D @ F ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__2 @ B @ E @ D @ F ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ E @ C @ F @ t_a ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) ) @ t_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(471,axiom,
class_Orderings_Oorder @ tc_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Oorder) ).
thf(1557,plain,
class_Orderings_Oorder @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
thf(48,axiom,
! [B: $i,A: $i] :
( ( c_Com_Ocom_OWhile @ A @ B )
!= c_Com_Ocom_OSKIP ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I17_J_0) ).
thf(609,plain,
! [B: $i,A: $i] :
( ( c_Com_Ocom_OWhile @ A @ B )
!= c_Com_Ocom_OSKIP ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(134,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I7_J_0) ).
thf(799,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(239,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ B @ C @ ( tc_fun @ D @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) )
| ( ( hAPP @ B @ E )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) )
| ~ ( hBOOL @ ( c_in @ E @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UNION__empty__conv_I2_J_0) ).
thf(1029,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ B @ C @ ( tc_fun @ D @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) )
| ( ( hAPP @ B @ E )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) )
| ~ ( hBOOL @ ( c_in @ E @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(394,axiom,
! [B: $i,A: $i] :
( ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
| ~ ( c_lessequals @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__empty_0) ).
thf(1381,plain,
! [B: $i,A: $i] :
( ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
| ~ ( c_lessequals @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(193,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
= ( c_Nitpick_Osko__Nitpick__XEx1__def__1__3 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nitpick_OEx1__def_3) ).
thf(932,plain,
! [C: $i,B: $i,A: $i] :
( ( A
= ( c_Nitpick_Osko__Nitpick__XEx1__def__1__3 @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(155,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__commute_0) ).
thf(848,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(88,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ( c_lessequals @ ( c_Set_Oimage @ D @ A @ C @ E ) @ ( c_Set_Oimage @ D @ B @ C @ E ) @ ( tc_fun @ E @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__image__iff_2) ).
thf(700,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ( c_lessequals @ ( c_Set_Oimage @ D @ A @ C @ E ) @ ( c_Set_Oimage @ D @ B @ C @ E ) @ ( tc_fun @ E @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(290,axiom,
! [C: $i,B: $i,A: $i] : ( c_Fun_Oinj__on @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B @ C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__empty_0) ).
thf(1149,plain,
! [C: $i,B: $i,A: $i] : ( c_Fun_Oinj__on @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B @ C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(209,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( C = B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__code_0) ).
thf(964,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( C = B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(56,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Ominus @ A )
| ( ( hAPP @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ t_a @ A ) ) @ v_x )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ B @ v_x ) @ ( hAPP @ C @ v_x ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__diff__def_0) ).
thf(626,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Ominus @ A )
| ( ( hAPP @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ t_a @ A ) ) @ v_x )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ B @ v_x ) @ ( hAPP @ C @ v_x ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(186,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( c_in @ A @ B @ C ) )
| ( hBOOL @ ( c_in @ ( hAPP @ D @ A ) @ ( c_Set_Oimage @ D @ B @ C @ E ) @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__image__eqI_0) ).
thf(915,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( c_in @ A @ B @ C ) )
| ( hBOOL @ ( c_in @ ( hAPP @ D @ A ) @ ( c_Set_Oimage @ D @ B @ C @ E ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(355,axiom,
! [B: $i,A: $i] : ( c_lessequals @ A @ A @ ( tc_fun @ B @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equalityE_0) ).
thf(1293,plain,
! [B: $i,A: $i] : ( c_lessequals @ A @ A @ ( tc_fun @ B @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(74,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ D ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) ) )
= ( hAPP @ ( hAPP @ E @ C ) @ D ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ F @ A @ G @ H @ I @ E @ J @ K @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OSup__binary_0) ).
thf(668,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ D ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) ) )
= ( hAPP @ ( hAPP @ E @ C ) @ D ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ F @ A @ G @ H @ I @ E @ J @ K @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(218,axiom,
class_Lattices_Olattice @ tc_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olattice) ).
thf(983,plain,
class_Lattices_Olattice @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(401,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_COMBB @ A @ B @ C @ D @ E ) @ F )
= ( hAPP @ A @ ( hAPP @ B @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBB__def_0) ).
thf(1396,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_COMBB @ A @ B @ C @ D @ E ) @ F )
= ( hAPP @ A @ ( hAPP @ B @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(144,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ C @ D @ t_a ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) ) @ t_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ B @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1 @ A @ B @ D @ C ) ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2 @ A @ B @ D @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conseq_0) ).
thf(827,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ C @ D @ t_a ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) ) @ t_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ B @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1 @ A @ B @ D @ C ) ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2 @ A @ B @ D @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(335,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__inf__absorb_0) ).
thf(1245,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(165,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__assoc_0) ).
thf(868,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(125,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Set_Oimage @ B @ ( c_HOL_Ominus__class_Ominus @ C @ D @ ( tc_fun @ E @ tc_bool ) ) @ E @ A ) ) @ ( c_Set_Oimage @ B @ ( c_HOL_Ominus__class_Ominus @ D @ C @ ( tc_fun @ E @ tc_bool ) ) @ E @ A ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( c_Fun_Oinj__on @ B @ D @ E @ A )
| ~ ( c_Fun_Oinj__on @ B @ C @ E @ A )
| ( c_Fun_Oinj__on @ B @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ E @ tc_bool ) ) @ C ) @ D ) @ E @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__Un_3) ).
thf(780,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Set_Oimage @ B @ ( c_HOL_Ominus__class_Ominus @ C @ D @ ( tc_fun @ E @ tc_bool ) ) @ E @ A ) ) @ ( c_Set_Oimage @ B @ ( c_HOL_Ominus__class_Ominus @ D @ C @ ( tc_fun @ E @ tc_bool ) ) @ E @ A ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( c_Fun_Oinj__on @ B @ D @ E @ A )
| ~ ( c_Fun_Oinj__on @ B @ C @ E @ A )
| ( c_Fun_Oinj__on @ B @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ E @ tc_bool ) ) @ C ) @ D ) @ E @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(303,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) @ A )
| ~ ( c_Finite__Set_Ofinite @ C @ A )
| ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__Un_2) ).
thf(1176,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) @ A )
| ~ ( c_Finite__Set_Ofinite @ C @ A )
| ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(220,axiom,
! [B: $i,A: $i] :
~ ( hBOOL @ ( c_in @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__iff_0) ).
thf(986,plain,
! [B: $i,A: $i] :
~ ( hBOOL @ ( c_in @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(436,axiom,
! [B: $i,A: $i] : ( c_lessequals @ A @ A @ ( tc_fun @ B @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__refl_0) ).
thf(1477,plain,
! [B: $i,A: $i] : ( c_lessequals @ A @ A @ ( tc_fun @ B @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(337,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ ( c_SetInterval_Oord__class_OlessThan @ B @ A ) @ ( tc_fun @ A @ tc_bool ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_single__Diff__lessThan_0) ).
thf(1250,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ ( c_SetInterval_Oord__class_OlessThan @ B @ A ) @ ( tc_fun @ A @ tc_bool ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(444,axiom,
class_Finite__Set_Ofinite_Ofinite @ tc_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Finite__Set_Ofinite_Ofinite) ).
thf(1496,plain,
class_Finite__Set_Ofinite_Ofinite @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(10,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Com_Ocom_OWhile @ A @ B )
!= ( c_Com_Ocom_OWhile @ C @ D ) )
| ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I5_J_0) ).
thf(505,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Com_Ocom_OWhile @ A @ B )
!= ( c_Com_Ocom_OWhile @ C @ D ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(189,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) )
!= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ E ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ) )
| ( B = E )
| ( B = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_0) ).
thf(922,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) )
!= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ E ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ) )
| ( B = E )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(70,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I8_J_0) ).
thf(658,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(185,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
= ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ~ ( c_Finite__Set_Ofun__left__comm__idem @ A @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__left__comm__idem_Ofun__left__idem_0) ).
thf(912,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
= ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ~ ( c_Finite__Set_Ofun__left__comm__idem @ A @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(16,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Ocomp @ A @ ( c_Fun_Ocomp @ B @ C @ D @ E @ F ) @ E @ G @ F )
= ( c_Fun_Ocomp @ ( c_Fun_Ocomp @ A @ B @ E @ G @ D ) @ C @ D @ G @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_o__assoc_0) ).
thf(521,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Ocomp @ A @ ( c_Fun_Ocomp @ B @ C @ D @ E @ F ) @ E @ G @ F )
= ( c_Fun_Ocomp @ ( c_Fun_Ocomp @ A @ B @ E @ G @ D ) @ C @ D @ G @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(301,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__empty_0) ).
thf(1171,plain,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(482,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_SetInterval_Oord__class_OlessThan @ B @ A ) @ ( c_SetInterval_Oord__class_OlessThan @ C @ A ) @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lessThan__subset__iff_0) ).
thf(1583,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_SetInterval_Oord__class_OlessThan @ B @ A ) @ ( c_SetInterval_Oord__class_OlessThan @ C @ A ) @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).
thf(360,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( c_Collect @ D @ B ) ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ D @ A ) )
| ~ ( hBOOL @ ( c_in @ A @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__Collect_2) ).
thf(1304,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( c_Collect @ D @ B ) ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ D @ A ) )
| ~ ( hBOOL @ ( c_in @ A @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(317,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ D ) @ A ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__subset_1) ).
thf(1203,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ D ) @ A ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(198,axiom,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__code_1) ).
thf(944,plain,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(132,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Oinj__on @ A @ B @ C @ D )
| ~ ( c_Fun_Oinj__on @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ E ) @ B ) @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__insert_0) ).
thf(795,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Oinj__on @ A @ B @ C @ D )
| ~ ( c_Fun_Oinj__on @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ E ) @ B ) @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(72,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ D @ E @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ E @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__mono_0) ).
thf(663,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ D @ E @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ E @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(348,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ ( c_SetInterval_Oord__class_OlessThan @ B @ A ) @ ( c_SetInterval_Oord__class_OlessThan @ C @ A ) @ ( tc_fun @ A @ tc_bool ) )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lessThan__subset__iff_1) ).
thf(1277,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ ( c_SetInterval_Oord__class_OlessThan @ B @ A ) @ ( c_SetInterval_Oord__class_OlessThan @ C @ A ) @ ( tc_fun @ A @ tc_bool ) )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(283,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ A @ tc_bool ) ) ) @ D )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__Int__distrib2_0) ).
thf(1134,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ A @ tc_bool ) ) ) @ D )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(450,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C )
!= ( c_Orderings_Obot__class_Obot @ A ) )
| ( B
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__eq__bot__eq1_0) ).
thf(1509,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C )
!= ( c_Orderings_Obot__class_Obot @ A ) )
| ( B
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(196,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ ( hAPP @ B @ C ) ) @ ( c_Set_Oimage @ B @ D @ E @ A ) )
= ( c_Set_Oimage @ B @ D @ E @ A ) )
| ~ ( hBOOL @ ( c_in @ C @ D @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__image_0) ).
thf(939,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ ( hAPP @ B @ C ) ) @ ( c_Set_Oimage @ B @ D @ E @ A ) )
= ( c_Set_Oimage @ B @ D @ E @ A ) )
| ~ ( hBOOL @ ( c_in @ C @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(234,axiom,
class_Orderings_Opreorder @ tc_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Opreorder) ).
thf(1018,plain,
class_Orderings_Opreorder @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(114,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ B @ C )
| ~ ( c_lessequals @ B @ D @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ C ) @ tc_bool ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ D @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_weaken_0) ).
thf(754,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ B @ C )
| ~ ( c_lessequals @ B @ D @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ C ) @ tc_bool ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(27,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OSemi @ A @ B )
!= ( c_Com_Ocom_OCond @ C @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I44_J_0) ).
thf(553,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OSemi @ A @ B )
!= ( c_Com_Ocom_OCond @ C @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(149,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ C ) @ D ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distrib__inf__le_0) ).
thf(836,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ C ) @ D ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(247,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ C @ tc_bool ) ) @ A ) @ D ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf1E_0) ).
thf(1049,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ C @ tc_bool ) ) @ A ) @ D ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(123,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) @ D @ ( tc_fun @ A @ tc_bool ) )
| ~ ( c_lessequals @ C @ D @ ( tc_fun @ A @ tc_bool ) )
| ~ ( c_lessequals @ B @ D @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__least_0) ).
thf(776,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) @ D @ ( tc_fun @ A @ tc_bool ) )
| ~ ( c_lessequals @ C @ D @ ( tc_fun @ A @ tc_bool ) )
| ~ ( c_lessequals @ B @ D @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(158,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ C @ ( c_Com_Ocom_OCond @ D @ E @ F ) @ G @ B ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ B ) @ tc_bool ) ) ) @ B )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ ( c_Hoare__Mirabelle_Opeek__and @ C @ ( c_Fun_Ocomp @ c_Not @ D @ tc_bool @ tc_bool @ tc_Com_Ostate ) @ B ) @ F @ G @ B ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ B ) @ tc_bool ) ) ) @ B )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ ( c_Hoare__Mirabelle_Opeek__and @ C @ D @ B ) @ E @ G @ B ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ B ) @ tc_bool ) ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hoare__derivs_OIf_0) ).
thf(855,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ C @ ( c_Com_Ocom_OCond @ D @ E @ F ) @ G @ B ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ B ) @ tc_bool ) ) ) @ B )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ ( c_Hoare__Mirabelle_Opeek__and @ C @ ( c_Fun_Ocomp @ c_Not @ D @ tc_bool @ tc_bool @ tc_Com_Ostate ) @ B ) @ F @ G @ B ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ B ) @ tc_bool ) ) ) @ B )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ B ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ ( c_Hoare__Mirabelle_Opeek__and @ C @ D @ B ) @ E @ G @ B ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ B ) @ tc_bool ) ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(256,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I2_J_0) ).
thf(1070,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(212,axiom,
! [B: $i,A: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bot1E_0) ).
thf(971,plain,
! [B: $i,A: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(389,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_HOL_Ominus__class_Ominus @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ ( tc_fun @ A @ tc_bool ) ) )
= C )
| ~ ( hBOOL @ ( c_in @ B @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__Diff_0) ).
thf(1368,plain,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_HOL_Ominus__class_Ominus @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ ( tc_fun @ A @ tc_bool ) ) )
= C )
| ~ ( hBOOL @ ( c_in @ B @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(460,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ D ) @ C ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__infE_1) ).
thf(1531,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ D ) @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).
thf(439,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__trans_0) ).
thf(1484,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(223,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ E @ C ) @ ( hAPP @ A @ D ) ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ A @ F @ G @ H @ E @ I @ J @ K @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OInf__insert_0) ).
thf(993,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ E @ C ) @ ( hAPP @ A @ D ) ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ A @ F @ G @ H @ E @ I @ J @ K @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(95,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ D ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__sup__iff_0) ).
thf(712,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ D ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(227,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__distrib1_0) ).
thf(1003,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(83,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Int__distrib2_0) ).
thf(690,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(453,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__ord_I3_J_0) ).
thf(1516,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(91,axiom,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ A @ ( tc_fun @ C @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__subset_0) ).
thf(705,plain,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ A @ ( tc_fun @ C @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(294,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ( A = D )
| ~ ( hBOOL @ ( c_in @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ D ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insertE_0) ).
thf(1156,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ( A = D )
| ~ ( hBOOL @ ( c_in @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ D ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(249,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_COMBK @ A @ B @ C ) @ D )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBK__def_0) ).
thf(1053,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_COMBK @ A @ B @ C ) @ D )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(308,axiom,
class_Complete__Lattice_Ocomplete__lattice @ tc_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Complete__Lattice_Ocomplete__lattice) ).
thf(1186,plain,
class_Complete__Lattice_Ocomplete__lattice @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(39,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
!= ( c_HOL_Ominus__class_Ominus @ D @ E @ A ) )
| ( c_lessequals @ E @ D @ A )
| ~ ( c_lessequals @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__eqI_0) ).
thf(585,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
!= ( c_HOL_Ominus__class_Ominus @ D @ E @ A ) )
| ( c_lessequals @ E @ D @ A )
| ~ ( c_lessequals @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(331,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( hAPP @ B @ C ) )
!= ( hAPP @ D @ ( hAPP @ E @ F ) ) )
| ( ( hAPP @ ( c_Fun_Ocomp @ A @ B @ G @ H @ I ) @ C )
= ( hAPP @ ( c_Fun_Ocomp @ D @ E @ J @ H @ K ) @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comp__cong_0) ).
thf(1235,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( hAPP @ B @ C ) )
!= ( hAPP @ D @ ( hAPP @ E @ F ) ) )
| ( ( hAPP @ ( c_Fun_Ocomp @ A @ B @ G @ H @ I ) @ C )
= ( hAPP @ ( c_Fun_Ocomp @ D @ E @ J @ H @ K ) @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(63,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( c_lessequals @ C @ A @ ( tc_fun @ D @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__predicate1D_0) ).
thf(643,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( c_lessequals @ C @ A @ ( tc_fun @ D @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(325,axiom,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ ( c_Orderings_Obot__class_Obot @ A ) ) @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__bot__left_0) ).
thf(1220,plain,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ ( c_Orderings_Obot__class_Obot @ A ) ) @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(182,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__absorb_0) ).
thf(907,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(463,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
!= ( c_Set_Oimage @ B @ C @ D @ A ) )
| ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__is__image_0) ).
thf(1538,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
!= ( c_Set_Oimage @ B @ C @ D @ A ) )
| ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(203,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ B @ C @ D @ ( tc_fun @ E @ tc_bool ) ) @ E ) )
| ~ ( hBOOL @ ( c_in @ A @ ( hAPP @ C @ F ) @ E ) )
| ~ ( hBOOL @ ( c_in @ F @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UN__iff_2) ).
thf(951,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ B @ C @ D @ ( tc_fun @ E @ tc_bool ) ) @ E ) )
| ~ ( hBOOL @ ( c_in @ A @ ( hAPP @ C @ F ) @ E ) )
| ~ ( hBOOL @ ( c_in @ F @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(404,axiom,
( ( c_COMBS @ v_P @ v_Q @ v_R @ t_a @ t_b @ t_c )
= ( hAPP @ ( hAPP @ v_P @ v_R ) @ ( hAPP @ v_Q @ v_R ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBS__def__raw_0) ).
thf(1404,plain,
( ( c_COMBS @ v_P @ v_Q @ v_R @ t_a @ t_b @ t_c )
= ( hAPP @ ( hAPP @ v_P @ v_R ) @ ( hAPP @ v_Q @ v_R ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(109,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ A @ C @ ( tc_fun @ B @ tc_bool ) ) @ B )
| ~ ( c_Finite__Set_Ofinite @ C @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__Diff2_0) ).
thf(744,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ A @ C @ ( tc_fun @ B @ tc_bool ) ) @ B )
| ~ ( c_Finite__Set_Ofinite @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(90,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ C @ D @ t_a ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) ) @ t_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ E @ F ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3 @ A @ B @ D @ C @ G @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ G @ F ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2 @ A @ B @ D @ C ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ G @ C @ E @ t_a ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) ) @ t_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conseq_1) ).
thf(703,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ C @ D @ t_a ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) ) @ t_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ E @ F ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3 @ A @ B @ D @ C @ G @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ G @ F ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__2 @ A @ B @ D @ C ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ G @ C @ E @ t_a ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) ) @ t_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(462,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ A @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Diff__Int_0) ).
thf(1536,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ A @ tc_bool ) ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).
thf(69,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) @ D @ ( tc_fun @ A @ tc_bool ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ B @ D @ ( tc_fun @ A @ tc_bool ) ) ) @ ( c_HOL_Ominus__class_Ominus @ C @ D @ ( tc_fun @ A @ tc_bool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Diff_0) ).
thf(656,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) @ D @ ( tc_fun @ A @ tc_bool ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ B @ D @ ( tc_fun @ A @ tc_bool ) ) ) @ ( c_HOL_Ominus__class_Ominus @ C @ D @ ( tc_fun @ A @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(351,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) @ D @ A @ ( tc_fun @ E @ tc_bool ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ E @ tc_bool ) ) @ ( hAPP @ D @ B ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ D @ A @ ( tc_fun @ E @ tc_bool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UN__insert_0) ).
thf(1284,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) @ D @ A @ ( tc_fun @ E @ tc_bool ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ E @ tc_bool ) ) @ ( hAPP @ D @ B ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ D @ A @ ( tc_fun @ E @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(101,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__empty_0) ).
thf(727,plain,
! [B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(229,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) @ D @ ( tc_fun @ A @ tc_bool ) )
| ~ ( c_lessequals @ C @ D @ ( tc_fun @ A @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ B @ D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__subset_2) ).
thf(1008,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) @ D @ ( tc_fun @ A @ tc_bool ) )
| ~ ( c_lessequals @ C @ D @ ( tc_fun @ A @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ B @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(42,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( B = C )
| ~ ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__antisym__conv_0) ).
thf(595,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( B = C )
| ~ ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(49,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Set_Oimage @ A @ B @ C @ D ) @ D )
| ~ ( c_Finite__Set_Ofinite @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__imageI_0) ).
thf(612,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Set_Oimage @ A @ B @ C @ D ) @ D )
| ~ ( c_Finite__Set_Ofinite @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(7,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OSemi @ A @ B )
!= ( c_Com_Ocom_OWhile @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I46_J_0) ).
thf(497,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Com_Ocom_OSemi @ A @ B )
!= ( c_Com_Ocom_OWhile @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(160,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E ) )
| ~ ( hBOOL @ ( c_in @ B @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__eqI_0) ).
thf(859,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E ) )
| ~ ( hBOOL @ ( c_in @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(333,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D ) @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ C @ ( tc_fun @ B @ tc_bool ) ) @ D @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__subset__conv_0) ).
thf(1240,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D ) @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ C @ ( tc_fun @ B @ tc_bool ) ) @ D @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(382,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ D ) @ ( tc_fun @ B @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) @ ( tc_fun @ B @ tc_bool ) ) @ D @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__insert2_0) ).
thf(1353,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ D ) @ ( tc_fun @ B @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) @ ( tc_fun @ B @ tc_bool ) ) @ D @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(44,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( c_lessequals @ D @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I6_J_0) ).
thf(600,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( c_lessequals @ D @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(483,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oimage @ A @ B @ C @ D ) @ ( c_Set_Oimage @ A @ E @ C @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ ( c_Set_Oimage @ A @ ( c_HOL_Ominus__class_Ominus @ B @ E @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) @ ( tc_fun @ D @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__diff__subset_0) ).
thf(1585,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oimage @ A @ B @ C @ D ) @ ( c_Set_Oimage @ A @ E @ C @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ ( c_Set_Oimage @ A @ ( c_HOL_Ominus__class_Ominus @ B @ E @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) @ ( tc_fun @ D @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).
thf(267,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( c_in @ B @ D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__insert__left_0) ).
thf(1094,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) )
| ~ ( hBOOL @ ( c_in @ B @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(153,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) @ D @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__infI1_0) ).
thf(845,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) @ D @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(411,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ C @ tc_bool ) ) @ A ) @ D ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__subset__iff_0) ).
thf(1421,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ C @ tc_bool ) ) @ A ) @ D ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(365,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) )
| ( hBOOL @ ( c_in @ C @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__insert__right_1) ).
thf(1316,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) )
| ( hBOOL @ ( c_in @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(428,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ A @ B @ C @ D @ E ) @ F )
= ( hAPP @ A @ ( hAPP @ B @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_o__apply_0) ).
thf(1459,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ A @ B @ C @ D @ E ) @ F )
= ( hAPP @ A @ ( hAPP @ B @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(305,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ C @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__finite__subset_0) ).
thf(1180,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(28,axiom,
! [C: $i,B: $i,A: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OCond @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I14_J_0) ).
thf(556,plain,
! [C: $i,B: $i,A: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OCond @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(23,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ B @ A )
!= ( c_HOL_Ominus__class_Ominus @ C @ D @ A ) )
| ( C = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__eqI_0) ).
thf(539,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ B @ A )
!= ( c_HOL_Ominus__class_Ominus @ C @ D @ A ) )
| ( C = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(75,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ A @ B @ C @ D )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) )
| ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__is__empty_0) ).
thf(671,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ A @ B @ C @ D )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) )
| ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(367,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( c_COMBI @ A ) @ B )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBI__def_0) ).
thf(1321,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( c_COMBI @ A ) @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(38,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Com_Ocom_OWhile @ A @ B )
!= ( c_Com_Ocom_OWhile @ C @ D ) )
| ( B = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I5_J_1) ).
thf(581,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Com_Ocom_OWhile @ A @ B )
!= ( c_Com_Ocom_OWhile @ C @ D ) )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(323,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__inf__distrib1_0) ).
thf(1216,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(280,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( c_lessequals @ B @ A @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__eq__subset_2) ).
thf(1126,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( c_lessequals @ B @ A @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(310,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( hAPP @ A @ B ) @ C @ D ) )
| ~ ( hBOOL @ ( c_in @ B @ E @ F ) )
| ~ ( c_lessequals @ ( c_Set_Oimage @ A @ E @ F @ D ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__subset__iff_0) ).
thf(1189,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( hAPP @ A @ B ) @ C @ D ) )
| ~ ( hBOOL @ ( c_in @ B @ E @ F ) )
| ~ ( c_lessequals @ ( c_Set_Oimage @ A @ E @ F @ D ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(230,axiom,
( ( c_COMBC @ v_P @ v_Q @ v_R @ t_a @ t_b @ t_c )
= ( hAPP @ ( hAPP @ v_P @ v_R ) @ v_Q ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBC__def__raw_0) ).
thf(1010,plain,
( ( c_COMBC @ v_P @ v_Q @ v_R @ t_a @ t_b @ t_c )
= ( hAPP @ ( hAPP @ v_P @ v_R ) @ v_Q ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(425,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ C @ tc_bool ) ) @ B ) @ ( c_Collect @ D @ C ) ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__Collect_0) ).
thf(1453,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ C @ tc_bool ) ) @ B ) @ ( c_Collect @ D @ C ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(273,axiom,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ A ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__bot__right_0) ).
thf(1108,plain,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ A ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(214,axiom,
! [B: $i,A: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__subsetI_0) ).
thf(976,plain,
! [B: $i,A: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(82,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oimage @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B @ C )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__empty_0) ).
thf(688,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oimage @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B @ C )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(180,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_HOL_Ominus__class_Ominus @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ ( tc_fun @ A @ tc_bool ) ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__Diff__single_0) ).
thf(903,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_HOL_Ominus__class_Ominus @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ ( tc_fun @ A @ tc_bool ) ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(6,axiom,
! [A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_Finite__Set_Ofun__left__comm__idem @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ A @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__left__comm__idem__inf_0) ).
thf(495,plain,
! [A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_Finite__Set_Ofun__left__comm__idem @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ A @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(407,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_HOL_Ominus__class_Ominus @ C @ B @ ( tc_fun @ A @ tc_bool ) ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Diff__cancel_0) ).
thf(1412,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_HOL_Ominus__class_Ominus @ C @ B @ ( tc_fun @ A @ tc_bool ) ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(370,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofold1 @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) @ B )
= C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fold1__singleton_0) ).
thf(1326,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofold1 @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) @ B )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(396,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntE_1) ).
thf(1385,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(438,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) )
!= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ E ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ) )
| ( C = D )
| ( B = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_1) ).
thf(1481,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) )
!= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ E ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ) )
| ( C = D )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).
thf(67,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
!= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ B @ C @ D @ ( tc_fun @ A @ tc_bool ) ) )
| ( ( hAPP @ C @ E )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( hBOOL @ ( c_in @ E @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UNION__empty__conv_I1_J_0) ).
thf(652,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
!= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ B @ C @ D @ ( tc_fun @ A @ tc_bool ) ) )
| ( ( hAPP @ C @ E )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( hBOOL @ ( c_in @ E @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(128,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D ) @ ( tc_fun @ B @ tc_bool ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ B @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ A @ C @ ( tc_fun @ B @ tc_bool ) ) ) @ ( c_HOL_Ominus__class_Ominus @ A @ D @ ( tc_fun @ B @ tc_bool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__Un_0) ).
thf(786,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D ) @ ( tc_fun @ B @ tc_bool ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ B @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ A @ C @ ( tc_fun @ B @ tc_bool ) ) ) @ ( c_HOL_Ominus__class_Ominus @ A @ D @ ( tc_fun @ B @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(472,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( c_in @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_singletonE_0) ).
thf(1558,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( c_in @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).
thf(40,axiom,
! [B: $i,A: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OSemi @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I12_J_0) ).
thf(588,plain,
! [B: $i,A: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OSemi @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(338,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ B @ A )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastAtMost__singleton_0) ).
thf(1253,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ B @ A )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(377,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ B )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__empty__left_0) ).
thf(1341,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ B )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(177,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__absorb2_0) ).
thf(896,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(111,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ C @ D ) )
| ~ ( hBOOL @ ( hAPP @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf1I_0) ).
thf(748,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ C @ D ) )
| ~ ( hBOOL @ ( hAPP @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(200,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ C ) @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__ord_I4_J_0) ).
thf(946,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ C ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(270,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
!= ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A ) )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastatMost__empty__iff2_0) ).
thf(1101,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
!= ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A ) )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(442,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Int__crazy_0) ).
thf(1491,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).
thf(356,axiom,
! [B: $i,A: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Complete__Lattice_Ocomplete__lattice @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Complete__Lattice_Ocomplete__lattice) ).
thf(1294,plain,
! [B: $i,A: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Complete__Lattice_Ocomplete__lattice @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(312,axiom,
! [B: $i,A: $i] :
( ( c_Collect @ ( c_fequal @ A @ B ) @ B )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_singleton__conv2_0) ).
thf(1193,plain,
! [B: $i,A: $i] :
( ( c_Collect @ ( c_fequal @ A @ B ) @ B )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(321,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ C @ D @ t_a ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) ) @ t_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ E @ F ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3 @ A @ B @ D @ C @ G @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ G @ F ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2 @ A @ B @ D @ C ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ G @ C @ E @ t_a ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) ) @ t_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hoare__derivs_Ointros_I6_J_1) ).
thf(1212,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ C @ D @ t_a ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) ) @ t_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ E @ F ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3 @ A @ B @ D @ C @ G @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ G @ F ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__2 @ A @ B @ D @ C ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ G @ C @ E @ t_a ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) ) @ t_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(147,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C ) @ D @ A )
| ~ ( c_lessequals @ C @ D @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__sup__iff_2) ).
thf(832,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C ) @ D @ A )
| ~ ( c_lessequals @ C @ D @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(362,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( c_in @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ball__empty_0) ).
thf(1309,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( c_in @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(245,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ C @ D @ t_a ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) ) @ t_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ E @ ( v_sko__Hoare__Mirabelle__Xconseq1__1 @ B @ E ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq1__2 @ B @ E ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ E @ C @ D @ t_a ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) ) @ t_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conseq1_1) ).
thf(1045,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ C @ D @ t_a ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) ) @ t_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ E @ ( v_sko__Hoare__Mirabelle__Xconseq1__1 @ B @ E ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq1__2 @ B @ E ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ E @ C @ D @ t_a ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) ) @ t_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(296,axiom,
( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_bool ) ) @ v_x )
= ( c_in @ v_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_bool ) ) @ t_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bot__empty__eq_0) ).
thf(1161,plain,
( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_bool ) ) @ v_x )
= ( c_in @ v_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_bool ) ) @ t_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(26,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Com_Ocom_OSemi @ A @ B )
!= ( c_Com_Ocom_OSemi @ C @ D ) )
| ( B = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_com_Osimps_I3_J_1) ).
thf(549,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Com_Ocom_OSemi @ A @ B )
!= ( c_Com_Ocom_OSemi @ C @ D ) )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(421,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
!= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__not__insert_0) ).
thf(1444,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
!= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(420,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__ord_I2_J_0) ).
thf(1442,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(53,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__Un_1) ).
thf(620,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(113,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__idemp_0) ).
thf(752,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(451,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oimage @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ D ) @ B @ E )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ ( hAPP @ A @ C ) ) @ ( c_Set_Oimage @ A @ D @ B @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__insert_0) ).
thf(1512,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oimage @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ D ) @ B @ E )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ ( hAPP @ A @ C ) ) @ ( c_Set_Oimage @ A @ D @ B @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).
thf(480,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ D @ C ) )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ B )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_disjoint__iff__not__equal_0) ).
thf(1578,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ D @ C ) )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ B )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).
thf(210,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ C @ D @ t_a ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) ) @ t_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ D @ ( v_sko__Hoare__Mirabelle__Xconseq12__1 @ B @ E @ D @ F ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__3 @ B @ E @ D @ F ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ E @ C @ F @ t_a ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) ) @ t_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conseq12_2) ).
thf(967,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ C @ D @ t_a ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) ) @ t_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ D @ ( v_sko__Hoare__Mirabelle__Xconseq12__1 @ B @ E @ D @ F ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__3 @ B @ E @ D @ F ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ E @ C @ F @ t_a ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) ) @ t_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(268,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ A @ B @ C @ C )
= B )
| ~ ( c_Fun_Oinj__on @ A @ B @ C @ C )
| ~ ( c_lessequals @ ( c_Set_Oimage @ A @ B @ C @ C ) @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_endo__inj__surj_0) ).
thf(1097,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ A @ B @ C @ C )
= B )
| ~ ( c_Fun_Oinj__on @ A @ B @ C @ C )
| ~ ( c_lessequals @ ( c_Set_Oimage @ A @ B @ C @ C ) @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(328,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ C @ tc_bool ) ) @ B ) @ D ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__subset__conv_1) ).
thf(1229,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ C @ tc_bool ) ) @ B ) @ D ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(466,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ C )
| ~ ( c_Finite__Set_Ofinite @ A @ C )
| ~ ( c_Finite__Set_Ofinite @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__Diff2_1) ).
thf(1546,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ C )
| ~ ( c_Finite__Set_Ofinite @ A @ C )
| ~ ( c_Finite__Set_Ofinite @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).
thf(141,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ C @ B @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_INT__extend__simps_I4_J_0) ).
thf(818,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ C @ B @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(458,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Otriple_Otriple__rec @ A @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ C @ D @ E ) @ E @ F )
= ( hAPP @ ( hAPP @ ( hAPP @ A @ B ) @ C ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_triple_Orecs_0) ).
thf(1527,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Otriple_Otriple__rec @ A @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ C @ D @ E ) @ E @ F )
= ( hAPP @ ( hAPP @ ( hAPP @ A @ B ) @ C ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).
thf(164,axiom,
! [B: $i,A: $i] : ( hBOOL @ ( c_in @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_singleton__iff_1) ).
thf(867,plain,
! [B: $i,A: $i] : ( hBOOL @ ( c_in @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(163,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__left__commute_0) ).
thf(865,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(336,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__left__absorb_0) ).
thf(1248,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(130,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D ) @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__subset__iff_2) ).
thf(790,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D ) @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(31,axiom,
! [B: $i,A: $i] :
( ( c_Set_Oimage @ ( c_COMBI @ A ) @ B @ A @ A )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__ident_0) ).
thf(564,plain,
! [B: $i,A: $i] :
( ( c_Set_Oimage @ ( c_COMBI @ A ) @ B @ A @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(417,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__left__idem_0) ).
thf(1436,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(386,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ C ) @ ( tc_fun @ A @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) @ D @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__Int2_0) ).
thf(1363,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ C ) @ ( tc_fun @ A @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) @ D @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(137,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__left__absorb_0) ).
thf(807,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(374,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ D ) @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insertI2_0) ).
thf(1335,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ D ) @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(473,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C )
= B )
| ~ ( c_lessequals @ B @ C @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__absorb2_0) ).
thf(1561,plain,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C )
= B )
| ~ ( c_lessequals @ B @ C @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).
thf(120,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) )
!= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ E ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ) )
| ( C = D )
| ( C = E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_3) ).
thf(767,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) )
!= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ E ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ) )
| ( C = D )
| ( C = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(254,axiom,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ A ) )
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__bot__right_0) ).
thf(1065,plain,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ A ) )
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(86,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ( hBOOL @ ( c_in @ A @ D @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UnE_0) ).
thf(696,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ( hBOOL @ ( c_in @ A @ D @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(298,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ B @ C )
| ~ ( c_lessequals @ B @ A @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ C ) @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_asm_0) ).
thf(1165,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ B @ C )
| ~ ( c_lessequals @ B @ A @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ C ) @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(205,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__ord_I1_J_0) ).
thf(955,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(191,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D ) @ B ) )
| ~ ( hBOOL @ ( c_in @ A @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UnCI_1) ).
thf(928,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D ) @ B ) )
| ~ ( hBOOL @ ( c_in @ A @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(353,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D ) @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__greatest_0) ).
thf(1288,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D ) @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(314,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Oinj__on @ A @ B @ C @ D )
| ~ ( c_Fun_Oinj__on @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ C @ tc_bool ) ) @ B ) @ E ) @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__Un_0) ).
thf(1197,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Oinj__on @ A @ B @ C @ D )
| ~ ( c_Fun_Oinj__on @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ C @ tc_bool ) ) @ B ) @ E ) @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(207,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ D @ C ) )
| ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subsetD_0) ).
thf(960,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ D @ C ) )
| ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(60,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ t_a @ A ) ) @ B ) @ C ) @ v_x )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ ( hAPP @ B @ v_x ) ) @ ( hAPP @ C @ v_x ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__fun__eq_0) ).
thf(635,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ t_a @ A ) ) @ B ) @ C ) @ v_x )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ ( hAPP @ B @ v_x ) ) @ ( hAPP @ C @ v_x ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(434,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Int__distrib_0) ).
thf(1473,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(107,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D ) @ B ) )
| ~ ( hBOOL @ ( c_in @ A @ D @ B ) )
| ~ ( hBOOL @ ( c_in @ A @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntI_0) ).
thf(740,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D ) @ B ) )
| ~ ( hBOOL @ ( c_in @ A @ D @ B ) )
| ~ ( hBOOL @ ( c_in @ A @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(281,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__insert_0) ).
thf(1129,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(341,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ C @ D @ t_a ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) ) @ t_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ D @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1 @ A @ B @ D @ C ) ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3 @ A @ B @ D @ C @ E @ F ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ E @ C @ F @ t_a ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) ) @ t_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conseq_2) ).
thf(1261,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ C @ D @ t_a ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) ) @ t_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ D @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1 @ A @ B @ D @ C ) ) @ ( v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__3 @ A @ B @ D @ C @ E @ F ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ E @ C @ F @ t_a ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) ) @ t_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(292,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ A @ B @ C @ D @ t_a ) @ v_x )
= ( hAPP @ A @ ( hAPP @ B @ v_x ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_o__def_0) ).
thf(1152,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ A @ B @ C @ D @ t_a ) @ v_x )
= ( hAPP @ A @ ( hAPP @ B @ v_x ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(395,axiom,
! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( c_fequal @ A @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ATP__Linkup_Oequal__imp__fequal_0) ).
thf(1384,plain,
! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( c_fequal @ A @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(393,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ t_a @ A ) ) @ B ) @ C ) @ v_x )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ ( hAPP @ B @ v_x ) ) @ ( hAPP @ C @ v_x ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__fun__eq_0) ).
thf(1378,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ t_a @ A ) ) @ B ) @ C ) @ v_x )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ ( hAPP @ B @ v_x ) ) @ ( hAPP @ C @ v_x ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(235,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ D @ C @ ( tc_fun @ A @ tc_bool ) ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UN__extend__simps_I3_J_0) ).
thf(1019,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ D @ C @ ( tc_fun @ A @ tc_bool ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(468,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ C @ B @ ( tc_fun @ A @ tc_bool ) ) ) @ D )
= D ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UN__extend__simps_I2_J_0) ).
thf(1550,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ C @ B @ ( tc_fun @ A @ tc_bool ) ) ) @ D )
= D ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
thf(384,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E )
= ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oimage @ A @ B @ D @ E ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ ( tc_fun @ E @ tc_bool ) ) )
| ~ ( c_lessequals @ C @ F @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ B @ F @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ A @ F @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__image__set__diff_0) ).
thf(1357,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E )
= ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oimage @ A @ B @ D @ E ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ ( tc_fun @ E @ tc_bool ) ) )
| ~ ( c_lessequals @ C @ F @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ B @ F @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ A @ F @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(446,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ A @ tc_bool ) ) ) @ C )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Diff__cancel2_0) ).
thf(1500,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ A @ tc_bool ) ) ) @ C )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(156,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I6_J_0) ).
thf(850,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(415,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ B @ tc_bool ) ) @ A ) @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__Un_0) ).
thf(1431,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ B @ tc_bool ) ) @ A ) @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(358,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastatMost__empty__iff_0) ).
thf(1299,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(448,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ C @ D @ t_a ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) ) @ t_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ E @ F ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__3 @ B @ G @ D @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ G @ F ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__2 @ B @ G @ D @ E ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ G @ C @ E @ t_a ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) ) @ t_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conseq12_1) ).
thf(1505,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ C @ D @ t_a ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) ) @ t_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ E @ F ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__3 @ B @ G @ D @ E ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ G @ F ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__2 @ B @ G @ D @ E ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ ( c_Hoare__Mirabelle_Otriple_Otriple @ G @ C @ E @ t_a ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) ) @ t_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).
thf(47,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ D @ C @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__trans_0) ).
thf(607,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ D @ C @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(266,axiom,
! [A: $i] : ( c_Finite__Set_Ofinite @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite_OemptyI_0) ).
thf(1093,plain,
! [A: $i] : ( c_Finite__Set_Ofinite @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(55,axiom,
! [B: $i,A: $i] :
( ( c_Set_Ocontents @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ A )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_contents__eq_0) ).
thf(624,plain,
! [B: $i,A: $i] :
( ( c_Set_Ocontents @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(344,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( c_Complete__Lattice_OSup__class_OSup @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ ( c_Complete__Lattice_OSup__class_OSup @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sup__insert_0) ).
thf(1268,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( c_Complete__Lattice_OSup__class_OSup @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ B ) @ C ) @ A )
= ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ B ) @ ( c_Complete__Lattice_OSup__class_OSup @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(35,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofold1 @ A @ B @ C )
= ( c_The @ ( c_Finite__Set_Ofold1Set @ A @ B @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fold1__def_0) ).
thf(575,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofold1 @ A @ B @ C )
= ( c_The @ ( c_Finite__Set_Ofold1Set @ A @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(3,negated_conjecture,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ v_Q @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ v_Q_H @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(486,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ v_Q @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ v_Q_H @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(194,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ ( hAPP @ B @ C ) ) @ D ) )
| ~ ( hBOOL @ ( c_in @ D @ C @ E ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ B @ F @ A @ G @ H @ I @ J @ K @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OInf__lower_0) ).
thf(935,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ ( hAPP @ B @ C ) ) @ D ) )
| ~ ( hBOOL @ ( c_in @ D @ C @ E ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ B @ F @ A @ G @ H @ I @ J @ K @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(430,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A ) )
| ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastatMost__empty__iff2_1) ).
thf(1463,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A ) )
| ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(242,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__le2_0) ).
thf(1037,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(409,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__insert__right_0) ).
thf(1416,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(263,axiom,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ A ) @ ( tc_fun @ B @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insertI_0) ).
thf(1088,plain,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ A @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ C ) @ A ) @ ( tc_fun @ B @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(423,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ D ) @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__greatest_0) ).
thf(1449,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ D ) @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(432,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D ) @ B ) )
| ~ ( hBOOL @ ( c_in @ A @ D @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UnCI_0) ).
thf(1468,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D ) @ B ) )
| ~ ( hBOOL @ ( c_in @ A @ D @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(93,axiom,
! [B: $i,A: $i] :
( ( class_Orderings_Opreorder @ ( tc_fun @ A @ B ) )
| ~ ( class_Orderings_Opreorder @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Opreorder) ).
thf(708,plain,
! [B: $i,A: $i] :
( ( class_Orderings_Opreorder @ ( tc_fun @ A @ B ) )
| ~ ( class_Orderings_Opreorder @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(171,axiom,
( ( hAPP @ ( c_COMBK @ v_P @ t_a @ t_b ) @ v_Q )
= v_P ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBK__def__raw_0) ).
thf(882,plain,
( ( hAPP @ ( c_COMBK @ v_P @ t_a @ t_b ) @ v_Q )
= v_P ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(232,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ C ) @ D ) @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__supI1_0) ).
thf(1014,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A ) @ C ) @ D ) @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(14658,plain,
$false,
inference(e,[status(thm)],[645,809,1337,629,1024,760,893,518,1554,1083,962,977,1406,683,1290,1068,1522,1401,1569,1073,1544,1142,1533,861,1486,523,762,873,1205,655,511,614,677,1497,1078,500,797,1275,1233,698,945,1063,1507,930,829,898,1001,1441,841,1475,1366,1529,1518,1391,1576,973,885,570,719,1330,802,1455,1191,949,542,724,1055,1409,1323,838,917,702,1313,1279,559,1514,1147,770,1398,1100,638,853,1319,870,969,1347,1489,492,591,1418,937,1581,1183,1051,905,1302,756,485,1136,834,1169,734,1447,1119,998,1433,1201,527,1564,602,981,877,692,1345,988,1104,1242,942,661,925,1306,1199,1338,1470,714,1311,534,1047,1057,1163,1343,1042,1519,1355,862,1174,598,788,815,729,1238,1387,910,957,1223,746,1091,1021,778,1502,820,1423,1032,1365,1178,1457,830,1159,1210,1195,1281,710,1012,1106,847,566,484,1296,665,742,1259,1328,1121,1111,1425,1006,1138,783,857,1360,1350,1089,1541,650,948,1567,1493,884,1182,489,1214,706,1461,537,686,1075,1414,526,1016,1207,679,1039,622,1131,1552,1060,721,1525,1324,1114,647,1263,515,1150,1478,1451,738,1266,1231,984,911,1393,503,605,1333,792,1086,633,805,765,1466,530,953,773,1286,1035,1187,674,1026,1167,718,888,750,618,513,1273,1548,573,1374,1219,824,1154,562,694,732,1389,843,579,1124,875,577,1256,1226,545,1139,919,641,1428,1271,1371,979,900,681,1574,736,1144,616,784,1117,990,996,509,880,1571,1376,1439,890,811,1080,631,758,1557,609,799,1029,1381,932,848,700,1149,964,626,915,1293,668,983,1396,827,1245,868,780,1176,986,1477,1250,1496,505,922,658,912,521,1171,1583,1304,1203,944,795,663,1277,1134,1509,939,1018,754,553,836,1049,776,855,1070,971,1368,1531,1484,993,712,1003,690,1516,705,1156,1053,1186,585,1235,643,1220,907,1538,951,1404,744,703,1536,656,1284,727,1008,595,612,497,859,1240,1353,600,1585,1094,845,1421,1316,1459,1180,556,539,671,1321,581,1216,1126,1189,1010,1453,1108,976,688,903,495,1412,1326,1385,1481,652,786,1558,588,1253,1341,896,748,946,1101,1491,1294,1193,1212,832,1309,1045,1161,549,1444,1442,620,752,1512,1578,967,1097,1229,1546,818,1527,867,865,1248,790,564,1436,1363,807,1335,1561,767,1065,696,1165,955,928,1288,1197,960,635,1473,740,1129,1261,1152,1384,1378,1019,1550,1357,1500,850,1431,1299,1505,607,1093,624,1268,575,486,935,1463,1037,1416,1088,1449,1468,708,882,1014]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : SWV827-1 : TPTP v8.1.2. Released v4.1.0.
% 0.08/0.17 % Command : run_Leo-III %s %d
% 0.18/0.38 % Computer : n026.cluster.edu
% 0.18/0.38 % Model : x86_64 x86_64
% 0.18/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.38 % Memory : 8042.1875MB
% 0.18/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.18/0.38 % CPULimit : 300
% 0.18/0.38 % WCLimit : 300
% 0.18/0.38 % DateTime : Fri May 19 02:35:21 EDT 2023
% 0.18/0.39 % CPUTime :
% 0.97/0.90 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.45/1.12 % [INFO] Parsing done (227ms).
% 1.45/1.13 % [INFO] Running in sequential loop mode.
% 2.23/1.35 % [INFO] eprover registered as external prover.
% 2.23/1.35 % [INFO] cvc4 registered as external prover.
% 2.23/1.35 % [INFO] Scanning for conjecture ...
% 2.68/1.49 % [INFO] Found a conjecture and 480 axioms. Running axiom selection ...
% 3.63/1.69 % [INFO] Axiom selection finished. Selected 480 axioms (removed 0 axioms).
% 4.13/1.89 % [INFO] Problem is propositional (TPTP CNF).
% 4.43/1.90 % [INFO] Type checking passed.
% 4.43/1.91 % [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 ...
% 54.37/11.54 % External prover 'e' found a proof!
% 54.37/11.54 % [INFO] Killing All external provers ...
% 54.37/11.54 % Time passed: 10985ms (effective reasoning time: 10405ms)
% 54.37/11.54 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 54.37/11.55 % Axioms used in derivation (480): cls_inf__sup__absorb_0, cls_inf__sup__aci_I2_J_0, cls_atLeastatMost__subset__iff_2, cls_the__sym__eq__trivial_0, cls_Int__absorb2_0, cls_Diff__iff_2, cls_bot__fun__eq_0, cls_Int__Un__distrib_0, clsarity_fun__Lattices_Olower__semilattice, cls_Diff__cancel_0, cls_INT__extend__simps_I4_J_0, cls_asm_0, cls_subset__insert_1, cls_sup__ge1_0, cls_image__constant_0, cls_insertE_0, cls_Un__Diff_0, cls_com_Osimps_I3_J_0, cls_Un__subset__iff_0, cls_equalityI_0, cls_insert__inter__insert_0, cls_inj__on__Un_2, cls_order__eq__iff_0, cls_com_Osimps_I5_J_0, cls_COMBC__def_0, cls_subset__empty_1, cls_subset__image__iff_2, cls_finite__insert_0, cls_inj__on__image__Int_0, cls_empty__is__image_1, cls_com_Osimps_I44_J_0, cls_com_Osimps_I14_J_0, cls_image__mono_0, cls_Un__empty__left_0, cls_le__funD_0, cls_sup__bot__right_0, cls_insert__code_1, clsarity_bool__Lattices_Olower__semilattice, cls_le__SUPI_0, cls_inf__sup__aci_I6_J_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, 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_Diff__subset__conv_0, cls_inj__on__image__set__diff_0, cls_Int__Un__distrib2_0, cls_mem__def_1, cls_Int__Collect_1, cls_Inf__lower_0, cls_insert__absorb_0, cls_empty__iff_0, cls_Min__le_0, cls_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_K__record__comp_0, clsarity_fun__Lattices_Oupper__semilattice, cls_com_Osimps_I4_J_2, cls_le__sup__iff_0, cls_inj__on__Un__image__eq__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_COMBB__def_0, cls_CollectI_0, cls_subset__insert__iff_2, 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_COMBS__def_0, cls_Un__Int__distrib2_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_COMBC__def__raw_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_empty__is__image_0, cls_SUP__const_0, cls_inj__on__Un_3, cls_rev__image__eqI_0, cls_inj__on__insert_0, cls_SUP1__I_0, cls_triple_Oinject_2, cls_le__supE_1, 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_image__constant__conv_1, cls_lessThan__subset__iff_1, cls_finite__Int_0, cls_conseq1_1, cls_Un__absorb2_0, cls_atLeastatMost__subset__iff_3, cls_inf__sup__aci_I8_J_0, cls_Un__empty__right_0, cls_insert__ident_0, clsarity_bool__Orderings_Oorder, cls_bot__least_0, cls_sup__eq__bot__eq2_0, cls_hoare__derivs_Ointros_I6_J_0, cls_UnCI_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_comp__inj__on_0, cls_lessThan__eq__iff_0, cls_inj__on__imageI_0, cls_subset__iff_0, cls_insert__code_2, 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_image__insert_0, cls_UN__subset__iff_0, cls_finite__Diff_0, cls_SUP1__iff_2, cls_inf__absorb2_0, cls_atLeastatMost__empty__iff2_0, clsarity_bool__Lattices_Oupper__semilattice, cls_COMBB__def__raw_0, cls_doubleton__eq__iff_2, cls_subset__insert__iff_3, 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_Inf__insert_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_ivl__disj__int_I4_J_0, cls_finite__surj_0, cls_le__inf__iff_0, cls_Int__subset__iff_1, cls_COMBK__def__raw_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_order__trans_0, cls_image__empty_0, cls_com_Osimps_I46_J_0, cls_inf__le2_0, cls_insert__is__Un_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_inj__on__insert_1, cls_le__supE_0, cls_empty__not__insert_0, cls_sup__assoc_0, cls_insert__Diff1_0, cls_lessThan__subset__iff_0, cls_Diff__Int__distrib2_0, cls_image__constant__conv_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_Nitpick_OEx1__def_2, cls_fun__left__comm__idem__sup_0, cls_hoare__derivs_Oinsert_0, cls_empty__subsetI_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_image__ident_0, cls_atLeastatMost__subset__iff_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_image__diff__subset_0, cls_fun__left__comm__idem_Ofun__left__idem_0, cls_inj__on__empty_0, cls_DiffE_0, cls_Int__Diff_0, cls_image__iff_2, cls_insertCI_0, cls_complete__lattice_OSup__binary_0, cls_image__Int__subset_0, cls_le__inf__iff_2, cls_COMBS__def__raw_0, cls_Un__Diff__cancel_0, cls_complete__lattice_OInf__insert_0, cls_image__Un_0, cls_insert__Diff_0, cls_sup1CI_1, cls_complete__lattice_OInf__binary_0, cls_below__fold1__iff_0, cls_le__infE_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_Int__lower2_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_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_o__eq__dest__lhs_0, cls_Diff__mono_0, cls_order__antisym__conv_0, cls_UnE_0, cls_inj__on__Un_0, cls_subset__insertI2_0, cls_doubleton__eq__iff_3, cls_conseq_1, cls_atLeastatMost__empty__iff_0, cls_finite__Diff__insert_1, 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_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_subsetD_0, cls_finite__imageD_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_insert__absorb2_0, cls_sup__fun__eq_0, cls_UNION__empty__conv_I1_J_0, cls_finite__Diff__insert_0, cls_inf__sup__aci_I4_J_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__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_inf__sup__ord_I3_J_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_eq__eqI_1, cls_com_Osimps_I4_J_1, 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_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, clsarity_bool__Lattices_Odistrib__lattice, cls_finite__UN_0, cls_le__infE_1, cls_finite_OemptyI_0, cls_image__subset__iff_0, cls_inf__le1_0, cls_finite__imageI_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_finite__surj__inj_0, cls_fold1Set__sing_0, cls_Nitpick_OThe__psimp_0, cls_image__eqI_0, cls_inj__on__diff_0, cls_inj__on__insert_2, cls_insert__code_0, cls_le__eqI_1, cls_inj__on__id2_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__partition_0, cls_sup__bot__left_0, cls_insert__image_0, cls_rev__finite__subset_0, cls_finite__Un_1, cls_disjoint__iff__not__equal_0, cls_inj__on__Un_1, cls_com_Osimps_I16_J_0, cls_sup__inf__distrib1_0, cls_com_Osimps_I15_J_0, cls_Un__Int__assoc__eq_0, cls_COMBI__def_0, cls_endo__inj__surj_0, cls_insert__commute_0, cls_insert__iff_2, cls_image__image_0, cls_Diff__insert__absorb_0, cls_le__infI2_0, cls_UNION__empty__conv_I2_J_0, cls_finite__Diff2_0, cls_image__compose_0, cls_image__is__empty_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, cls_imageI_0, clsarity_fun__Lattices_Odistrib__lattice, clsarity_fun__HOL_Ominus, cls_com_Osimps_I4_J_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_single__Diff__lessThan_0, cls_ball__empty_0, cls_Int__insert__right_0, cls_singleton__conv2_0, cls_Min__antimono_0, cls_o__assoc_0, cls_subset__insert__iff_1, cls_Diff__subset_0, cls_conseq1_0, cls_predicate1D_0, cls_inf1E_0, cls_empty__Diff_0, cls_Int__Collect_2
% 54.37/11.55 % No. of inferences in proof: 967
% 54.37/11.55 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 10985 ms resp. 10405 ms w/o parsing
% 54.71/11.77 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 54.71/11.78 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------