TSTP Solution File: SWV839-1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SWV839-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n004.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 12:18:50 EDT 2023
% Result : Unsatisfiable 9.69s 3.20s
% Output : Refutation 10.77s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 536
% Syntax : Number of formulae : 991 ( 205 unt; 82 typ; 0 def)
% Number of atoms : 2201 ( 448 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 15718 (1192 ~;1292 |; 0 &;13234 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 11 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 180 ( 180 >; 0 *; 0 +; 0 <<)
% Number of symbols : 84 ( 82 usr; 12 con; 0-9 aty)
% Number of variables : 3134 ( 0 ^;3134 !; 0 ?;3134 :)
% Comments :
%------------------------------------------------------------------------------
thf(hBOOL_type,type,
hBOOL: $i > $o ).
thf(hAPP_type,type,
hAPP: $i > $i > $i ).
thf(c_lessequals_type,type,
c_lessequals: $i > $i ).
thf(tc_fun_type,type,
tc_fun: $i > $i > $i ).
thf(tc_Hoare__Mirabelle_Otriple_type,type,
tc_Hoare__Mirabelle_Otriple: $i > $i ).
thf(t_a_type,type,
t_a: $i ).
thf(tc_bool_type,type,
tc_bool: $i ).
thf(v_G_type,type,
v_G: $i ).
thf(v_Ga_type,type,
v_Ga: $i ).
thf(c_Hoare__Mirabelle_Ohoare__derivs_type,type,
c_Hoare__Mirabelle_Ohoare__derivs: $i > $i > $i > $o ).
thf(c_Set_Oinsert_type,type,
c_Set_Oinsert: $i > $i > $i > $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(c_Com_Ocom_OSKIP_type,type,
c_Com_Ocom_OSKIP: $i ).
thf(c_Orderings_Obot__class_Obot_type,type,
c_Orderings_Obot__class_Obot: $i > $i ).
thf(class_OrderedGroup_Ogroup__add_type,type,
class_OrderedGroup_Ogroup__add: $i > $o ).
thf(c_HOL_Ouminus__class_Ouminus_type,type,
c_HOL_Ouminus__class_Ouminus: $i > $i > $i ).
thf(class_Orderings_Olinorder_type,type,
class_Orderings_Olinorder: $i > $o ).
thf(c_HOL_Oord__class_Oless_type,type,
c_HOL_Oord__class_Oless: $i > $i > $i > $o ).
thf(class_Ring__and__Field_Oordered__idom_type,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
thf(class_Orderings_Oorder_type,type,
class_Orderings_Oorder: $i > $o ).
thf(class_Orderings_Opreorder_type,type,
class_Orderings_Opreorder: $i > $o ).
thf(class_OrderedGroup_Opordered__ab__group__add_type,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
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 > $i > $i ).
thf(class_Lattices_Oboolean__algebra_type,type,
class_Lattices_Oboolean__algebra: $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(class_Lattices_Olattice_type,type,
class_Lattices_Olattice: $i > $o ).
thf(tc_nat_type,type,
tc_nat: $i ).
thf(class_Orderings_Obot_type,type,
class_Orderings_Obot: $i > $o ).
thf(c_Com_Ocom_OSemi_type,type,
c_Com_Ocom_OSemi: $i > $i > $i ).
thf(class_HOL_Ominus_type,type,
class_HOL_Ominus: $i > $o ).
thf(c_Finite__Set_Ofold1_type,type,
c_Finite__Set_Ofold1: $i > $i > $i > $i ).
thf(c_The_type,type,
c_The: $i > $i > $i ).
thf(c_Finite__Set_Ofold1Set_type,type,
c_Finite__Set_Ofold1Set: $i > $i > $i > $i ).
thf(c_Finite__Set_Ofinite_type,type,
c_Finite__Set_Ofinite: $i > $i > $o ).
thf(c_Finite__Set_Ofold__graph_type,type,
c_Finite__Set_Ofold__graph: $i > $i > $i > $i > $i > $i > $o ).
thf(class_HOL_Oord_type,type,
class_HOL_Oord: $i > $o ).
thf(c_Collect_type,type,
c_Collect: $i > $i > $i ).
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(c_Complete__Lattice_Ocomplete__lattice_type,type,
c_Complete__Lattice_Ocomplete__lattice: $i > $i > $i > $i > $i > $i > $i > $i > $i > $o ).
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__3_type,type,
v_sko__Hoare__Mirabelle__Xconseq12__3: $i > $i > $i > $i > $i ).
thf(v_x_type,type,
v_x: $i ).
thf(c_SetInterval_Oord__class_OgreaterThanAtMost_type,type,
c_SetInterval_Oord__class_OgreaterThanAtMost: $i > $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(c_Set_Ocontents_type,type,
c_Set_Ocontents: $i > $i > $i ).
thf(c_SetInterval_Oord__class_OatLeastAtMost_type,type,
c_SetInterval_Oord__class_OatLeastAtMost: $i > $i > $i > $i ).
thf(c_SetInterval_Oord__class_OatLeastLessThan_type,type,
c_SetInterval_Oord__class_OatLeastLessThan: $i > $i > $i > $i ).
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_Complete__Lattice_Ocomplete__lattice__axioms_type,type,
c_Complete__Lattice_Ocomplete__lattice__axioms: $i > $i > $i > $i > $o ).
thf(c_Complete__Lattice_OInf__class_OInf_type,type,
c_Complete__Lattice_OInf__class_OInf: $i > $i ).
thf(c_Complete__Lattice_OSup__class_OSup_type,type,
c_Complete__Lattice_OSup__class_OSup: $i > $i ).
thf(class_Lattices_Obounded__lattice_type,type,
class_Lattices_Obounded__lattice: $i > $o ).
thf(c_COMBK_type,type,
c_COMBK: $i > $i > $i > $i ).
thf(v_sko__Hoare__Mirabelle__Xconseq2__1_type,type,
v_sko__Hoare__Mirabelle__Xconseq2__1: $i > $i > $i ).
thf(v_sko__Hoare__Mirabelle__Xconseq2__2_type,type,
v_sko__Hoare__Mirabelle__Xconseq2__2: $i > $i > $i ).
thf(c_Finite__Set_Osetsum_type,type,
c_Finite__Set_Osetsum: $i > $i > $i > $i > $i ).
thf(c_Nitpick_Ofold__graph_H_type,type,
c_Nitpick_Ofold__graph_H: $i > $i > $i > $i > $i > $i > $o ).
thf(c_COMBC_type,type,
c_COMBC: $i > $i > $i > $i > $i ).
thf(c_fequal_type,type,
c_fequal: $i > $i ).
thf(tc_Com_Ostate_type,type,
tc_Com_Ostate: $i ).
thf(v_sko__Hoare__Mirabelle__Xescape__2_type,type,
v_sko__Hoare__Mirabelle__Xescape__2: $i > $i > $i > $i > $i ).
thf(v_sko__Hoare__Mirabelle__Xescape__1_type,type,
v_sko__Hoare__Mirabelle__Xescape__1: $i > $i > $i > $i > $i ).
thf(class_HOL_Ouminus_type,type,
class_HOL_Ouminus: $i > $o ).
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_Finite__Set_Olinorder__class_OMax_type,type,
c_Finite__Set_Olinorder__class_OMax: $i > $i > $i ).
thf(t_b_type,type,
t_b: $i ).
thf(v_A_type,type,
v_A: $i ).
thf(v_sko__Hoare__Mirabelle__Xconseq12__2_type,type,
v_sko__Hoare__Mirabelle__Xconseq12__2: $i > $i > $i > $i > $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__1_type,type,
v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__1: $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__Xconseq__1_type,type,
v_sko__Hoare__Mirabelle__Xhoare__derivs__Xconseq__1: $i > $i > $i > $i > $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__Xintros__6__3_type,type,
v_sko__Hoare__Mirabelle__Xhoare__derivs__Xintros__6__3: $i > $i > $i > $i > $i > $i > $i ).
thf(class_Ring__and__Field_Oring_type,type,
class_Ring__and__Field_Oring: $i > $o ).
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(189,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Oord @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ B @ A ) ) @ C ) @ D ) )
| ~ ( c_HOL_Oord__class_Oless @ C @ D @ ( tc_fun @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__fun__def_0) ).
thf(892,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Oord @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ B @ A ) ) @ C ) @ D ) )
| ~ ( c_HOL_Oord__class_Oless @ C @ D @ ( tc_fun @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(254,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ D @ tc_bool ) ) @ A ) @ C ) )
| ( hBOOL @ ( c_in @ B @ A @ D ) )
| ( hBOOL @ ( c_in @ B @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_psubset__insert__iff_3) ).
thf(1036,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ D @ tc_bool ) ) @ A ) @ C ) )
| ( hBOOL @ ( c_in @ B @ A @ D ) )
| ( hBOOL @ ( c_in @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(428,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ ( tc_fun @ A @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ A @ tc_bool ) ) ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__subset__conv_0) ).
thf(1411,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ ( tc_fun @ A @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ A @ tc_bool ) ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(75,axiom,
! [B: $i,A: $i] :
( ( c_The @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nitpick_OThe__psimp_0) ).
thf(629,plain,
! [B: $i,A: $i] :
( ( c_The @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(453,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D ) )
| ~ ( hBOOL @ ( c_in @ A @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UnCI_1) ).
thf(1469,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D ) )
| ~ ( hBOOL @ ( c_in @ A @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(314,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__commute_0) ).
thf(1168,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(11,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__left__idem_0) ).
thf(479,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(168,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ B @ A ) ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__sup__iff_1) ).
thf(846,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ B @ A ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(319,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ t_a @ A ) ) @ v_x )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ B @ v_x ) @ ( hAPP @ C @ v_x ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__fun__eq_0) ).
thf(1179,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ t_a @ A ) ) @ v_x )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ B @ v_x ) @ ( hAPP @ C @ v_x ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(91,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Set_Oinsert @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) )
| ( hBOOL @ ( c_in @ C @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert_1) ).
thf(666,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Set_Oinsert @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) )
| ( hBOOL @ ( c_in @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(410,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Set_Oinsert @ B @ C @ A ) ) @ ( c_Set_Oinsert @ B @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__mono_0) ).
thf(1369,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Set_Oinsert @ B @ C @ A ) ) @ ( c_Set_Oinsert @ B @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(324,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(1190,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)],[324]) ).
thf(197,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(909,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)],[197]) ).
thf(252,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ B @ ( tc_fun @ A @ tc_bool ) ) ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__subset__iff_1) ).
thf(1031,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ B @ ( tc_fun @ A @ tc_bool ) ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(383,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ D )
| ~ ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__Diff__insert_1) ).
thf(1315,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ D )
| ~ ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(26,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__trans_0) ).
thf(518,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(139,axiom,
class_Lattices_Obounded__lattice @ tc_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Obounded__lattice) ).
thf(777,plain,
class_Lattices_Obounded__lattice @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(43,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).
thf(555,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(329,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ A @ tc_bool ) ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__least_0) ).
thf(1200,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ A @ tc_bool ) ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(228,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(977,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)],[228]) ).
thf(335,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( c_Finite__Set_Ofold__graph @ C @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ A @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__fold__graphE_0) ).
thf(1211,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( c_Finite__Set_Ofold__graph @ C @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ A @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(426,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Ouminus__class_Ouminus @ A @ ( tc_fun @ B @ tc_bool ) )
!= ( c_HOL_Ouminus__class_Ouminus @ C @ ( tc_fun @ B @ tc_bool ) ) )
| ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Compl__eq__Compl__iff_0) ).
thf(1406,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Ouminus__class_Ouminus @ A @ ( tc_fun @ B @ tc_bool ) )
!= ( c_HOL_Ouminus__class_Ouminus @ C @ ( tc_fun @ B @ tc_bool ) ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(99,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
!= ( c_Orderings_Obot__class_Obot @ A ) )
| ( B
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__eq__bot__eq1_0) ).
thf(683,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
!= ( c_Orderings_Obot__class_Obot @ A ) )
| ( B
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(118,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(730,plain,
! [B: $i,A: $i] :
( ( c_Com_Ocom_OSemi @ A @ B )
!= c_Com_Ocom_OSKIP ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(268,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__le_0) ).
thf(1068,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(443,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(1443,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)],[443]) ).
thf(235,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(994,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)],[235]) ).
thf(424,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(1401,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)],[424]) ).
thf(433,axiom,
class_Lattices_Oboolean__algebra @ tc_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oboolean__algebra) ).
thf(1422,plain,
class_Lattices_Oboolean__algebra @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(332,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(1205,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)],[332]) ).
thf(69,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(614,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)],[69]) ).
thf(256,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__minus__iff_1) ).
thf(1041,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(316,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ B @ C @ ( tc_Hoare__Mirabelle_Otriple @ D ) ) @ D )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ C @ D )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ D ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ D ) ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hoare__derivs_Oinsert_0) ).
thf(1173,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ B @ C @ ( tc_Hoare__Mirabelle_Otriple @ D ) ) @ D )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ C @ D )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ D ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ D ) ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(28,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( C = B )
| ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__less__linear_0) ).
thf(523,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( C = B )
| ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(132,axiom,
! [B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__empty__left_0) ).
thf(762,plain,
! [B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(183,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
!= C )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__sup_1) ).
thf(878,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
!= C )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(86,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_HOL_Ouminus__class_Ouminus @ B @ ( tc_fun @ C @ tc_bool ) ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ComplD_0) ).
thf(655,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_HOL_Ouminus__class_Ouminus @ B @ ( tc_fun @ C @ tc_bool ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(273,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Set_Oinsert @ A @ ( c_HOL_Ominus__class_Ominus @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ C ) )
| ( hBOOL @ ( c_in @ A @ D @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__Diff__if_1) ).
thf(1078,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Set_Oinsert @ A @ ( c_HOL_Ominus__class_Ominus @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ C ) )
| ( hBOOL @ ( c_in @ A @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(31,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).
thf(533,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(312,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(1164,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)],[312]) ).
thf(345,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
!= ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
| ( A = E )
| ( A = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_0) ).
thf(1233,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
!= ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
| ( A = E )
| ( A = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(359,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(1260,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)],[359]) ).
thf(266,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__supI_0) ).
thf(1063,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(449,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 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastatMost__empty__iff_0) ).
thf(1458,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 ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).
thf(154,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ ( c_HOL_Ouminus__class_Ouminus @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ A @ tc_bool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__Compl__self__eq_1) ).
thf(814,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ ( c_HOL_Ouminus__class_Ouminus @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ A @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(390,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ D @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ C @ tc_bool ) ) @ A ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__psubset__trans_0) ).
thf(1327,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ D @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ C @ tc_bool ) ) @ A ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(125,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ C @ ( tc_fun @ E @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ D @ C @ ( tc_fun @ E @ tc_bool ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ B @ D @ C @ ( tc_fun @ E @ tc_bool ) ) @ ( tc_fun @ E @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UN__Un_0) ).
thf(747,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ C @ ( tc_fun @ E @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ D @ C @ ( tc_fun @ E @ tc_bool ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ B @ D @ C @ ( tc_fun @ E @ tc_bool ) ) @ ( tc_fun @ E @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(199,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ B ) )
| ~ ( hBOOL @ ( c_in @ A @ D @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__rev__mp_0) ).
thf(913,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ B ) )
| ~ ( hBOOL @ ( c_in @ A @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(34,axiom,
class_Orderings_Olinorder @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
thf(538,plain,
class_Orderings_Olinorder @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(403,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
!= ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
| ( A = E )
| ( B = E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_2) ).
thf(1354,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
!= ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
| ( A = E )
| ( B = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(340,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_HOL_Oord__class_Oless @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastatMost__empty_0) ).
thf(1222,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_HOL_Oord__class_Oless @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(206,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ C @ tc_bool ) ) @ B ) @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ C @ tc_bool ) ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__eq__subset_2) ).
thf(930,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ C @ tc_bool ) ) @ B ) @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ C @ tc_bool ) ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(327,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Oord @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ B @ C ) ) @ ( hAPP @ D @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ E @ A ) ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__funD_0) ).
thf(1196,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Oord @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ B @ C ) ) @ ( hAPP @ D @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ E @ A ) ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(350,axiom,
! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equalityE_0) ).
thf(1243,plain,
! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(109,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( c_SetInterval_Oord__class_OgreaterThanAtMost @ B @ C @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_greaterThanAtMost__empty__iff_1) ).
thf(709,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( c_SetInterval_Oord__class_OgreaterThanAtMost @ B @ C @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(417,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__less_1) ).
thf(1386,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(408,axiom,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insertI1_0) ).
thf(1366,plain,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(142,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) )
| ( hBOOL @ ( c_in @ D @ B @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Set_Oinsert @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert__iff_1) ).
thf(782,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) )
| ( hBOOL @ ( c_in @ D @ B @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Set_Oinsert @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(442,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Diff__cancel2_0) ).
thf(1441,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).
thf(371,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( c_Finite__Set_Olinorder__class_OMax @ C @ 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(1287,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( c_Finite__Set_Olinorder__class_OMax @ C @ A ) ) )
| ~ ( hBOOL @ ( c_in @ B @ C @ A ) )
| ~ ( c_Finite__Set_Ofinite @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(437,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__least_0) ).
thf(1430,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(113,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_Finite__Set_Osetsum @ B @ ( c_HOL_Ominus__class_Ominus @ C @ ( c_Set_Oinsert @ D @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_bool ) ) @ E ) @ ( tc_fun @ E @ tc_bool ) ) @ E @ A )
= ( c_Finite__Set_Osetsum @ B @ C @ E @ A ) )
| ( hBOOL @ ( c_in @ D @ C @ E ) )
| ~ ( c_Finite__Set_Ofinite @ C @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setsum__diff1_1) ).
thf(719,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_Finite__Set_Osetsum @ B @ ( c_HOL_Ominus__class_Ominus @ C @ ( c_Set_Oinsert @ D @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_bool ) ) @ E ) @ ( tc_fun @ E @ tc_bool ) ) @ E @ A )
= ( c_Finite__Set_Osetsum @ B @ C @ E @ A ) )
| ( hBOOL @ ( c_in @ D @ C @ E ) )
| ~ ( c_Finite__Set_Ofinite @ C @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(71,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_SetInterval_Oord__class_OgreaterThanAtMost @ B @ C @ A ) @ ( c_SetInterval_Oord__class_OgreaterThanAtMost @ C @ D @ A ) @ ( tc_fun @ A @ tc_bool ) )
= ( c_SetInterval_Oord__class_OgreaterThanAtMost @ B @ D @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ivl__disj__un_I20_J_0) ).
thf(619,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_SetInterval_Oord__class_OgreaterThanAtMost @ B @ C @ A ) @ ( c_SetInterval_Oord__class_OgreaterThanAtMost @ C @ D @ A ) @ ( tc_fun @ A @ tc_bool ) )
= ( c_SetInterval_Oord__class_OgreaterThanAtMost @ B @ D @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(214,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ ( tc_fun @ A @ tc_bool ) ) ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ ( tc_fun @ A @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Compl__anti__mono_0) ).
thf(949,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ ( tc_fun @ A @ tc_bool ) ) ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ ( tc_fun @ A @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(427,axiom,
! [B: $i,A: $i] :
( ( c_The @ ( hAPP @ ( c_fequal @ A ) @ B ) @ A )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_the__sym__eq__trivial_0) ).
thf(1409,plain,
! [B: $i,A: $i] :
( ( c_The @ ( hAPP @ ( c_fequal @ A ) @ B ) @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(115,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(724,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)],[115]) ).
thf(201,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ ( c_Com_Ocom_OSemi @ C @ D ) @ E @ F ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ F ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ F ) ) @ F )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ G @ D @ E @ F ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ F ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ F ) ) @ F )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ C @ G @ F ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ F ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ F ) ) @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Comp_0) ).
thf(917,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ ( c_Com_Ocom_OSemi @ C @ D ) @ E @ F ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ F ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ F ) ) @ F )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ G @ D @ E @ F ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ F ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ F ) ) @ F )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ C @ G @ F ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ F ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ F ) ) @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(127,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ B @ A ) ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__supE_1) ).
thf(751,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ B @ A ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(264,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ B @ C ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ B @ E @ A ) ) )
| ~ ( hBOOL @ ( c_in @ C @ D @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__SUPI_0) ).
thf(1059,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ B @ C ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ D @ B @ E @ A ) ) )
| ~ ( hBOOL @ ( c_in @ C @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(298,axiom,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Orderings_Obot__class_Obot @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__bot__right_0) ).
thf(1132,plain,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Orderings_Obot__class_Obot @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(171,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 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastatMost__empty__iff_1) ).
thf(853,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 ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(414,axiom,
! [B: $i,A: $i] :
~ ( c_HOL_Oord__class_Oless @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__psubset__empty_0) ).
thf(1379,plain,
! [B: $i,A: $i] :
~ ( c_HOL_Oord__class_Oless @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(276,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( 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_subset__empty_1) ).
thf(1087,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( 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)],[276]) ).
thf(353,axiom,
class_HOL_Ouminus @ tc_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__HOL_Ouminus) ).
thf(1247,plain,
class_HOL_Ouminus @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(386,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Set_Oinsert @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( c_in @ C @ B @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ B @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ ( tc_fun @ A @ tc_bool ) ) ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert__iff_3) ).
thf(1319,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Set_Oinsert @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( c_in @ C @ B @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ B @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ ( tc_fun @ A @ tc_bool ) ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
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(969,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(136,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastLessThan__empty__iff_1) ).
thf(770,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(184,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(881,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)],[184]) ).
thf(406,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__neq__le__trans_0) ).
thf(1362,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(282,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__trans_0) ).
thf(1100,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(430,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ D @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__mp_0) ).
thf(1415,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ D @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(286,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ D @ E @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastatMost__subset__iff_2) ).
thf(1109,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ D @ E @ A ) ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(393,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D ) @ E ) )
| ( hBOOL @ ( c_in @ B @ C @ D ) )
| ~ ( c_Finite__Set_Ofold__graph @ A @ B @ C @ E @ D @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fold1Set_Ointros_0) ).
thf(1334,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D ) @ E ) )
| ( hBOOL @ ( c_in @ B @ C @ D ) )
| ~ ( c_Finite__Set_Ofold__graph @ A @ B @ C @ E @ D @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(248,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Set_Oinsert @ A @ B @ C ) @ C )
| ~ ( c_Finite__Set_Ofinite @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__insert_1) ).
thf(1020,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Set_Oinsert @ A @ B @ C ) @ C )
| ~ ( c_Finite__Set_Ofinite @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(369,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(1283,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)],[369]) ).
thf(157,axiom,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insertCI_1) ).
thf(821,plain,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(195,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ouminus__class_Ouminus @ A @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Compl__Diff__eq_0) ).
thf(905,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ouminus__class_Ouminus @ A @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(9,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__asym_0) ).
thf(475,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(204,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ C ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ATP__Linkup_Ofequal__imp__equal_0) ).
thf(924,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ C ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(13,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ B @ A )
!= ( c_HOL_Ouminus__class_Ouminus @ C @ A ) )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_compl__eq__compl__iff_0) ).
thf(485,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ B @ A )
!= ( c_HOL_Ouminus__class_Ouminus @ C @ A ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(300,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ A ) )
| ~ ( hBOOL @ ( hAPP @ D @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__predicate1D_0) ).
thf(1136,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ A ) )
| ~ ( hBOOL @ ( hAPP @ D @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(163,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
= B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__absorb1_0) ).
thf(834,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
= B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(306,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__ord_I4_J_0) ).
thf(1151,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(209,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__le__iff_1) ).
thf(937,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(337,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_Finite__Set_Osetsum @ B @ ( c_HOL_Ominus__class_Ominus @ C @ D @ ( tc_fun @ E @ tc_bool ) ) @ E @ A )
= ( c_HOL_Ominus__class_Ominus @ ( c_Finite__Set_Osetsum @ B @ C @ E @ A ) @ ( c_Finite__Set_Osetsum @ B @ D @ E @ A ) @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ E @ tc_bool ) ) @ D ) @ C ) )
| ~ ( c_Finite__Set_Ofinite @ C @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setsum__diff_0) ).
thf(1215,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_Finite__Set_Osetsum @ B @ ( c_HOL_Ominus__class_Ominus @ C @ D @ ( tc_fun @ E @ tc_bool ) ) @ E @ A )
= ( c_HOL_Ominus__class_Ominus @ ( c_Finite__Set_Osetsum @ B @ C @ E @ A ) @ ( c_Finite__Set_Osetsum @ B @ D @ E @ A ) @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ E @ tc_bool ) ) @ D ) @ C ) )
| ~ ( c_Finite__Set_Ofinite @ C @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(270,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(1072,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)],[270]) ).
thf(237,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ B @ A @ D ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) )
| ( hBOOL @ ( c_in @ B @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_psubset__insert__iff_4) ).
thf(998,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ B @ A @ D ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) )
| ( hBOOL @ ( c_in @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(284,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ D @ B @ C ) )
| ~ ( c_HOL_Oord__class_Oless @ A @ ( c_Set_Oinsert @ D @ B @ C ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_psubset__insert__iff_0) ).
thf(1104,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ D @ B @ C ) )
| ~ ( c_HOL_Oord__class_Oless @ A @ ( c_Set_Oinsert @ D @ B @ C ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(64,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B )
!= ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) )
| ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_singleton__inject_0) ).
thf(602,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B )
!= ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(134,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) )
| ( hBOOL @ ( c_in @ D @ B @ A ) )
| ( hBOOL @ ( c_in @ D @ C @ A ) )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_Set_Oinsert @ D @ C @ A ) @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_psubset__insert__iff_2) ).
thf(766,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) )
| ( hBOOL @ ( c_in @ D @ B @ A ) )
| ( hBOOL @ ( c_in @ D @ C @ A ) )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_Set_Oinsert @ D @ C @ A ) @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(271,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(1074,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)],[271]) ).
thf(211,axiom,
! [B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__empty__right_0) ).
thf(942,plain,
! [B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(97,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ D @ tc_bool ) ) @ A ) @ C ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ A @ C @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_psubset__insert__iff_9) ).
thf(678,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ D @ tc_bool ) ) @ A ) @ C ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ A @ C @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
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_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ E @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__eqI_1) ).
thf(546,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_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ E @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(379,axiom,
class_HOL_Oord @ tc_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__HOL_Oord) ).
thf(1306,plain,
class_HOL_Oord @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(307,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__leE_0) ).
thf(1153,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(153,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(810,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)],[153]) ).
thf(395,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( c_Set_Oinsert @ B @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ D ) )
= ( hAPP @ ( hAPP @ E @ B ) @ C ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ A @ F @ G @ H @ E @ I @ J @ K @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OInf__binary_0) ).
thf(1338,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( c_Set_Oinsert @ B @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ D ) )
= ( hAPP @ ( hAPP @ E @ B ) @ C ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ A @ F @ G @ H @ E @ I @ J @ K @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(111,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(714,plain,
! [B: $i,A: $i] :
( ( class_Orderings_Opreorder @ ( tc_fun @ A @ B ) )
| ~ ( class_Orderings_Opreorder @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(259,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ A @ tc_bool ) ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ ( tc_fun @ A @ tc_bool ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__subset__conv_1) ).
thf(1047,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ A @ tc_bool ) ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ ( tc_fun @ A @ tc_bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(441,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( B = C )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_0) ).
thf(1438,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( B = C )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).
thf(89,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ B @ C ) ) @ D ) )
| ~ ( hBOOL @ ( c_in @ C @ E @ F ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ B @ F @ ( tc_fun @ A @ tc_bool ) ) ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UN__subset__iff_0) ).
thf(661,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ B @ C ) ) @ D ) )
| ~ ( hBOOL @ ( c_in @ C @ E @ F ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ E @ B @ F @ ( tc_fun @ A @ tc_bool ) ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(366,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ B @ C )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__not__empty_0) ).
thf(1274,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ B @ C )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(140,axiom,
! [B: $i,A: $i] :
( ( c_Collect @ ( hAPP @ ( c_COMBC @ ( c_fequal @ A ) @ A @ A @ tc_bool ) @ B ) @ A )
= ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_singleton__conv_0) ).
thf(778,plain,
! [B: $i,A: $i] :
( ( c_Collect @ ( hAPP @ ( c_COMBC @ ( c_fequal @ A ) @ A @ A @ tc_bool ) @ B ) @ A )
= ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(175,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( c_Complete__Lattice_OInf__class_OInf @ A ) @ B ) ) @ C ) )
| ~ ( hBOOL @ ( c_in @ C @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Inf__lower_0) ).
thf(862,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( hAPP @ ( c_Complete__Lattice_OInf__class_OInf @ A ) @ B ) ) @ C ) )
| ~ ( hBOOL @ ( c_in @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(62,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(598,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)],[62]) ).
thf(103,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ ( tc_fun @ A @ tc_bool ) ) ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ ( tc_fun @ A @ tc_bool ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Compl__subset__Compl__iff_0) ).
thf(693,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ ( tc_fun @ A @ tc_bool ) ) ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ ( tc_fun @ A @ tc_bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(155,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_HOL_Ominus__class_Ominus @ B @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
= B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ C @ tc_bool ) ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__partition_0) ).
thf(815,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_HOL_Ominus__class_Ominus @ B @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
= B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ C @ tc_bool ) ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(347,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ ( tc_fun @ A @ tc_bool ) ) ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ ( tc_fun @ A @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Compl__subset__Compl__iff_1) ).
thf(1238,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ ( tc_fun @ A @ tc_bool ) ) ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ ( tc_fun @ A @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(218,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(957,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)],[218]) ).
thf(190,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
!= B )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ C @ tc_bool ) ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__Un__eq_1) ).
thf(894,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
!= B )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ C @ tc_bool ) ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(159,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( hAPP @ ( c_Complete__Lattice_OSup__class_OSup @ A ) @ C ) ) )
| ~ ( hBOOL @ ( c_in @ B @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sup__upper_0) ).
thf(825,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( hAPP @ ( c_Complete__Lattice_OSup__class_OSup @ A ) @ C ) ) )
| ~ ( hBOOL @ ( c_in @ B @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(397,axiom,
class_Lattices_Oupper__semilattice @ tc_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oupper__semilattice) ).
thf(1343,plain,
class_Lattices_Oupper__semilattice @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(434,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__left__commute_0) ).
thf(1423,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(6,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( B = C )
| ( c_HOL_Oord__class_Oless @ C @ B @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_0) ).
thf(467,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( B = C )
| ( c_HOL_Oord__class_Oless @ C @ B @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(48,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__assoc_0) ).
thf(566,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(407,axiom,
class_Finite__Set_Ofinite_Ofinite @ tc_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Finite__Set_Ofinite_Ofinite) ).
thf(1365,plain,
class_Finite__Set_Ofinite_Ofinite @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(375,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring @ A )
| ( ( c_Finite__Set_Osetsum @ B @ ( c_HOL_Ominus__class_Ominus @ C @ ( c_Set_Oinsert @ D @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_bool ) ) @ E ) @ ( tc_fun @ E @ tc_bool ) ) @ E @ A )
= ( c_HOL_Ominus__class_Ominus @ ( c_Finite__Set_Osetsum @ B @ C @ E @ A ) @ ( hAPP @ B @ D ) @ A ) )
| ~ ( hBOOL @ ( c_in @ D @ C @ E ) )
| ~ ( c_Finite__Set_Ofinite @ C @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setsum__diff1__ring_0) ).
thf(1296,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring @ A )
| ( ( c_Finite__Set_Osetsum @ B @ ( c_HOL_Ominus__class_Ominus @ C @ ( c_Set_Oinsert @ D @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_bool ) ) @ E ) @ ( tc_fun @ E @ tc_bool ) ) @ E @ A )
= ( c_HOL_Ominus__class_Ominus @ ( c_Finite__Set_Osetsum @ B @ C @ E @ A ) @ ( hAPP @ B @ D ) @ A ) )
| ~ ( hBOOL @ ( c_in @ D @ C @ E ) )
| ~ ( c_Finite__Set_Ofinite @ C @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(161,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_HOL_Ominus__class_Ominus @ B @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Diff__cancel_0) ).
thf(830,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_HOL_Ominus__class_Ominus @ B @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(4,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_HOL_Oord__class_Oless @ C @ B @ A )
| ( C = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neqE_0) ).
thf(461,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_HOL_Oord__class_Oless @ C @ B @ A )
| ( C = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(16,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(493,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)],[16]) ).
thf(130,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( c_COMBK @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) @ C ) @ C @ ( tc_fun @ B @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UN__empty2_0) ).
thf(757,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( c_COMBK @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) @ C ) @ C @ ( tc_fun @ B @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(420,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 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastatMost__empty__iff2_1) ).
thf(1392,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 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(373,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
!= ( c_Orderings_Obot__class_Obot @ A ) )
| ( C
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__eq__bot__eq2_0) ).
thf(1291,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
!= ( c_Orderings_Obot__class_Obot @ A ) )
| ( C
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(227,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_OatLeastLessThan @ B @ C @ A ) )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastLessThan__empty__iff2_0) ).
thf(974,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_OatLeastLessThan @ B @ C @ A ) )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(244,axiom,
! [B: $i,A: $i] :
~ ( c_HOL_Oord__class_Oless @ A @ A @ ( tc_fun @ B @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_psubset__eq_1) ).
thf(1012,plain,
! [B: $i,A: $i] :
~ ( c_HOL_Oord__class_Oless @ A @ A @ ( tc_fun @ B @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(285,axiom,
! [B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( hAPP @ ( c_Complete__Lattice_OSup__class_OSup @ A ) @ ( c_Set_Oinsert @ 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(1106,plain,
! [B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( hAPP @ ( c_Complete__Lattice_OSup__class_OSup @ A ) @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(41,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__less__iff_0) ).
thf(551,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(296,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ B @ C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ C ) @ tc_bool ) ) @ B ) @ D ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ D @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_weaken_0) ).
thf(1128,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ B @ C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ C ) @ tc_bool ) ) @ B ) @ D ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(2,negated_conjecture,
~ ( c_Hoare__Mirabelle_Ohoare__derivs @ v_Ga @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ v_P @ c_Com_Ocom_OSKIP @ v_P @ t_a ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(456,plain,
~ ( c_Hoare__Mirabelle_Ohoare__derivs @ v_Ga @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ v_P @ c_Com_Ocom_OSKIP @ v_P @ t_a ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(166,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ A @ tc_bool ) ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ E @ ( tc_fun @ A @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__mono_0) ).
thf(842,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ A @ tc_bool ) ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ E @ ( tc_fun @ A @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(123,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(742,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)],[123]) ).
thf(105,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(697,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)],[105]) ).
thf(364,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( c_Finite__Set_Ofold__graph @ A @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ B @ C @ D ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fold__graph_OemptyI_0) ).
thf(1270,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( c_Finite__Set_Ofold__graph @ A @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ B @ C @ D ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(84,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
= C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__sup_0) ).
thf(650,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
= C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(229,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ A @ tc_bool ) ) ) @ ( c_HOL_Ominus__class_Ominus @ D @ E @ ( tc_fun @ A @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ E ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__mono_0) ).
thf(980,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ A @ tc_bool ) ) ) @ ( c_HOL_Ominus__class_Ominus @ D @ E @ ( tc_fun @ A @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ E ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(435,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ B @ C )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Collect @ ( hAPP @ ( c_COMBC @ ( c_fequal @ C ) @ C @ C @ tc_bool ) @ A ) @ C ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__def_0) ).
thf(1425,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ B @ C )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Collect @ ( hAPP @ ( c_COMBC @ ( c_fequal @ C ) @ C @ C @ tc_bool ) @ A ) @ C ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(280,axiom,
! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__refl_0) ).
thf(1096,plain,
! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(241,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(1006,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)],[241]) ).
thf(301,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ D ) )
| ~ ( c_HOL_Oord__class_Oless @ ( 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__psubset__iff_0) ).
thf(1138,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ D ) )
| ~ ( c_HOL_Oord__class_Oless @ ( 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)],[301]) ).
thf(67,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ A @ B @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__code_2) ).
thf(610,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ A @ B @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(291,axiom,
! [A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ A @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__empty_2) ).
thf(1118,plain,
! [A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ A @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(18,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ C @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__left__commute_0) ).
thf(499,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ C @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(233,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ( A = D )
| ~ ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ D @ B @ C ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insertE_0) ).
thf(989,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ( A = D )
| ~ ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ D @ B @ C ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(422,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D ) )
| ~ ( hBOOL @ ( c_in @ A @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__iff_2) ).
thf(1397,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D ) )
| ~ ( hBOOL @ ( c_in @ A @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(405,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofold__graph @ A @ B @ ( c_Set_Oinsert @ C @ D @ E ) @ ( hAPP @ ( hAPP @ A @ C ) @ F ) @ E @ G )
| ~ ( c_Finite__Set_Ofold__graph @ A @ B @ D @ F @ E @ G )
| ( hBOOL @ ( c_in @ C @ D @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fold__graph_OinsertI_0) ).
thf(1360,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofold__graph @ A @ B @ ( c_Set_Oinsert @ C @ D @ E ) @ ( hAPP @ ( hAPP @ A @ C ) @ F ) @ E @ G )
| ~ ( c_Finite__Set_Ofold__graph @ A @ B @ D @ F @ E @ G )
| ( hBOOL @ ( c_in @ C @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(401,axiom,
! [B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ A @ ( tc_fun @ B @ tc_bool ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__absorb_0) ).
thf(1350,plain,
! [B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ A @ ( tc_fun @ B @ tc_bool ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(180,axiom,
! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) @ ( c_Nitpick_Osko__Nitpick__XEx1__def__1__3 @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nitpick_OEx1__def_2) ).
thf(874,plain,
! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) @ ( c_Nitpick_Osko__Nitpick__XEx1__def__1__3 @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(303,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ D ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I8_J_0) ).
thf(1143,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ D ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(287,axiom,
class_Complete__Lattice_Ocomplete__lattice @ tc_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Complete__Lattice_Ocomplete__lattice) ).
thf(1111,plain,
class_Complete__Lattice_Ocomplete__lattice @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(342,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Set_Oinsert @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ B @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ ( tc_fun @ A @ tc_bool ) ) ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert__iff_4) ).
thf(1227,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Set_Oinsert @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ B @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ ( tc_fun @ A @ tc_bool ) ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(391,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(1329,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)],[391]) ).
thf(310,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D ) )
| ~ ( hBOOL @ ( c_in @ A @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insertCI_0) ).
thf(1160,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D ) )
| ~ ( hBOOL @ ( c_in @ A @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(251,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_Finite__Set_Olinorder__class_OMax @ B @ A ) ) @ ( c_Finite__Set_Olinorder__class_OMax @ C @ A ) ) )
| ~ ( c_Finite__Set_Ofinite @ C @ A )
| ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Max__mono_0) ).
thf(1028,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_Finite__Set_Olinorder__class_OMax @ B @ A ) ) @ ( c_Finite__Set_Olinorder__class_OMax @ C @ A ) ) )
| ~ ( c_Finite__Set_Ofinite @ C @ A )
| ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(14,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__minus_0) ).
thf(488,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(207,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__less_0) ).
thf(933,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(128,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__less_1) ).
thf(753,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(320,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(1182,plain,
! [B: $i,A: $i] :
( ( class_Orderings_Oorder @ ( tc_fun @ A @ B ) )
| ~ ( class_Orderings_Oorder @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(450,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_Finite__Set_Osetsum @ B @ ( c_HOL_Ominus__class_Ominus @ C @ ( c_Set_Oinsert @ D @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_bool ) ) @ E ) @ ( tc_fun @ E @ tc_bool ) ) @ E @ A )
= ( c_HOL_Ominus__class_Ominus @ ( c_Finite__Set_Osetsum @ B @ C @ E @ A ) @ ( hAPP @ B @ D ) @ A ) )
| ~ ( hBOOL @ ( c_in @ D @ C @ E ) )
| ~ ( c_Finite__Set_Ofinite @ C @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setsum__diff1_0) ).
thf(1461,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_Finite__Set_Osetsum @ B @ ( c_HOL_Ominus__class_Ominus @ C @ ( c_Set_Oinsert @ D @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_bool ) ) @ E ) @ ( tc_fun @ E @ tc_bool ) ) @ E @ A )
= ( c_HOL_Ominus__class_Ominus @ ( c_Finite__Set_Osetsum @ B @ C @ E @ A ) @ ( hAPP @ B @ D ) @ A ) )
| ~ ( hBOOL @ ( c_in @ D @ C @ E ) )
| ~ ( c_Finite__Set_Ofinite @ C @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(93,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(669,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)],[93]) ).
thf(81,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ D @ B @ A ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ E @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastLessThan__subset__iff_1) ).
thf(642,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ D @ B @ A ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ E @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(29,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(526,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)],[29]) ).
thf(79,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_HOL_Oord__class_Oless @ D @ E @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ E ) @ B ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ E @ B @ A ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ D @ C @ A ) @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastatMost__psubset__iff_2) ).
thf(637,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_HOL_Oord__class_Oless @ D @ E @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ E ) @ B ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ E @ B @ A ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ D @ C @ A ) @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(336,axiom,
! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ A ) @ B ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ATP__Linkup_Oequal__imp__fequal_0) ).
thf(1214,plain,
! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ A ) @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(308,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ A @ tc_bool ) ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__subset__iff_2) ).
thf(1155,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ A @ tc_bool ) ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(108,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 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastatMost__empty__iff2_0) ).
thf(706,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 ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(193,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ D ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ C @ D @ A ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ E @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastLessThan__subset__iff_0) ).
thf(901,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ D ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ C @ D @ A ) ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ E @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(100,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__le__not__le_1) ).
thf(686,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(246,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( hAPP @ ( c_Complete__Lattice_OSup__class_OSup @ A ) @ ( c_Set_Oinsert @ B @ C @ A ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( hAPP @ ( c_Complete__Lattice_OSup__class_OSup @ A ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sup__insert_0) ).
thf(1016,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( hAPP @ ( c_Complete__Lattice_OSup__class_OSup @ A ) @ ( c_Set_Oinsert @ B @ C @ A ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( hAPP @ ( c_Complete__Lattice_OSup__class_OSup @ A ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(333,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ D @ tc_bool ) ) @ A ) @ C ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) )
| ( hBOOL @ ( c_in @ B @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_psubset__insert__iff_5) ).
thf(1207,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ D @ tc_bool ) ) @ A ) @ C ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) )
| ( hBOOL @ ( c_in @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(231,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(985,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)],[231]) ).
thf(106,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ C @ D @ t_a ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ D @ ( v_sko__Hoare__Mirabelle__Xconseq2__1 @ D @ E ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq2__2 @ D @ E ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ C @ E @ t_a ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conseq2_1) ).
thf(701,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ C @ D @ t_a ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ D @ ( v_sko__Hoare__Mirabelle__Xconseq2__1 @ D @ E ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq2__2 @ D @ E ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ C @ E @ t_a ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(446,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ C @ D @ t_a ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ B @ ( v_sko__Hoare__Mirabelle__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(1451,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ C @ D @ t_a ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ B @ ( v_sko__Hoare__Mirabelle__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)],[446]) ).
thf(448,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_HOL_Ouminus__class_Ouminus @ B @ ( tc_fun @ C @ tc_bool ) ) @ C ) )
| ( hBOOL @ ( c_in @ A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ComplI_0) ).
thf(1456,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_HOL_Ouminus__class_Ouminus @ B @ ( tc_fun @ C @ tc_bool ) ) @ C ) )
| ( hBOOL @ ( c_in @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).
thf(325,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ ( c_HOL_Ominus__class_Ominus @ B @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) ) @ C )
= ( c_Set_Oinsert @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__Diff__single_0) ).
thf(1192,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ ( c_HOL_Ominus__class_Ominus @ B @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) ) @ C )
= ( c_Set_Oinsert @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(198,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( c_COMBK @ B @ ( tc_fun @ C @ tc_bool ) @ A ) @ A @ ( tc_fun @ C @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UN__constant_0) ).
thf(911,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( c_COMBK @ B @ ( tc_fun @ C @ tc_bool ) @ A ) @ A @ ( tc_fun @ C @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(239,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
= ( c_Set_Oinsert @ B @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_4) ).
thf(1002,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
= ( c_Set_Oinsert @ B @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(49,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_Finite__Set_Ofold__graph @ C @ D @ A @ E @ B @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fold__graph__imp__finite_0) ).
thf(569,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_Finite__Set_Ofold__graph @ C @ D @ A @ E @ B @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(65,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( c_Set_Oinsert @ B @ C @ D ) )
= ( hAPP @ ( hAPP @ E @ B ) @ ( hAPP @ A @ C ) ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ F @ A @ G @ H @ I @ E @ J @ K @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OSup__insert_0) ).
thf(605,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( c_Set_Oinsert @ B @ C @ D ) )
= ( hAPP @ ( hAPP @ E @ B ) @ ( hAPP @ A @ C ) ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ F @ A @ G @ H @ I @ E @ J @ K @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(72,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__imp__neg__le_0) ).
thf(622,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(164,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
!= ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
| ( B = D )
| ( A = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_1) ).
thf(837,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
!= ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
| ( B = D )
| ( A = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(388,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(1324,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)],[388]) ).
thf(289,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ C )
| ~ ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ D @ B @ C ) @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__Diff__insert_0) ).
thf(1114,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ C )
| ~ ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ D @ B @ C ) @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(83,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(647,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)],[83]) ).
thf(361,axiom,
! [B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( hAPP @ ( c_Complete__Lattice_OInf__class_OInf @ A ) @ ( c_Set_Oinsert @ 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(1263,plain,
! [B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( hAPP @ ( c_Complete__Lattice_OInf__class_OInf @ A ) @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(362,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ D @ E @ A ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A ) @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastatMost__psubset__iff_3) ).
thf(1266,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ D @ E @ A ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A ) @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(344,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C )
= ( c_Set_Oinsert @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__absorb2_0) ).
thf(1231,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C )
= ( c_Set_Oinsert @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(439,axiom,
class_Orderings_Oorder @ tc_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Oorder) ).
thf(1434,plain,
class_Orderings_Oorder @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(385,axiom,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ ( tc_fun @ A @ tc_bool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__upper2_0) ).
thf(1318,plain,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ ( tc_fun @ A @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(349,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__le__iff_0) ).
thf(1241,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(77,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__left__absorb_0) ).
thf(633,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(151,axiom,
! [B: $i,A: $i] :
( ~ ( class_HOL_Ouminus @ A )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ B @ ( tc_fun @ t_a @ A ) ) @ v_x )
= ( c_HOL_Ouminus__class_Ouminus @ ( hAPP @ B @ v_x ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__Compl__def_0) ).
thf(805,plain,
! [B: $i,A: $i] :
( ~ ( class_HOL_Ouminus @ A )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ B @ ( tc_fun @ t_a @ A ) ) @ v_x )
= ( c_HOL_Ouminus__class_Ouminus @ ( hAPP @ B @ v_x ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(21,axiom,
class_Orderings_Opreorder @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).
thf(508,plain,
class_Orderings_Opreorder @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(203,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ C @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ D ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fold1Set__sing_0) ).
thf(921,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ C @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ D ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(37,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_HOL_Oord__class_Oless @ D @ E @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__eqI_0) ).
thf(541,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_HOL_Oord__class_Oless @ D @ E @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(87,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ D @ C ) )
| ~ ( c_HOL_Oord__class_Oless @ D @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_psubsetD_0) ).
thf(657,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ D @ C ) )
| ~ ( c_HOL_Oord__class_Oless @ D @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(262,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ B @ C ) ) @ ( 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__upper_0) ).
thf(1054,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ B @ C ) ) @ ( 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)],[262]) ).
thf(315,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
!= ( c_Set_Oinsert @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__not__insert_0) ).
thf(1170,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
!= ( c_Set_Oinsert @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(452,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
| ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__empty_0) ).
thf(1466,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
| ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(30,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(530,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)],[30]) ).
thf(216,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ D @ E @ A ) @ ( tc_fun @ A @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ D ) @ E ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastatMost__psubset__iff_4) ).
thf(953,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ D @ E @ A ) @ ( tc_fun @ A @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ D ) @ E ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(187,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ B @ tc_bool ) ) @ A ) @ C ) )
| ~ ( c_Finite__Set_Ofinite @ C @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__finite__subset_0) ).
thf(888,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ B @ tc_bool ) ) @ A ) @ C ) )
| ~ ( c_Finite__Set_Ofinite @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(330,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__insert2_0) ).
thf(1202,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(146,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ B @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_1) ).
thf(792,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ B @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(137,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ C @ D @ t_a ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ E @ ( v_sko__Hoare__Mirabelle__Xconseq2__1 @ D @ E ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq2__2 @ D @ E ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ C @ E @ t_a ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conseq2_0) ).
thf(773,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ C @ D @ t_a ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ E @ ( v_sko__Hoare__Mirabelle__Xconseq2__1 @ D @ E ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq2__2 @ D @ E ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ C @ E @ t_a ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(147,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(794,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)],[147]) ).
thf(57,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(586,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)],[57]) ).
thf(299,axiom,
class_HOL_Ominus @ tc_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__HOL_Ominus) ).
thf(1135,plain,
class_HOL_Ominus @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(222,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(965,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)],[222]) ).
thf(355,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__ge1_0) ).
thf(1251,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(24,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( B = C )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv3_0) ).
thf(513,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( B = C )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(172,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ A @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup1CI_1) ).
thf(856,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(377,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ ( c_SetInterval_Oord__class_OgreaterThanAtMost @ B @ C @ A ) @ ( tc_fun @ A @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ivl__disj__un_I5_J_0) ).
thf(1301,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ ( c_SetInterval_Oord__class_OgreaterThanAtMost @ B @ C @ A ) @ ( tc_fun @ A @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(412,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Set_Oinsert @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( c_in @ C @ B @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ B @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ ( tc_fun @ A @ tc_bool ) ) ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__single__insert_0) ).
thf(1374,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Set_Oinsert @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( c_in @ C @ B @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ B @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ ( tc_fun @ A @ tc_bool ) ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(119,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D )
= ( c_Set_Oinsert @ B @ ( c_Set_Oinsert @ A @ C @ D ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__commute_0) ).
thf(733,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D )
= ( c_Set_Oinsert @ B @ ( c_Set_Oinsert @ A @ C @ D ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(56,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__le_1) ).
thf(584,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(46,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__asym_H_0) ).
thf(562,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(242,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ D ) @ B ) )
| ~ ( c_HOL_Oord__class_Oless @ ( 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__psubset__iff_1) ).
thf(1007,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ D ) @ B ) )
| ~ ( c_HOL_Oord__class_Oless @ ( 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)],[242]) ).
thf(418,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Set_Oinsert @ D @ C @ A ) ) )
| ( hBOOL @ ( c_in @ D @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert_0) ).
thf(1388,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Set_Oinsert @ D @ C @ A ) ) )
| ( hBOOL @ ( c_in @ D @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(181,axiom,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ A @ tc_bool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__upper1_0) ).
thf(875,plain,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ A @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(54,axiom,
! [B: $i,A: $i] :
( ( c_Collect @ A @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Collect__def_0) ).
thf(579,plain,
! [B: $i,A: $i] :
( ( c_Collect @ A @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(294,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_psubset__eq_0) ).
thf(1124,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(357,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ C @ D @ t_a ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ 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 @ ( c_Set_Oinsert @ ( 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 ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hoare__derivs_Ointros_I6_J_2) ).
thf(1256,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ C @ D @ t_a ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ 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 @ ( c_Set_Oinsert @ ( 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 ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(51,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ C @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I7_J_0) ).
thf(572,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ C @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(382,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ B @ A )
= ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastAtMost__singleton_0) ).
thf(1312,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ B @ A )
= ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(144,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( B = C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__le_2) ).
thf(787,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( B = C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(392,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__complement_0) ).
thf(1332,plain,
! [B: $i,A: $i] :
( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(278,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_singletonE_0) ).
thf(1090,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(202,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__sup__iff_2) ).
thf(919,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(358,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBC @ A @ B @ C @ D ) @ E ) @ F )
= ( hAPP @ ( hAPP @ A @ F ) @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBC__def_0) ).
thf(1258,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_COMBC @ A @ B @ C @ D ) @ E ) @ F )
= ( hAPP @ ( hAPP @ A @ F ) @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(451,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(1464,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)],[451]) ).
thf(36,axiom,
class_HOL_Ominus @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__HOL_Ominus) ).
thf(540,plain,
class_HOL_Ominus @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(365,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( c_Set_Oinsert @ B @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ D ) )
= ( hAPP @ ( hAPP @ E @ B ) @ C ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ F @ A @ G @ H @ I @ E @ J @ K @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OSup__binary_0) ).
thf(1271,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( c_Set_Oinsert @ B @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ D ) )
= ( hAPP @ ( hAPP @ E @ B ) @ C ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ F @ A @ G @ H @ I @ E @ J @ K @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(411,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ B @ C )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
| ( hBOOL @ ( c_in @ A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Ononempty__iff_2) ).
thf(1371,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ B @ C )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
| ( hBOOL @ ( c_in @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(133,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ D ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I6_J_0) ).
thf(764,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ D ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(326,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__le__not__le_2) ).
thf(1194,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(334,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ A @ tc_bool ) ) ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__subset__iff_0) ).
thf(1209,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ A @ tc_bool ) ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(143,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 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ E ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__eqI_0) ).
thf(784,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 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ E ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(236,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ D ) )
| ~ ( c_HOL_Oord__class_Oless @ D @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I7_J_0) ).
thf(996,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ D ) )
| ~ ( c_HOL_Oord__class_Oless @ D @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(121,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__insert_0) ).
thf(737,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(413,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A ) @ ( c_SetInterval_Oord__class_OgreaterThanAtMost @ C @ D @ A ) @ ( tc_fun @ A @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ D @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ivl__disj__un_I22_J_0) ).
thf(1376,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A ) @ ( c_SetInterval_Oord__class_OgreaterThanAtMost @ C @ D @ A ) @ ( tc_fun @ A @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ D @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(380,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ C @ ( tc_fun @ E @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ D @ A ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ B @ D @ C @ ( tc_fun @ E @ tc_bool ) ) @ ( tc_fun @ E @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UN__insert_0) ).
thf(1307,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ C @ ( tc_fun @ E @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ D @ A ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ B @ D @ C @ ( tc_fun @ E @ tc_bool ) ) @ ( tc_fun @ E @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(317,axiom,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__iff_1) ).
thf(1175,plain,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(22,axiom,
class_Orderings_Obot @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Obot) ).
thf(509,plain,
class_Orderings_Obot @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(257,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).
thf(1043,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(70,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(616,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)],[70]) ).
thf(293,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(1122,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)],[293]) ).
thf(188,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ B @ A @ C ) )
| ( hBOOL @ ( c_in @ B @ D @ C ) )
| ~ ( c_HOL_Oord__class_Oless @ A @ ( c_Set_Oinsert @ B @ D @ C ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_psubset__insert__iff_1) ).
thf(890,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ B @ A @ C ) )
| ( hBOOL @ ( c_in @ B @ D @ C ) )
| ~ ( c_HOL_Oord__class_Oless @ A @ ( c_Set_Oinsert @ B @ D @ C ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(10,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__minus__iff_0) ).
thf(477,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(454,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__le__iff__le_0) ).
thf(1471,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).
thf(76,axiom,
! [B: $i,A: $i] :
( ( c_Set_Ocontents @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_contents__eq_0) ).
thf(631,plain,
! [B: $i,A: $i] :
( ( c_Set_Ocontents @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(173,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ C @ B @ ( tc_fun @ D @ tc_bool ) ) @ D )
= ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UN__extend__simps_I1_J_0) ).
thf(858,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ C @ B @ ( tc_fun @ D @ tc_bool ) ) @ D )
= ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(32,axiom,
class_Lattices_Oupper__semilattice @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Lattices_Oupper__semilattice) ).
thf(535,plain,
class_Lattices_Oupper__semilattice @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(60,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ( hBOOL @ ( c_in @ A @ D @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ B @ ( tc_fun @ C @ tc_bool ) ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UnE_0) ).
thf(594,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ( hBOOL @ ( c_in @ A @ D @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ B @ ( tc_fun @ C @ tc_bool ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(200,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(915,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)],[200]) ).
thf(398,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ C @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__less__trans_0) ).
thf(1344,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ C @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(249,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( B = C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_0) ).
thf(1022,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( B = C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(92,axiom,
! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__subsetI_0) ).
thf(668,plain,
! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(415,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(1381,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)],[415]) ).
thf(265,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ C @ D @ t_a ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ B @ ( v_sko__Hoare__Mirabelle__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(1061,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ C @ D @ t_a ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ B @ ( v_sko__Hoare__Mirabelle__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)],[265]) ).
thf(288,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ B @ C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ C ) @ tc_bool ) ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_asm_0) ).
thf(1112,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ B @ C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ C ) @ tc_bool ) ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(311,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ B @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ ( tc_fun @ A @ tc_bool ) ) ) @ D ) )
| ~ ( hBOOL @ ( c_in @ C @ B @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Set_Oinsert @ C @ D @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert__iff_0) ).
thf(1162,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ B @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ ( tc_fun @ A @ tc_bool ) ) ) @ D ) )
| ~ ( hBOOL @ ( c_in @ C @ B @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Set_Oinsert @ C @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(116,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ B @ A @ D ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ A @ C @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_psubset__insert__iff_8) ).
thf(726,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ B @ A @ D ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ A @ C @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(169,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ C )
| ~ ( c_Finite__Set_Ofinite @ B @ C )
| ~ ( c_Finite__Set_Ofinite @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__Un_2) ).
thf(848,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ C )
| ~ ( c_Finite__Set_Ofinite @ B @ C )
| ~ ( c_Finite__Set_Ofinite @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(27,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ A )
= ( c_HOL_Ominus__class_Ominus @ C @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__diff__eq_0) ).
thf(520,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ominus__class_Ominus @ B @ C @ A ) @ A )
= ( c_HOL_Ominus__class_Ominus @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(328,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__ge2_0) ).
thf(1198,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(219,axiom,
class_Lattices_Olattice @ tc_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olattice) ).
thf(959,plain,
class_Lattices_Olattice @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(141,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Oord @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ B @ A ) ) @ C ) @ D ) )
| ~ ( c_HOL_Oord__class_Oless @ D @ C @ ( tc_fun @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__fun__def_1) ).
thf(780,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Oord @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ B @ A ) ) @ C ) @ D ) )
| ~ ( c_HOL_Oord__class_Oless @ D @ C @ ( tc_fun @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(283,axiom,
! [B: $i,A: $i] :
( ( c_Collect @ ( hAPP @ ( c_fequal @ A ) @ B ) @ A )
= ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_singleton__conv2_0) ).
thf(1102,plain,
! [B: $i,A: $i] :
( ( c_Collect @ ( hAPP @ ( c_fequal @ A ) @ B ) @ A )
= ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(20,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I6_J_0) ).
thf(505,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(85,axiom,
! [A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( c_Complete__Lattice_Ocomplete__lattice__axioms @ ( c_Complete__Lattice_OInf__class_OInf @ A ) @ ( c_Complete__Lattice_OSup__class_OSup @ A ) @ ( c_lessequals @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice__class_Oaxioms_0) ).
thf(653,plain,
! [A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( c_Complete__Lattice_Ocomplete__lattice__axioms @ ( c_Complete__Lattice_OInf__class_OInf @ A ) @ ( c_Complete__Lattice_OSup__class_OSup @ A ) @ ( c_lessequals @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(135,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(768,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)],[135]) ).
thf(160,axiom,
! [B: $i,A: $i] :
( ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ B @ tc_bool ) ) @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ A @ ( tc_fun @ B @ tc_bool ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__Compl__self__eq_0) ).
thf(827,plain,
! [B: $i,A: $i] :
( ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ B @ tc_bool ) ) @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ A @ ( tc_fun @ B @ tc_bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(104,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__assoc_0) ).
thf(695,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(352,axiom,
! [B: $i,A: $i] :
( ( class_Lattices_Oboolean__algebra @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Oboolean__algebra @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Oboolean__algebra) ).
thf(1245,plain,
! [B: $i,A: $i] :
( ( class_Lattices_Oboolean__algebra @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Oboolean__algebra @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(444,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ B @ D @ ( tc_fun @ C @ tc_bool ) ) )
| ~ ( hBOOL @ ( c_in @ A @ D @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__Diff1_0) ).
thf(1445,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ B @ D @ ( tc_fun @ C @ tc_bool ) ) )
| ~ ( hBOOL @ ( c_in @ A @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(178,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastLessThan__empty_0) ).
thf(868,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(1,negated_conjecture,
hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ v_G ) @ v_Ga ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(455,plain,
hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ v_G ) @ v_Ga ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(185,axiom,
( ~ ( class_HOL_Ouminus @ t_b )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ v_A @ ( tc_fun @ t_a @ t_b ) ) @ v_x )
= ( c_HOL_Ouminus__class_Ouminus @ ( hAPP @ v_A @ v_x ) @ t_b ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__Compl__def__raw_0) ).
thf(883,plain,
( ~ ( class_HOL_Ouminus @ t_b )
| ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ v_A @ ( tc_fun @ t_a @ t_b ) ) @ v_x )
= ( c_HOL_Ouminus__class_Ouminus @ ( hAPP @ v_A @ v_x ) @ t_b ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(318,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
!= ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
| ( B = D )
| ( B = E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_3) ).
thf(1176,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
!= ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
| ( B = D )
| ( B = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(66,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ C @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ A @ ( tc_fun @ D @ tc_bool ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup1E_0) ).
thf(608,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ C @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ A @ ( tc_fun @ D @ tc_bool ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(238,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ D @ tc_bool ) ) @ A ) @ C ) )
| ( hBOOL @ ( c_in @ B @ A @ D ) )
| ~ ( c_HOL_Oord__class_Oless @ A @ C @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_psubset__insert__iff_7) ).
thf(1000,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ D @ tc_bool ) ) @ A ) @ C ) )
| ( hBOOL @ ( c_in @ B @ A @ D ) )
| ~ ( c_HOL_Oord__class_Oless @ A @ C @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(440,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Finite__Set_Olinorder__class_OMax @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Max__singleton_0) ).
thf(1435,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Finite__Set_Olinorder__class_OMax @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).
thf(114,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__ord_I3_J_0) ).
thf(722,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(378,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ C @ D @ t_a ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ 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 @ ( c_Set_Oinsert @ ( 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 ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conseq_1) ).
thf(1304,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ C @ D @ t_a ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ 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 @ ( c_Set_Oinsert @ ( 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 ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(313,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ C @ B @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UN__extend__simps_I3_J_0) ).
thf(1166,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ C @ B @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(212,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__le_1) ).
thf(944,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(98,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( c_COMBK @ B @ ( tc_fun @ C @ tc_bool ) @ D ) @ D @ ( tc_fun @ C @ tc_bool ) )
= B )
| ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UN__constant_1) ).
thf(680,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ A @ ( c_COMBK @ B @ ( tc_fun @ C @ tc_bool ) @ D ) @ D @ ( tc_fun @ C @ tc_bool ) )
= B )
| ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(90,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(663,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)],[90]) ).
thf(432,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ C @ D @ t_a ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ 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 @ ( c_Set_Oinsert @ ( 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 ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hoare__derivs_Ointros_I6_J_1) ).
thf(1420,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ C @ D @ t_a ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ 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 @ ( c_Set_Oinsert @ ( 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 ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(205,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( c_Set_Oinsert @ B @ C @ D ) )
= ( hAPP @ ( hAPP @ E @ B ) @ ( hAPP @ A @ C ) ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ A @ F @ G @ H @ E @ I @ J @ K @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OInf__insert_0) ).
thf(927,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( c_Set_Oinsert @ B @ C @ D ) )
= ( hAPP @ ( hAPP @ E @ B ) @ ( hAPP @ A @ C ) ) )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ A @ F @ G @ H @ E @ I @ J @ K @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(367,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(1277,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)],[367]) ).
thf(25,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__less__iff__less_1) ).
thf(516,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(210,axiom,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ A ) @ B @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__bot__left_0) ).
thf(939,plain,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ A ) @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(304,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ( C = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I12_J_0) ).
thf(1145,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ( C = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(42,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__less__iff_1) ).
thf(553,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(3,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( B
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equation__minus__iff_0) ).
thf(458,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( B
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(260,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ C @ tc_bool ) ) @ B ) @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ C @ tc_bool ) ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equalityI_0) ).
thf(1049,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ C @ tc_bool ) ) @ B ) @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ C @ tc_bool ) ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(429,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(1413,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)],[429]) ).
thf(8,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I10_J_0) ).
thf(473,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(272,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(1076,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)],[272]) ).
thf(274,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ A @ B ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ A @ D @ ( tc_fun @ E @ tc_bool ) ) @ ( tc_fun @ E @ tc_bool ) )
= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ A @ D @ ( tc_fun @ E @ tc_bool ) ) )
| ~ ( hBOOL @ ( c_in @ B @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UN__absorb_0) ).
thf(1081,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ A @ B ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ A @ D @ ( tc_fun @ E @ tc_bool ) ) @ ( tc_fun @ E @ tc_bool ) )
= ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ C @ A @ D @ ( tc_fun @ E @ tc_bool ) ) )
| ~ ( hBOOL @ ( c_in @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(126,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Obot @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_Orderings_Obot__class_Obot @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bot__least_0) ).
thf(749,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Obot @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_Orderings_Obot__class_Obot @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(102,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ B @ C )
= B )
| ~ ( hBOOL @ ( c_in @ A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__absorb_0) ).
thf(690,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ B @ C )
= B )
| ~ ( hBOOL @ ( c_in @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(250,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ( c_HOL_Oord__class_Oless @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ C @ tc_bool ) ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__iff__psubset__eq_0) ).
thf(1025,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ( c_HOL_Oord__class_Oless @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ C @ tc_bool ) ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(269,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Set_Oinsert @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__insert__left_0) ).
thf(1070,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Set_Oinsert @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(341,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ B ) )
| ~ ( c_HOL_Oord__class_Oless @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_psubset__subset__trans_0) ).
thf(1225,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ B ) )
| ~ ( c_HOL_Oord__class_Oless @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(225,axiom,
class_Orderings_Opreorder @ tc_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Opreorder) ).
thf(971,plain,
class_Orderings_Opreorder @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(122,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
= A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ C @ tc_bool ) ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__absorb2_0) ).
thf(739,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
= A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ C @ tc_bool ) ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(110,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ D ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ D @ B @ A ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ E @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastatMost__subset__iff_1) ).
thf(712,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ D ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ D @ B @ A ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ E @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(44,axiom,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ B @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__idem_0) ).
thf(557,plain,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(95,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 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ D @ tc_bool ) ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ D @ tc_bool ) ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__diff_0) ).
thf(673,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 )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ D @ tc_bool ) ) @ A ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ D @ tc_bool ) ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(438,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Oord @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ ( tc_fun @ D @ A ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ D @ A ) ) @ C ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ D @ A ) ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__fun__def_2) ).
thf(1432,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Oord @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ ( tc_fun @ D @ A ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ D @ A ) ) @ C ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ D @ A ) ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).
thf(322,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( B = C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__antisym_0) ).
thf(1186,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( B = C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(255,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(1038,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)],[255]) ).
thf(19,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I8_J_0) ).
thf(502,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(165,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(840,plain,
! [B: $i,A: $i] :
( ( class_HOL_Oord @ ( tc_fun @ A @ B ) )
| ~ ( class_HOL_Oord @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(384,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( c_Nitpick_Ofold__graph_H @ A @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ B @ C @ D ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fold__graph_H_Ointros_I1_J_0) ).
thf(1317,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( c_Nitpick_Ofold__graph_H @ A @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ B @ C @ D ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(297,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_Finite__Set_Ofinite @ ( c_Set_Oinsert @ C @ A @ B ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__insert_0) ).
thf(1130,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_Finite__Set_Ofinite @ ( c_Set_Oinsert @ C @ A @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(394,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(1336,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)],[394]) ).
thf(339,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ C @ D @ t_a ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ 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 @ ( c_Set_Oinsert @ ( 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 ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conseq_2) ).
thf(1220,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ C @ D @ t_a ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ 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 @ ( c_Set_Oinsert @ ( 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 ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(7,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( B
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equation__minus__iff_1) ).
thf(470,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( B
= ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(53,axiom,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__compl_0) ).
thf(576,plain,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Oboolean__algebra @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(215,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Set_Oinsert @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insertI2_0) ).
thf(951,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Set_Oinsert @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(152,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__imp__le_0) ).
thf(808,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(370,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Set_Oinsert @ A @ D @ C ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__subset_0) ).
thf(1285,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Set_Oinsert @ A @ D @ C ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(338,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ B ) )
| ~ ( c_HOL_Oord__class_Oless @ B @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_1) ).
thf(1218,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ B ) )
| ~ ( c_HOL_Oord__class_Oless @ B @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(38,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__supI2_0) ).
thf(544,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(196,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(907,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)],[196]) ).
thf(425,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ C @ D @ A ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ E @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastatMost__subset__iff_0) ).
thf(1404,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ C @ D @ A ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ E @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(124,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
= ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) )
| ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ C @ tc_bool ) ) @ A ) @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__singletonD_0) ).
thf(744,plain,
! [C: $i,B: $i,A: $i] :
( ( A
= ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) )
| ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ C @ tc_bool ) ) @ A ) @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(107,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ A @ B @ C ) @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) )
= B )
| ( hBOOL @ ( c_in @ A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__insert__absorb_0) ).
thf(703,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ A @ B @ C ) @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) )
= B )
| ( hBOOL @ ( c_in @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(63,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__supE_0) ).
thf(600,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(261,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ D @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_psubset__trans_0) ).
thf(1052,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ D @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(176,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
= B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ C @ tc_bool ) ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__absorb1_0) ).
thf(864,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
= B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ C @ tc_bool ) ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(436,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( c_SetInterval_Oord__class_OgreaterThanAtMost @ B @ C @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_greaterThanAtMost__empty_0) ).
thf(1427,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( c_SetInterval_Oord__class_OgreaterThanAtMost @ B @ C @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(302,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(1140,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)],[302]) ).
thf(50,axiom,
class_HOL_Oord @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__HOL_Oord) ).
thf(571,plain,
class_HOL_Oord @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(68,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ C @ D @ t_a ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ 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 @ ( c_Set_Oinsert @ ( 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 ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conseq12_2) ).
thf(612,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ C @ D @ t_a ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ 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 @ ( c_Set_Oinsert @ ( 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 ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(182,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ C @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ D @ tc_bool ) ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_predicate1D_0) ).
thf(876,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ C @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ D @ tc_bool ) ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(348,axiom,
! [C: $i,B: $i,A: $i] : ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ c_Com_Ocom_OSKIP @ B @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ C ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ C ) ) @ C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_hoare__derivs_OSkip_0) ).
thf(1240,plain,
! [C: $i,B: $i,A: $i] : ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ c_Com_Ocom_OSKIP @ B @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ C ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ C ) ) @ C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(74,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ A @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Diff_0) ).
thf(627,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ A @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(275,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ B @ C )
!= ( c_Set_Oinsert @ A @ D @ C ) )
| ( hBOOL @ ( c_in @ A @ D @ C ) )
| ( hBOOL @ ( c_in @ A @ B @ C ) )
| ( B = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__ident_0) ).
thf(1084,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ B @ C )
!= ( c_Set_Oinsert @ A @ D @ C ) )
| ( hBOOL @ ( c_in @ A @ D @ C ) )
| ( hBOOL @ ( c_in @ A @ B @ C ) )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(35,axiom,
class_Lattices_Olattice @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Lattices_Olattice) ).
thf(539,plain,
class_Lattices_Olattice @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(12,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__commute_0) ).
thf(482,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(94,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_Finite__Set_Ofinite @ C @ B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ B @ tc_bool ) ) @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__subset_0) ).
thf(671,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_Finite__Set_Ofinite @ C @ B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ B @ tc_bool ) ) @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(55,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ B @ A )
!= ( c_HOL_Ouminus__class_Ouminus @ C @ A ) )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__equal__iff__equal_0) ).
thf(581,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ B @ A )
!= ( c_HOL_Ouminus__class_Ouminus @ C @ A ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(131,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(759,plain,
! [B: $i,A: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OSemi @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(295,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Set_Oinsert @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) )
| ( hBOOL @ ( c_in @ C @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert__iff_2) ).
thf(1126,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Set_Oinsert @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) )
| ( hBOOL @ ( c_in @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(419,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__supI1_0) ).
thf(1390,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(309,axiom,
! [B: $i,A: $i] :
( ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ B @ tc_bool ) ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__empty_0) ).
thf(1157,plain,
! [B: $i,A: $i] :
( ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ B @ tc_bool ) ) @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(387,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Finite__Set_Olinorder__class_OMin @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Min__singleton_0) ).
thf(1321,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Finite__Set_Olinorder__class_OMin @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
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(688,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(194,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ C @ D @ t_a ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ E @ ( v_sko__Hoare__Mirabelle__Xconseq1__1 @ B @ E ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq1__2 @ B @ E ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( 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 ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conseq1_1) ).
thf(903,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ C @ D @ t_a ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ E @ ( v_sko__Hoare__Mirabelle__Xconseq1__1 @ B @ E ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq1__2 @ B @ E ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( 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 ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(445,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_Finite__Set_Olinorder__class_OMin @ B @ A ) ) @ ( c_Finite__Set_Olinorder__class_OMin @ C @ A ) ) )
| ~ ( c_Finite__Set_Ofinite @ B @ A )
| ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Min__antimono_0) ).
thf(1448,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_Finite__Set_Olinorder__class_OMin @ B @ A ) ) @ ( c_Finite__Set_Olinorder__class_OMin @ C @ A ) ) )
| ~ ( c_Finite__Set_Ofinite @ B @ A )
| ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(323,axiom,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Set_Oinsert @ C @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insertI_0) ).
thf(1189,plain,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Set_Oinsert @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(372,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).
thf(1289,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(167,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ D @ E @ A ) @ ( tc_fun @ A @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ D ) @ E ) )
| ~ ( c_HOL_Oord__class_Oless @ C @ E @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ D ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastatMost__psubset__iff_6) ).
thf(844,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ D @ E @ A ) @ ( tc_fun @ A @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ D ) @ E ) )
| ~ ( c_HOL_Oord__class_Oless @ C @ E @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ D ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(447,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastLessThan__empty__iff_0) ).
thf(1453,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(389,axiom,
! [B: $i,A: $i] : ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_singleton__iff_1) ).
thf(1326,plain,
! [B: $i,A: $i] : ( hBOOL @ ( c_in @ A @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(221,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D ) )
| ~ ( hBOOL @ ( c_in @ A @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UnCI_0) ).
thf(963,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D ) )
| ~ ( hBOOL @ ( c_in @ A @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(396,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(1341,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)],[396]) ).
thf(213,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( B = C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__neq__trans_0) ).
thf(946,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( B = C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(351,axiom,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fold1Set__sing_1) ).
thf(1244,plain,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold1Set @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(58,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(588,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)],[58]) ).
thf(356,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) )
= B )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ D @ A @ E @ F @ G @ H @ I @ J @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OSup__singleton_0) ).
thf(1253,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) )
= B )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ D @ A @ E @ F @ G @ H @ I @ J @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(23,axiom,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_minus__equation__iff_1) ).
thf(510,plain,
! [B: $i,A: $i] :
( ~ ( class_OrderedGroup_Ogroup__add @ A )
| ( ( c_HOL_Ouminus__class_Ouminus @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(374,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ D @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__iff_0) ).
thf(1294,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ D @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(192,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ C @ D @ t_a ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ B @ ( v_sko__Hoare__Mirabelle__Xconseq12__1 @ B @ E @ D @ F ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__2 @ B @ E @ D @ F ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( 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 ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conseq12_0) ).
thf(899,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ C @ D @ t_a ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ B @ ( v_sko__Hoare__Mirabelle__Xconseq12__1 @ B @ E @ D @ F ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq12__2 @ B @ E @ D @ F ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( 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 ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(162,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ C @ D @ t_a ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ B @ ( v_sko__Hoare__Mirabelle__Xconseq1__1 @ B @ E ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq1__2 @ B @ E ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( 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 ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conseq1_0) ).
thf(832,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ C @ D @ t_a ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ B @ ( v_sko__Hoare__Mirabelle__Xconseq1__1 @ B @ E ) ) @ ( v_sko__Hoare__Mirabelle__Xconseq1__2 @ B @ E ) ) )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( 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 ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(381,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 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ E ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__eqI_1) ).
thf(1309,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 ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ E ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(40,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__supI1_0) ).
thf(549,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(33,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_1) ).
thf(536,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(258,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(1045,plain,
! [B: $i,A: $i] :
( ( class_Lattices_Olattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Olattice @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(112,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( c_SetInterval_Oord__class_OgreaterThanAtMost @ B @ C @ A )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_greaterThanAtMost__empty__iff_0) ).
thf(716,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( c_SetInterval_Oord__class_OgreaterThanAtMost @ B @ C @ A )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(149,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_OatLeastLessThan @ B @ C @ A ) )
| ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastLessThan__empty__iff2_1) ).
thf(800,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_OatLeastLessThan @ B @ C @ A ) )
| ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(290,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__sup__iff_0) ).
thf(1116,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(400,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(1348,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)],[400]) ).
thf(368,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( B = C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__iff_2) ).
thf(1280,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( B = C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(223,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice @ A @ B @ ( c_COMBC @ C @ D @ D @ tc_bool ) @ ( c_COMBC @ E @ D @ D @ tc_bool ) @ F @ G @ H @ I @ D )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ B @ A @ C @ E @ G @ F @ I @ H @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_Odual__complete__lattice_0) ).
thf(967,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice @ A @ B @ ( c_COMBC @ C @ D @ D @ tc_bool ) @ ( c_COMBC @ E @ D @ D @ tc_bool ) @ F @ G @ H @ I @ D )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ B @ A @ C @ E @ G @ F @ I @ H @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(281,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
| ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__empty_1) ).
thf(1097,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
| ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(343,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ B @ C @ D ) )
| ~ ( c_HOL_Oord__class_Oless @ A @ C @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_psubset__insert__iff_6) ).
thf(1229,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ B @ C @ D ) )
| ~ ( c_HOL_Oord__class_Oless @ A @ C @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(421,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ A @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
= D ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UN__extend__simps_I2_J_0) ).
thf(1395,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Complete__Lattice_Ocomplete__lattice__class_OSUPR @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ A @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
= D ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(156,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( c_HOL_Ominus__class_Ominus @ B @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) ) @ C )
= B )
| ~ ( hBOOL @ ( c_in @ A @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__Diff_0) ).
thf(818,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( c_HOL_Ominus__class_Ominus @ B @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) ) @ C )
= B )
| ~ ( hBOOL @ ( c_in @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(305,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( C = B )
| ~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ C @ A @ D ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__code_0) ).
thf(1148,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( C = B )
| ~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ C @ A @ D ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(177,axiom,
class_Orderings_Obot @ tc_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Obot) ).
thf(867,plain,
class_Orderings_Obot @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(120,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(735,plain,
! [B: $i,A: $i] :
( ( class_HOL_Ominus @ ( tc_fun @ A @ B ) )
| ~ ( class_HOL_Ominus @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(354,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( B = C )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__less_0) ).
thf(1248,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( B = C )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(145,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ B @ tc_bool ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__Un_0) ).
thf(790,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ B @ tc_bool ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(47,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__minus__iff_1) ).
thf(564,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(191,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ D @ E @ A ) @ ( tc_fun @ A @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ D ) @ E ) )
| ~ ( c_HOL_Oord__class_Oless @ D @ B @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ D ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastatMost__psubset__iff_5) ).
thf(897,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_HOL_Oord__class_Oless @ ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ D @ E @ A ) @ ( tc_fun @ A @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ D ) @ E ) )
| ~ ( c_HOL_Oord__class_Oless @ D @ B @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ D ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(263,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( hAPP @ ( c_Complete__Lattice_OSup__class_OSup @ A ) @ ( c_Set_Oinsert @ B @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ A ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sup__binary_0) ).
thf(1056,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( hAPP @ ( c_Complete__Lattice_OSup__class_OSup @ A ) @ ( c_Set_Oinsert @ B @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ A ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(253,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ C @ D @ A ) @ ( tc_fun @ A @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ D @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ivl__disj__un_I17_J_0) ).
thf(1033,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ C @ D @ A ) @ ( tc_fun @ A @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ D @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(267,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ( A = B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ C @ tc_bool ) ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_psubset__eq_2) ).
thf(1065,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ( A = B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ C @ tc_bool ) ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(217,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(955,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)],[217]) ).
thf(399,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ C @ D @ t_a ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ B @ ( v_sko__Hoare__Mirabelle__Xescape__1 @ A @ B @ D @ C ) ) @ ( v_sko__Hoare__Mirabelle__Xescape__2 @ A @ B @ D @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_escape_0) ).
thf(1346,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ C @ D @ t_a ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ B @ ( v_sko__Hoare__Mirabelle__Xescape__1 @ A @ B @ D @ C ) ) @ ( v_sko__Hoare__Mirabelle__Xescape__2 @ A @ B @ D @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(148,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(796,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)],[148]) ).
thf(186,axiom,
! [B: $i,A: $i] :
( ( class_HOL_Ouminus @ ( tc_fun @ A @ B ) )
| ~ ( class_HOL_Ouminus @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__HOL_Ouminus) ).
thf(886,plain,
! [B: $i,A: $i] :
( ( class_HOL_Ouminus @ ( tc_fun @ A @ B ) )
| ~ ( class_HOL_Ouminus @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(220,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_OgreaterThanAtMost @ B @ C @ A ) )
| ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_greaterThanAtMost__empty__iff2_1) ).
thf(960,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_OgreaterThanAtMost @ B @ C @ A ) )
| ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(78,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__minus__iff_0) ).
thf(635,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(117,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Nitpick_Ofold__graph_H @ A @ B @ C @ ( hAPP @ ( hAPP @ A @ D ) @ E ) @ F @ G )
| ~ ( c_Nitpick_Ofold__graph_H @ A @ B @ ( c_HOL_Ominus__class_Ominus @ C @ ( c_Set_Oinsert @ D @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ F @ tc_bool ) ) @ F ) @ ( tc_fun @ F @ tc_bool ) ) @ E @ F @ G )
| ~ ( hBOOL @ ( c_in @ D @ C @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fold__graph_H_Ointros_I2_J_0) ).
thf(728,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Nitpick_Ofold__graph_H @ A @ B @ C @ ( hAPP @ ( hAPP @ A @ D ) @ E ) @ F @ G )
| ~ ( c_Nitpick_Ofold__graph_H @ A @ B @ ( c_HOL_Ominus__class_Ominus @ C @ ( c_Set_Oinsert @ D @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ F @ tc_bool ) ) @ F ) @ ( tc_fun @ F @ tc_bool ) ) @ E @ F @ G )
| ~ ( hBOOL @ ( c_in @ D @ C @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(360,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup1CI_0) ).
thf(1261,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(174,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(860,plain,
! [B: $i,A: $i] :
( ( class_Orderings_Obot @ ( tc_fun @ A @ B ) )
| ~ ( class_Orderings_Obot @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(416,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Set_Oinsert @ D @ B @ A ) ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__subset_1) ).
thf(1384,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Set_Oinsert @ D @ B @ A ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(61,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__linear_0) ).
thf(596,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(247,axiom,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( 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__subset_0) ).
thf(1019,plain,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( 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)],[247]) ).
thf(82,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) )
= B )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ A @ D @ E @ F @ G @ H @ I @ J @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OInf__singleton_0) ).
thf(644,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) )
= B )
| ~ ( c_Complete__Lattice_Ocomplete__lattice @ A @ D @ E @ F @ G @ H @ I @ J @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(404,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( B = C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__antisym__conv_0) ).
thf(1357,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( B = C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(234,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(992,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)],[234]) ).
thf(158,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_OgreaterThanAtMost @ B @ C @ A ) )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_greaterThanAtMost__empty__iff2_0) ).
thf(822,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_OgreaterThanAtMost @ B @ C @ A ) )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(170,axiom,
! [A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( hAPP @ ( c_Complete__Lattice_OSup__class_OSup @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sup__empty_0) ).
thf(850,plain,
! [A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( hAPP @ ( c_Complete__Lattice_OSup__class_OSup @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(376,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ D ) @ C ) )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__le__trans_0) ).
thf(1299,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ D ) @ C ) )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(179,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(871,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)],[179]) ).
thf(423,axiom,
! [B: $i,A: $i] :
( ( c_The @ ( hAPP @ ( c_COMBC @ ( c_fequal @ A ) @ A @ A @ tc_bool ) @ B ) @ A )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_the__eq__trivial_0) ).
thf(1399,plain,
! [B: $i,A: $i] :
( ( c_The @ ( hAPP @ ( c_COMBC @ ( c_fequal @ A ) @ A @ A @ tc_bool ) @ B ) @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(292,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ B @ C )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__is__Un_0) ).
thf(1120,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ B @ C )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(279,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ D @ A ) @ ( tc_fun @ A @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastLessThan @ D @ C @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ivl__diff_0) ).
thf(1093,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ D @ A ) @ ( tc_fun @ A @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastLessThan @ D @ C @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(73,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
= ( c_Nitpick_Osko__Nitpick__XEx1__def__1__3 @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nitpick_OEx1__def_3) ).
thf(624,plain,
! [C: $i,B: $i,A: $i] :
( ( A
= ( c_Nitpick_Osko__Nitpick__XEx1__def__1__3 @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(346,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_Finite__Set_Olinorder__class_OMin @ B @ A ) ) @ C ) )
| ~ ( hBOOL @ ( c_in @ C @ B @ A ) )
| ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Min__le_0) ).
thf(1236,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ ( c_Finite__Set_Olinorder__class_OMin @ B @ A ) ) @ C ) )
| ~ ( hBOOL @ ( c_in @ C @ B @ A ) )
| ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(232,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Set_Oinsert @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__insert__right_0) ).
thf(987,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Set_Oinsert @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(402,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ C @ D @ t_a ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ 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 @ ( c_Set_Oinsert @ ( 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 ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conseq12_1) ).
thf(1352,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ C @ D @ t_a ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ( hBOOL @ ( hAPP @ ( hAPP @ 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 @ ( c_Set_Oinsert @ ( 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 ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(5,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_HOL_Oord__class_Oless @ C @ B @ A )
| ( C = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neqE__ordered__idom_0) ).
thf(464,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_HOL_Oord__class_Oless @ C @ B @ A )
| ( C = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(363,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__supI2_0) ).
thf(1268,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(52,axiom,
class_Orderings_Oorder @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).
thf(575,plain,
class_Orderings_Oorder @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(230,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A ) @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ ( tc_fun @ A @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ivl__disj__un_I6_J_0) ).
thf(982,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A ) @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ ( tc_fun @ A @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(240,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ C )
| ~ ( c_Finite__Set_Ofinite @ B @ C )
| ~ ( c_Finite__Set_Ofinite @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__UnI_0) ).
thf(1004,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ C )
| ~ ( c_Finite__Set_Ofinite @ B @ C )
| ~ ( c_Finite__Set_Ofinite @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(150,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(803,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)],[150]) ).
thf(409,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ A @ ( tc_fun @ B @ tc_bool ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__Un_1) ).
thf(1367,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ A @ ( tc_fun @ B @ tc_bool ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(321,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ D @ E @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ D ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastatMost__subset__iff_3) ).
thf(1184,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ C @ A ) ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ D @ E @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ D ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(88,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ D ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__trans_0) ).
thf(659,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ D ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(80,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ C @ D @ A ) @ ( tc_fun @ A @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ D @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ivl__disj__un_I21_J_0) ).
thf(639,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ C @ D @ A ) @ ( tc_fun @ A @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastAtMost @ B @ D @ A ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(331,axiom,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ A @ B @ C ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__code_1) ).
thf(1204,plain,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ A @ B @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(59,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__irrefl_0) ).
thf(592,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(17,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I5_J_0) ).
thf(496,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(208,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Set_Oinsert @ B @ C @ A ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) )
| ~ ( hBOOL @ ( c_in @ B @ D @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__subset_2) ).
thf(935,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Set_Oinsert @ B @ C @ A ) ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) )
| ~ ( hBOOL @ ( c_in @ B @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(243,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( C = B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I11_J_0) ).
thf(1009,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( C = B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(138,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(775,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)],[138]) ).
thf(45,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(560,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)],[45]) ).
thf(129,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ C @ D @ t_a ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ ( c_COMBK @ ( hAPP @ ( c_COMBC @ ( c_fequal @ tc_Com_Ostate ) @ tc_Com_Ostate @ tc_Com_Ostate @ tc_bool ) @ ( v_sko__Hoare__Mirabelle__Xescape__2 @ A @ B @ D @ C ) ) @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) @ t_a ) @ C @ ( c_COMBK @ ( hAPP @ D @ ( v_sko__Hoare__Mirabelle__Xescape__1 @ A @ B @ D @ C ) ) @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) @ t_a ) @ t_a ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_escape_1) ).
thf(755,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ B @ C @ D @ t_a ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a )
| ~ ( c_Hoare__Mirabelle_Ohoare__derivs @ A @ ( c_Set_Oinsert @ ( c_Hoare__Mirabelle_Otriple_Otriple @ ( c_COMBK @ ( hAPP @ ( c_COMBC @ ( c_fequal @ tc_Com_Ostate ) @ tc_Com_Ostate @ tc_Com_Ostate @ tc_bool ) @ ( v_sko__Hoare__Mirabelle__Xescape__2 @ A @ B @ D @ C ) ) @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) @ t_a ) @ C @ ( c_COMBK @ ( hAPP @ D @ ( v_sko__Hoare__Mirabelle__Xescape__1 @ A @ B @ D @ C ) ) @ ( tc_fun @ tc_Com_Ostate @ tc_bool ) @ t_a ) @ t_a ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) @ tc_bool ) ) @ ( tc_Hoare__Mirabelle_Otriple @ t_a ) ) @ t_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(96,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(676,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)],[96]) ).
thf(15,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neg__less__iff__less_0) ).
thf(491,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ouminus__class_Ouminus @ C @ A ) @ ( c_HOL_Ouminus__class_Ouminus @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(277,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofold__graph @ A @ B @ C @ ( hAPP @ ( hAPP @ A @ D ) @ E ) @ F @ G )
| ~ ( hBOOL @ ( c_in @ D @ C @ F ) )
| ~ ( c_Finite__Set_Ofold__graph @ A @ B @ ( c_HOL_Ominus__class_Ominus @ C @ ( c_Set_Oinsert @ D @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ F @ tc_bool ) ) @ F ) @ ( tc_fun @ F @ tc_bool ) ) @ E @ F @ G ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff1__fold__graph_0) ).
thf(1088,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofold__graph @ A @ B @ C @ ( hAPP @ ( hAPP @ A @ D ) @ E ) @ F @ G )
| ~ ( hBOOL @ ( c_in @ D @ C @ F ) )
| ~ ( c_Finite__Set_Ofold__graph @ A @ B @ ( c_HOL_Ominus__class_Ominus @ C @ ( c_Set_Oinsert @ D @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ F @ tc_bool ) ) @ F ) @ ( tc_fun @ F @ tc_bool ) ) @ E @ F @ G ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(245,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ D @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subsetD_0) ).
thf(1014,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ D @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_lessequals @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(431,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Finite__Set_Osetsum @ A @ ( c_HOL_Ominus__class_Ominus @ B @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ D @ tc_nat )
= ( c_Finite__Set_Osetsum @ A @ B @ D @ tc_nat ) )
| ( hBOOL @ ( c_in @ C @ B @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setsum__diff1__nat_1) ).
thf(1417,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Finite__Set_Osetsum @ A @ ( c_HOL_Ominus__class_Ominus @ B @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ D @ tc_nat )
= ( c_Finite__Set_Osetsum @ A @ B @ D @ tc_nat ) )
| ( hBOOL @ ( c_in @ C @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(226,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofold1 @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fold1__singleton_0) ).
thf(972,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofold1 @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(1473,plain,
$false,
inference(e,[status(thm)],[892,1036,1411,629,1469,1168,479,846,1179,666,1369,1190,909,1031,1315,518,777,555,1200,977,1211,1406,683,730,1068,1443,994,1401,1422,1205,614,1041,1173,523,762,878,655,1078,533,1164,1233,1260,1063,1458,814,1327,747,913,538,1354,1222,930,1196,1243,709,1386,1366,782,1441,1287,1430,719,619,949,1409,724,917,751,1059,1132,853,1379,1087,1247,1319,969,770,881,1362,1100,1415,1109,1334,1020,1283,821,905,475,924,485,1136,834,1151,937,1215,1072,998,1104,602,766,1074,942,678,546,1306,1153,810,1338,714,1047,1438,661,1274,778,862,598,693,815,1238,957,894,825,1343,1423,467,566,1365,1296,830,461,493,757,1392,1291,974,1012,1106,551,1128,456,842,742,697,1270,650,980,1425,1096,1006,1138,610,1118,499,989,1397,1360,1350,874,1143,1111,1227,1329,1160,1028,488,933,753,1182,1461,669,642,526,637,1214,1155,706,901,686,1016,1207,985,701,1451,1456,1192,911,1002,569,605,622,837,1324,1114,647,1263,1266,1231,1434,1318,1241,633,805,508,921,541,657,1054,1170,1466,530,953,888,1202,792,773,794,586,1135,965,1251,513,856,1301,1374,733,584,562,1007,1388,875,579,1124,1256,572,1312,787,1332,1090,919,1258,1464,540,1271,1371,764,1194,1209,784,996,737,1376,1307,1175,509,1043,616,1122,890,477,1471,631,858,535,594,915,1344,1022,668,1381,1061,1112,1162,726,848,520,1198,959,780,1102,505,653,768,827,695,1245,1445,868,455,883,1176,608,1000,1435,722,1304,1166,944,680,663,1420,927,1277,516,939,1145,553,458,1049,1413,473,1076,1081,749,690,1025,1070,1225,971,739,712,557,673,1432,1186,1038,502,840,1317,1130,1336,1220,470,576,951,808,1285,1218,544,907,1404,744,703,600,1052,864,1427,1140,571,612,876,1240,627,1084,539,482,671,581,759,1126,1390,1157,1321,688,903,1448,1189,1289,844,1453,1326,963,1341,946,1244,588,1253,510,1294,899,832,1309,549,536,1045,716,800,1116,1348,1280,967,1097,1229,1395,818,1148,867,735,1248,790,564,897,1056,1033,1065,955,1346,796,886,960,635,728,1261,860,1384,596,1019,644,1357,992,822,850,1299,871,1399,1120,1093,624,1236,987,1352,464,1268,575,982,1004,803,1367,1184,659,639,1204,592,496,935,1009,775,560,755,676,491,1088,1014,1417,972]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SWV839-1 : TPTP v8.1.2. Released v4.1.0.
% 0.14/0.15 % Command : run_Leo-III %s %d
% 0.14/0.36 % Computer : n004.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri May 19 02:13:25 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.91/0.85 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.57/1.07 % [INFO] Parsing done (211ms).
% 1.78/1.08 % [INFO] Running in sequential loop mode.
% 2.30/1.37 % [INFO] eprover registered as external prover.
% 2.30/1.37 % [INFO] cvc4 registered as external prover.
% 2.41/1.37 % [INFO] Scanning for conjecture ...
% 2.74/1.51 % [INFO] Found a conjecture and 452 axioms. Running axiom selection ...
% 3.07/1.63 % [INFO] Axiom selection finished. Selected 452 axioms (removed 0 axioms).
% 3.92/1.78 % [INFO] Problem is propositional (TPTP CNF).
% 3.92/1.79 % [INFO] Type checking passed.
% 3.92/1.80 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 9.69/3.19 % External prover 'e' found a proof!
% 9.69/3.19 % [INFO] Killing All external provers ...
% 9.69/3.19 % Time passed: 2678ms (effective reasoning time: 2104ms)
% 9.69/3.19 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 9.69/3.20 % Axioms used in derivation (452): cls_atLeastatMost__psubset__iff_1, clsarity_nat__HOL_Oord, cls_atLeastatMost__subset__iff_2, cls_the__sym__eq__trivial_0, cls_xt1_I9_J_0, cls_linorder__antisym__conv2_1, cls_minus__le__iff_0, cls_Diff__iff_2, cls_Diff1__fold__graph_0, cls_Compl__subset__Compl__iff_1, cls_bot__fun__eq_0, cls_order__le__less__trans_0, cls_Diff__cancel_0, cls_INT__extend__simps_I4_J_0, cls_asm_0, cls_subset__insert_1, cls_Compl__Diff__eq_0, cls_insertE_0, cls_less__fun__def_1, cls_Un__Diff_0, cls_com_Osimps_I3_J_0, cls_Un__subset__iff_0, cls_ivl__disj__un_I20_J_0, cls_order__less__le__trans_0, cls_order__eq__iff_0, cls_equalityI_0, cls_sup__ge1_0, cls_ivl__disj__un_I21_J_0, cls_setsum__diff_0, cls_COMBC__def_0, cls_subset__empty_1, cls_finite__insert_0, cls_Un__empty__left_0, cls_le__funD_0, cls_atLeastatMost__psubset__iff_2, cls_xt1_I12_J_0, cls_complete__lattice__class_Oaxioms_0, cls_sup__bot__right_0, cls_insert__code_1, cls_atLeastLessThan__subset__iff_1, cls_le__SUPI_0, cls_linorder__neqE_0, cls_inf__sup__aci_I6_J_0, cls_Un__upper1_0, cls_fold1Set__sing_1, cls_Un__commute_0, cls_fun__Compl__def_0, cls_COMBK__def_0, cls_complete__lattice_OSup__singleton_0, cls_conseq_0, clsarity_fun__Orderings_Oorder, cls_finite__Un_2, cls_UnCI_1, cls_ivl__disj__un_I22_J_0, cls_triple_Oinject_1, cls_atLeastatMost__psubset__iff_3, cls_Diff__subset__conv_0, cls_compl__eq__compl__iff_0, cls_mem__def_1, clsarity_nat__Orderings_Olinorder, cls_Inf__lower_0, cls_insert__absorb_0, cls_empty__iff_0, cls_Min__le_0, cls_fold__graph__imp__finite_0, clsarity_bool__HOL_Ominus, cls_less__supI1_0, cls_minus__diff__eq_0, cls_minus__minus_0, cls_insert__iff_1, cls_insert__subset_0, cls_order__less__trans_0, clsarity_fun__Lattices_Oupper__semilattice, cls_fold__graph_H_Ointros_I1_J_0, cls_less__minus__iff_0, cls_fold__graph_H_Ointros_I2_J_0, cls_setsum__diff1__nat_1, cls_neg__less__iff__less_1, cls_conseq12_1, cls_le__sup__iff_0, cls_ComplD_0, cls_Diff__insert_0, cls_set__rev__mp_0, cls_insert__Diff__if_1, cls_CollectI_0, cls_subset__insert__iff_2, cls_hoare__derivs_OSkip_0, cls_finite__insert_1, cls_contents__eq_0, cls_Min__singleton_0, cls_Comp_0, cls_Un__left__commute_0, clsarity_bool__Finite__Set_Ofinite_Ofinite, clsarity_bool__HOL_Oord, cls_set__mp_0, cls_setsum__diff1_1, cls_neg__equal__iff__equal_0, cls_fold1__def_0, cls_not__psubset__empty_0, cls_Collect__empty__eq_0, cls_order__less__asym_0, cls_le__supI_0, cls_UN__extend__simps_I1_J_0, cls_Un__subset__iff_1, cls_psubset__insert__iff_8, cls_CollectD_0, cls_Un__empty_2, cls_le__iff__sup_1, cls_linorder__not__less_0, cls_Inf__singleton_0, cls_atLeastLessThan__empty__iff2_0, cls_psubset__eq_1, cls_SUP__const_0, cls_order__le__less_0, cls_order__less__asym_H_0, cls_linorder__antisym__conv1_0, cls_SUP1__I_0, cls_triple_Oinject_2, cls_le__supE_1, cls_UN__iff_2, cls_linorder__antisym__conv2_0, cls_le__iff__sup_0, cls_UN__extend__simps_I3_J_0, cls_order__eq__refl_0, cls_UN__absorb_0, clsarity_fun__Orderings_Obot, cls_minus__less__iff_1, cls_fun__Compl__def__raw_0, cls_psubset__insert__iff_5, cls_conseq1_1, cls_Un__absorb2_0, cls_atLeastatMost__subset__iff_3, cls_psubset__trans_0, cls_inf__sup__aci_I8_J_0, cls_Un__empty__right_0, cls_ivl__disj__un_I5_J_0, cls_insert__ident_0, clsarity_bool__Orderings_Oorder, cls_bot__least_0, cls_less__le__not__le_2, cls_xt1_I10_J_0, cls_le__minus__iff_0, cls_sup__eq__bot__eq2_0, cls_hoare__derivs_Ointros_I6_J_0, cls_UnCI_0, cls_Un__upper2_0, cls_atLeastatMost__psubset__iff_0, cls_conseq_2, cls_not__less__iff__gr__or__eq_0, cls_UN__Un_0, cls_Max__mono_0, cls_Sup__singleton_0, cls_UN__constant_0, cls_escape_0, cls_subset__iff_0, cls_insert__code_2, clsarity_fun__HOL_Oord, cls_Diff__idemp_0, cls_greaterThanAtMost__empty_0, cls_rev__predicate1D_0, cls_subset__Compl__self__eq_1, cls_insert__Diff__single_0, cls_singleton__iff_1, cls_atLeastatMost__empty__iff_1, cls_finite_0, cls_complete__lattice_OInf__empty_0, cls_greaterThanAtMost__empty__iff_0, cls_subset__empty_0, cls_UN__subset__iff_0, cls_finite__Diff_0, cls_SUP1__iff_2, cls_atLeastatMost__empty__iff2_0, clsarity_bool__Lattices_Oupper__semilattice, cls_le__minus__iff_1, cls_fold__graph_OinsertI_0, cls_Sup__binary_0, cls_Un__insert__left_0, cls_doubleton__eq__iff_2, cls_subset__insert__iff_3, cls_diff__single__insert_0, clsarity_fun__Finite__Set_Ofinite_Ofinite, clsarity_nat__Orderings_Obot, cls_xt1_I8_J_0, cls_finite__UnI_0, cls_set__eq__subset_2, cls_Un__mono_0, cls_insert__subset_1, cls_ATP__Linkup_Ofequal__imp__equal_0, cls_psubset__insert__iff_4, cls_ex__in__conv_0, cls_sup__commute_0, cls_Compl__anti__mono_0, cls_subset__iff__psubset__eq_0, cls_Un__subset__iff_2, cls_fold__graph_OemptyI_0, clsarity_fun__Lattices_Olattice, cls_linorder__linear_0, cls_Un__empty_0, cls_atLeastLessThan__empty__iff_1, cls_not__leE_0, cls_conseq12_2, cls_order__antisym_0, cls_order__trans_0, cls_psubset__insert__iff_9, cls_Compl__eq__Compl__iff_0, cls_insert__is__Un_0, cls_Compl__subset__Compl__iff_0, clsarity_bool__HOL_Ouminus, cls_subset__trans_0, cls_atLeastAtMost__singleton_0, cls_double__diff_0, cls_com_Osimps_I3_J_1, cls_atLeastatMost__psubset__iff_4, cls_insertI1_0, cls_DiffI_0, cls_linorder__antisym__conv1_1, cls_psubset__insert__iff_6, cls_le__supE_0, cls_subset__Compl__self__eq_0, cls_empty__not__insert_0, cls_sup__assoc_0, cls_insert__Diff1_0, cls_the__eq__trivial_0, cls_le__sup__iff_1, clsarity_bool__Orderings_Obot, cls_mem__def_0, cls_inf__sup__aci_I7_J_0, clsarity_bool__Orderings_Opreorder, cls_singleton__conv_0, cls_Nitpick_OEx1__def_2, cls_hoare__derivs_Oinsert_0, cls_empty__subsetI_0, cls_linorder__not__le_1, cls_atLeastatMost__subset__iff_0, cls_doubleton__eq__iff_0, cls_Un__absorb1_0, cls_sup1E_0, cls_Diff__insert2_0, cls_Sup__upper_0, cls_minus__less__iff_0, cls_sup__least_0, cls_subset__refl_0, cls_Max__singleton_0, cls_singletonE_0, clsarity_nat__Orderings_Opreorder, clsarity_nat__Lattices_Olattice, cls_DiffE_0, cls_conseq2_1, cls_less__minus__iff_1, cls_insertCI_0, cls_psubset__eq_0, cls_order__le__neq__trans_0, cls_Un__Diff__cancel_0, cls_complete__lattice_OInf__insert_0, cls_insert__Diff_0, cls_not__less__iff__gr__or__eq_1, cls_equation__minus__iff_0, cls_sup1CI_1, cls_complete__lattice_OInf__binary_0, cls_complete__lattice_OSup__binary_0, clsarity_fun__Lattices_Oboolean__algebra, cls_fold1Set_Ointros_0, cls_weaken_0, cls_linorder__neqE__ordered__idom_0, cls_insert__mono_0, cls_hoare__derivs_Ointros_I6_J_2, cls_le__supI2_0, cls_less__le__not__le_1, cls_Un__assoc_0, cls_fold1__singleton_0, cls_Collect__def_0, cls_greaterThanAtMost__empty__iff_1, cls_order__eq__iff_2, cls_bot1E_0, cls_linorder__antisym__conv3_0, cls_ivl__diff_0, cls_UN__constant_1, cls_Un__Diff__cancel2_0, cls_Max__ge_0, cls_empty__fold1SetE_0, cls_bex__empty_0, cls_inf__sup__ord_I4_J_0, cls_psubset__insert__iff_0, cls_finite__Diff2_1, cls_psubset__insert__iff_1, cls_UnE_0, cls_subset__insertI2_0, cls_order__neq__le__trans_0, cls_doubleton__eq__iff_3, cls_conseq_1, cls_atLeastatMost__empty__iff_0, cls_finite__Diff__insert_1, cls_complete__lattice_Odual__complete__lattice_0, cls_Diff__mono_0, cls_order__le__less_1, cls_linorder__neq__iff_1, cls_psubset__subset__trans_0, cls_com_Osimps_I13_J_0, cls_Un__absorb_0, cls_order__antisym__conv_0, cls_psubsetD_0, clsarity_bool__Lattices_Olattice, cls_le__imp__neg__le_0, cls_psubset__insert__iff_3, cls_order__less__le_2, clsarity_bool__Lattices_Obounded__lattice, cls_subset__insert__iff_4, cls_linorder__less__linear_0, cls_bot__empty__eq_0, cls_eq__eqI_0, cls_greaterThanAtMost__empty__iff2_1, cls_complete__lattice_OInf__lower_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_insert__not__empty_0, cls_le__sup__iff_2, clsarity_fun__Lattices_Obounded__lattice, clsarity_fun__Complete__Lattice_Ocomplete__lattice, cls_com_Osimps_I12_J_0, cls_finite__subset_0, cls_finite__Un_0, cls_xt1_I11_J_0, cls_insert__absorb2_0, cls_sup__fun__eq_0, cls_UNION__empty__conv_I1_J_0, cls_finite__Diff__insert_0, cls_atLeastatMost__psubset__iff_5, cls_double__compl_0, cls_subset__singletonD_0, 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_UN__I_0, cls_ComplI_0, cls_Sup__empty_0, cls_atLeastLessThan__empty__iff2_1, cls_Nitpick_OEx1__def_3, cls_subset__psubset__trans_0, clsarity_bool__Complete__Lattice_Ocomplete__lattice, cls_Diff__empty_0, cls_setsum__diff1_0, cls_atLeastatMost__psubset__iff_6, cls_minus__le__iff_1, cls_complete__lattice_OInf__singleton_0, cls_empty__Collect__eq_0, cls_atLeastatMost__subset__iff_1, cls_Un__left__absorb_0, cls_linorder__not__le_0, clsarity_bool__Lattices_Oboolean__algebra, cls_setsum__diff1__ring_0, cls_order__less__irrefl_0, cls_inf__sup__ord_I3_J_0, cls_ATP__Linkup_Oequal__imp__fequal_0, cls_inf__sup__aci_I5_J_0, cls_eq__eqI_1, cls_less__supI2_0, cls_neg__le__iff__le_0, cls_less__fun__def_2, cls_atLeastLessThan__empty_0, cls_triple_Oinject_0, cls_Un__empty_1, cls_subset__insert_0, cls_sup__idem_0, clsarity_nat__Lattices_Oupper__semilattice, cls_emptyE_0, cls_insert__def_0, cls_sup__eq__bot__eq1_0, cls_comm__monoid__add_Ononempty__iff_2, cls_singleton__inject_0, cls_less__eqI_0, cls_UN__upper_0, cls_atLeastLessThan__subset__iff_0, cls_Un__least_0, cls_double__complement_0, cls_conseq2_0, cls_hoare__derivs_Ointros_I6_J_1, cls_sup__ge2_0, clsarity_fun__Orderings_Opreorder, cls_atLeastatMost__empty__iff2_1, cls_equation__minus__iff_1, cls_sup1CI_0, cls_subset__Un__eq_1, cls_sup__left__commute_0, cls_empty__fold__graphE_0, cls_fold1Set__sing_0, cls_finite__UN_0, cls_finite_OemptyI_0, cls_Nitpick_OThe__psimp_0, cls_insertCI_1, cls_doubleton__eq__iff_4, cls_Max__in_0, cls_complete__lattice_OSup__upper_0, cls_atLeastLessThan__empty__iff_0, cls_insert__code_0, cls_le__eqI_1, cls_subset__insertI_0, cls_ivl__disj__un_I6_J_0, cls_DiffE_1, cls_complete__lattice_OSup__empty_0, cls_Diff__subset__conv_1, cls_conseq12_0, cls_order__less__imp__le_0, cls_minus__equation__iff_1, cls_Diff__insert__absorb_0, cls_Diff__partition_0, cls_UNION__empty__conv_I2_J_0, cls_sup__bot__left_0, cls_rev__finite__subset_0, cls_finite__Un_1, cls_psubset__insert__iff_2, cls_insert__commute_0, cls_insert__iff_2, clsarity_nat__Orderings_Oorder, cls_xt1_I7_J_0, cls_linorder__not__less_1, clsarity_fun__HOL_Ouminus, cls_UN__insert_0, cls_Min__in_0, cls_Un__insert__right_0, cls_psubset__insert__iff_7, cls_equalityE_0, cls_cut_0, cls_ivl__disj__un_I17_J_0, clsarity_fun__HOL_Ominus, cls_sup__absorb1_0, cls_less__eqI_1, cls_finite__Diff2_0, cls_order__less__le_1, cls_less__fun__def_0, cls_neg__less__iff__less_0, cls_ball__empty_0, cls_UN__empty2_0, cls_psubset__eq_2, cls_greaterThanAtMost__empty__iff2_0, cls_atLeastatMost__empty_0, cls_Min__antimono_0, cls_empty__Diff_0, clsarity_nat__HOL_Ominus, cls_subset__insert__iff_1, cls_escape_1, cls_singleton__conv2_0, cls_Diff__subset_0, cls_conseq1_0, cls_predicate1D_0
% 9.69/3.20 % No. of inferences in proof: 909
% 9.69/3.20 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2678 ms resp. 2104 ms w/o parsing
% 10.77/3.43 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 10.77/3.44 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------