%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SCT083-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:27:12 AM UTC 2026
% Result : Unsatisfiable 47.16s 11.80s
% Output : Refutation 50.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 752
% Syntax : Number of formulae : 1505 ( 351 unt; 0 typ; 0 def)
% Number of atoms : 3849 ( 988 equ; 0 cnn)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 36594 (1940 ~;2344 |; 0 &;32310 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 13 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 111 ( 109 usr; 10 con; 0-9 aty)
% Number of variables : 5886 ( 0 ^;5886 !; 0 ?;5886 :)
% Comments :
%------------------------------------------------------------------------------
thf(hBOOL_decl,type,
hBOOL: $i > $o ).
thf(hAPP_decl,type,
hAPP: $i > $i > $i ).
thf(c_in_decl,type,
c_in: $i > $i ).
thf(tc_fun_decl,type,
tc_fun: $i > $i > $i ).
thf(tc_prod_decl,type,
tc_prod: $i > $i > $i ).
thf(tc_Arrow__Order__Mirabelle_Oalt_decl,type,
tc_Arrow__Order__Mirabelle_Oalt: $i ).
thf(tc_bool_decl,type,
tc_bool: $i ).
thf(v_F_decl,type,
v_F: $i ).
thf(c_COMBK_decl,type,
c_COMBK: $i > $i > $i > $i ).
thf(v_Lab_____decl,type,
v_Lab____: $i ).
thf(tc_Arrow__Order__Mirabelle_Oindi_decl,type,
tc_Arrow__Order__Mirabelle_Oindi: $i ).
thf(c_Arrow__Order__Mirabelle_OLin_decl,type,
c_Arrow__Order__Mirabelle_OLin: $i ).
thf(c_Pair_decl,type,
c_Pair: $i > $i > $i > $i > $i ).
thf(c_Set_Oimage_decl,type,
c_Set_Oimage: $i > $i > $i > $i > $i ).
thf(c_FuncSet_Orestrict_decl,type,
c_FuncSet_Orestrict: $i > $i > $i > $i > $i ).
thf(class_Orderings_Opreorder_decl,type,
class_Orderings_Opreorder: $i > $o ).
thf(tc_nat_decl,type,
tc_nat: $i ).
thf(class_Orderings_Obot_decl,type,
class_Orderings_Obot: $i > $o ).
thf(c_Fun_Obij__betw_decl,type,
c_Fun_Obij__betw: $i > $i > $i > $i > $i > $o ).
thf(c_Fun_Oinj__on_decl,type,
c_Fun_Oinj__on: $i > $i > $i > $i > $o ).
thf(c_FuncSet_Ocompose_decl,type,
c_FuncSet_Ocompose: $i > $i > $i > $i > $i > $i > $i ).
thf(c_COMBI_decl,type,
c_COMBI: $i > $i ).
thf(c_COMBB_decl,type,
c_COMBB: $i > $i > $i > $i > $i > $i ).
thf(class_OrderedGroup_Oab__group__add_decl,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
thf(c_HOL_Ominus__class_Ominus_decl,type,
c_HOL_Ominus__class_Ominus: $i > $i > $i > $i ).
thf(class_Lattices_Oupper__semilattice_decl,type,
class_Lattices_Oupper__semilattice: $i > $o ).
thf(c_Hilbert__Choice_Oinv__into_decl,type,
c_Hilbert__Choice_Oinv__into: $i > $i > $i > $i > $i ).
thf(c_Fun_Ofun__upd_decl,type,
c_Fun_Ofun__upd: $i > $i > $i > $i > $i > $i ).
thf(c_Set_Oinsert_decl,type,
c_Set_Oinsert: $i > $i > $i > $i ).
thf(class_Orderings_Olinorder_decl,type,
class_Orderings_Olinorder: $i > $o ).
thf(c_Relation_Oconverse_decl,type,
c_Relation_Oconverse: $i > $i > $i > $i ).
thf(class_Lattices_Olattice_decl,type,
class_Lattices_Olattice: $i > $o ).
thf(c_Set_Ovimage_decl,type,
c_Set_Ovimage: $i > $i > $i > $i > $i ).
thf(class_HOL_Oord_decl,type,
class_HOL_Oord: $i > $o ).
thf(class_Orderings_Oorder_decl,type,
class_Orderings_Oorder: $i > $o ).
thf(c_Collect_decl,type,
c_Collect: $i > $i > $i ).
thf(class_Lattices_Odistrib__lattice_decl,type,
class_Lattices_Odistrib__lattice: $i > $o ).
thf(class_Complete__Lattice_Ocomplete__lattice_decl,type,
class_Complete__Lattice_Ocomplete__lattice: $i > $o ).
thf(c_Complete__Lattice_Ocomplete__lattice_decl,type,
c_Complete__Lattice_Ocomplete__lattice: $i > $i > $i > $i > $i > $i > $i > $i > $i > $o ).
thf(c_Complete__Lattice_OSup__class_OSup_decl,type,
c_Complete__Lattice_OSup__class_OSup: $i > $i ).
thf(c_Complete__Lattice_OInf__class_OInf_decl,type,
c_Complete__Lattice_OInf__class_OInf: $i > $i ).
thf(c_COMBC_decl,type,
c_COMBC: $i > $i > $i > $i > $i ).
thf(c_lessequals_decl,type,
c_lessequals: $i > $i ).
thf(c_HOL_Oord__class_Oless_decl,type,
c_HOL_Oord__class_Oless: $i > $i ).
thf(c_Lattices_Oupper__semilattice__class_Osup_decl,type,
c_Lattices_Oupper__semilattice__class_Osup: $i > $i ).
thf(c_Lattices_Olower__semilattice__class_Oinf_decl,type,
c_Lattices_Olower__semilattice__class_Oinf: $i > $i ).
thf(c_Orderings_Otop__class_Otop_decl,type,
c_Orderings_Otop__class_Otop: $i > $i ).
thf(c_Orderings_Obot__class_Obot_decl,type,
c_Orderings_Obot__class_Obot: $i > $i ).
thf(class_Lattices_Olower__semilattice_decl,type,
class_Lattices_Olower__semilattice: $i > $o ).
thf(c_Relation_OImage_decl,type,
c_Relation_OImage: $i > $i > $i > $i > $i ).
thf(c_Equiv__Relations_Oequiv_decl,type,
c_Equiv__Relations_Oequiv: $i > $i > $i > $o ).
thf(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR_decl,type,
c_Complete__Lattice_Ocomplete__lattice__class_OSUPR: $i > $i > $i > $i > $i ).
thf(class_Lattices_Obounded__lattice_decl,type,
class_Lattices_Obounded__lattice: $i > $o ).
thf(c_Arrow__Order__Mirabelle_Oabove_decl,type,
c_Arrow__Order__Mirabelle_Oabove: $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Set__XbexI__1__1_decl,type,
c_ATP__Linkup_Osko__Set__XbexI__1__1: $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1_decl,type,
c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1: $i > $i > $i > $i > $i ).
thf(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1_decl,type,
v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1: $i ).
thf(c_Equiv__Relations_Oquotient_decl,type,
c_Equiv__Relations_Oquotient: $i > $i > $i > $i ).
thf(c_FuncSet_OPi_decl,type,
c_FuncSet_OPi: $i > $i > $i > $i > $i ).
thf(c_FuncSet_Osko__FuncSet__XfuncsetI__1__1_decl,type,
c_FuncSet_Osko__FuncSet__XfuncsetI__1__1: $i > $i > $i > $i > $i > $i ).
thf(c_Product__Type_OSigma_decl,type,
c_Product__Type_OSigma: $i > $i > $i > $i > $i ).
thf(c_Arrow__Order__Mirabelle_Obelow_decl,type,
c_Arrow__Order__Mirabelle_Obelow: $i > $i > $i > $i ).
thf(c_Arrow__Order__Mirabelle_Omktop_decl,type,
c_Arrow__Order__Mirabelle_Omktop: $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Set__XbexE__1__1_decl,type,
c_ATP__Linkup_Osko__Set__XbexE__1__1: $i > $i > $i > $i ).
thf(v_sko__local__X3__1_decl,type,
v_sko__local__X3__1: $i > $i > $i > $i > $i ).
thf(c_Arrow__Order__Mirabelle_OProf_decl,type,
c_Arrow__Order__Mirabelle_OProf: $i ).
thf(c_ATP__Linkup_Osko__Set__XballE__1__1_decl,type,
c_ATP__Linkup_Osko__Set__XballE__1__1: $i > $i > $i > $i ).
thf(c_Arrow__Order__Mirabelle_OIIA_decl,type,
c_Arrow__Order__Mirabelle_OIIA: $i > $o ).
thf(c_HOL_Oundefined_decl,type,
c_HOL_Oundefined: $i > $i ).
thf(c_FuncSet_Oextensional_decl,type,
c_FuncSet_Oextensional: $i > $i > $i > $i ).
thf(c_SetInterval_Oord_OgreaterThan_decl,type,
c_SetInterval_Oord_OgreaterThan: $i > $i > $i > $i ).
thf(c_Arrow__Order__Mirabelle_Omkbot_decl,type,
c_Arrow__Order__Mirabelle_Omkbot: $i > $i > $i ).
thf(c_SetInterval_Oord_OatLeastLessThan_decl,type,
c_SetInterval_Oord_OatLeastLessThan: $i > $i > $i > $i > $i > $i ).
thf(c_FuncSet_Osko__FuncSet__Xrestrict__in__funcset__1__1_decl,type,
c_FuncSet_Osko__FuncSet__Xrestrict__in__funcset__1__1: $i > $i > $i > $i > $i > $i ).
thf(v_sko__local__X2__1_decl,type,
v_sko__local__X2__1: $i > $i > $i > $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Complete__Lattice__XInterI__1__1_decl,type,
c_ATP__Linkup_Osko__Complete__Lattice__XInterI__1__1: $i > $i > $i > $i ).
thf(c_SetInterval_Oord_OatLeastAtMost_decl,type,
c_SetInterval_Oord_OatLeastAtMost: $i > $i > $i > $i > $i ).
thf(c_fequal_decl,type,
c_fequal: $i > $i ).
thf(c_ATP__Linkup_Osko__Complete__Lattice__XUnion__disjoint__1__1_decl,type,
c_ATP__Linkup_Osko__Complete__Lattice__XUnion__disjoint__1__1: $i > $i > $i > $i ).
thf(class_OrderedGroup_Opordered__ab__group__add_decl,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
thf(class_Orderings_Otop_decl,type,
class_Orderings_Otop: $i > $o ).
thf(v_sko__local__Xpairwise__neutrality__1_decl,type,
v_sko__local__Xpairwise__neutrality__1: $i > $i > $i > $i > $i > $i > $i ).
thf(c_SetInterval_Oord_OgreaterThanLessThan_decl,type,
c_SetInterval_Oord_OgreaterThanLessThan: $i > $i > $i > $i > $i ).
thf(c_Set_OPow_decl,type,
c_Set_OPow: $i > $i > $i ).
thf(v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1_decl,type,
v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1: $i > $i > $i ).
thf(c_Finite__Set_Ofold__graph_decl,type,
c_Finite__Set_Ofold__graph: $i > $i > $i > $i > $i > $i > $o ).
thf(c_ATP__Linkup_Osko__Set__XbexCI__1__1_decl,type,
c_ATP__Linkup_Osko__Set__XbexCI__1__1: $i > $i > $i > $i ).
thf(c_FuncSet_Osko__FuncSet__XPi__I__1__1_decl,type,
c_FuncSet_Osko__FuncSet__XPi__I__1__1: $i > $i > $i > $i > $i > $i ).
thf(c_Finite__Set_Osetsum_decl,type,
c_Finite__Set_Osetsum: $i > $i > $i > $i > $i ).
thf(c_FuncSet_Osko__FuncSet__XPi__I_H__1__1_decl,type,
c_FuncSet_Osko__FuncSet__XPi__I_H__1__1: $i > $i > $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__1_decl,type,
c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__1: $i > $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1_decl,type,
c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1: $i > $i > $i > $i ).
thf(c_Arrow__Order__Mirabelle_Ounanimity_decl,type,
c_Arrow__Order__Mirabelle_Ounanimity: $i > $o ).
thf(v_sko__local__X4__1_decl,type,
v_sko__local__X4__1: $i > $i > $i > $i > $i > $i ).
thf(c_List_Osko__Equiv__Relations__XquotientE__1__1_decl,type,
c_List_Osko__Equiv__Relations__XquotientE__1__1: $i > $i > $i > $i > $i ).
thf(c_FuncSet_Osko__FuncSet__XrestrictI__1__1_decl,type,
c_FuncSet_Osko__FuncSet__XrestrictI__1__1: $i > $i > $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__2_decl,type,
c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__2: $i > $i > $i > $i > $i > $i ).
thf(c_Inductive_Ocomplete__lattice__class_Olfp_decl,type,
c_Inductive_Ocomplete__lattice__class_Olfp: $i > $i > $i ).
thf(v_sko__Arrow__Order__Mirabelle__XIIA__def__1_decl,type,
v_sko__Arrow__Order__Mirabelle__XIIA__def__1: $i > $i > $i > $i > $i ).
thf(class_Ring__and__Field_Oordered__idom_decl,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
thf(c_ATP__Linkup_Osko__Complete__Lattice__Xbex__UN__1__3_decl,type,
c_ATP__Linkup_Osko__Complete__Lattice__Xbex__UN__1__3: $i > $i > $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1_decl,type,
c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1: $i > $i > $i > $i > $i ).
thf(c_Record_Oiso__tuple__update__accessor__cong__assist_decl,type,
c_Record_Oiso__tuple__update__accessor__cong__assist: $i > $i > $i > $i > $o ).
thf(c_FuncSet_Osko__FuncSet__XextensionalityI__1__1_decl,type,
c_FuncSet_Osko__FuncSet__XextensionalityI__1__1: $i > $i > $i > $i > $i > $i ).
thf(c_SetInterval_Oord_OlessThan_decl,type,
c_SetInterval_Oord_OlessThan: $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3_decl,type,
c_ATP__Linkup_Osko__Set__Xbex__Un__1__3: $i > $i > $i > $i > $i ).
thf(v_sko__Arrow__Order__Mirabelle__Xunanimity__def__1_decl,type,
v_sko__Arrow__Order__Mirabelle__Xunanimity__def__1: $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Complete__Lattice__XUnionE__1__1_decl,type,
c_ATP__Linkup_Osko__Complete__Lattice__XUnionE__1__1: $i > $i > $i > $i ).
thf(c_SetInterval_Oord_OatMost_decl,type,
c_SetInterval_Oord_OatMost: $i > $i > $i > $i ).
thf(618,axiom,
! [A: $i] :
( ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Complete__Lattice_OInf__class_OInf @ hAPP ) )
= ( A @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Inf__UNIV_0) ).
thf(2163,plain,
! [A: $i] :
( ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Complete__Lattice_OInf__class_OInf @ hAPP ) )
= ( A @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[618]) ).
thf(633,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ hAPP ) @ hBOOL )
| ( ( B @ ( A @ c_Collect ) )
!= ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Collect__empty__eq_0) ).
thf(2199,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ hAPP ) @ hBOOL )
| ( ( B @ ( A @ c_Collect ) )
!= ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[633]) ).
thf(127,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__infI1_0) ).
thf(1036,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(587,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_SetInterval_Oord_OgreaterThan ) ) @ ( C @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ord_OgreaterThan__iff_0) ).
thf(2094,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_SetInterval_Oord_OgreaterThan ) ) @ ( C @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).
thf(389,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ ( E @ ( D @ c_FuncSet_Osko__FuncSet__XPi__I_H__1__1 ) ) ) ) @ ( E @ hAPP ) @ ( B @ ( A @ ( C @ ( E @ ( D @ c_FuncSet_Osko__FuncSet__XPi__I_H__1__1 ) ) ) ) @ ( C @ hAPP ) @ ( B @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( E @ ( D @ c_FuncSet_OPi ) ) ) @ ( C @ ( B @ ( A @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Pi__I_H_1) ).
thf(1633,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ ( E @ ( D @ c_FuncSet_Osko__FuncSet__XPi__I_H__1__1 ) ) ) ) @ ( E @ hAPP ) @ ( B @ ( A @ ( C @ ( E @ ( D @ c_FuncSet_Osko__FuncSet__XPi__I_H__1__1 ) ) ) ) @ ( C @ hAPP ) @ ( B @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( E @ ( D @ c_FuncSet_OPi ) ) ) @ ( C @ ( B @ ( A @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(543,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( E @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( A @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( C @ ( B @ c_ATP__Linkup_Osko__Set__Xbex__Un__1__3 ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bex__Un_5) ).
thf(1995,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( E @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( A @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( C @ ( B @ c_ATP__Linkup_Osko__Set__Xbex__Un__1__3 ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).
thf(357,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( E @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_Set_Ovimage ) ) ) )
= ( B @ ( E @ ( D @ ( A @ c_Set_Ovimage ) ) ) @ ( B @ ( E @ ( C @ ( A @ c_Set_Ovimage ) ) ) @ ( tc_bool @ ( E @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__Int_0) ).
thf(1559,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( E @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_Set_Ovimage ) ) ) )
= ( B @ ( E @ ( D @ ( A @ c_Set_Ovimage ) ) ) @ ( B @ ( E @ ( C @ ( A @ c_Set_Ovimage ) ) ) @ ( tc_bool @ ( E @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(478,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oimage ) ) ) )
= ( E @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__insert_0) ).
thf(1840,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oimage ) ) ) )
= ( E @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_Set_Oinsert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).
thf(482,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ c_Arrow__Order__Mirabelle_Omktop ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A = B )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__mktop_4) ).
thf(1850,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ c_Arrow__Order__Mirabelle_Omktop ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).
thf(86,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( A @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
| ( ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ hAPP ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OInf__singleton_0) ).
thf(941,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( A @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
| ( ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ hAPP ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(191,axiom,
! [B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__UNIV__right_0) ).
thf(1179,plain,
! [B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(13,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( E @ ( B @ ( A @ c_Fun_Obij__betw ) ) ) ) )
| ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bij__betw__def_0) ).
thf(777,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( E @ ( B @ ( A @ c_Fun_Obij__betw ) ) ) ) )
| ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(655,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D = E )
| ~ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A = B )
| ( B = D )
| ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( E @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__below_8) ).
thf(2250,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D = E )
| ~ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A = B )
| ( B = D )
| ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( E @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[655]) ).
thf(368,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__subset__iff_1) ).
thf(1586,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(740,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( tc_bool @ ( C @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( tc_bool @ ( C @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__iff__psubset__eq_0) ).
thf(2452,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( tc_bool @ ( C @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( tc_bool @ ( C @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[740]) ).
thf(494,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ c_Collect ) @ ( B @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CollectD_0) ).
thf(1879,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ c_Collect ) @ ( B @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).
thf(257,axiom,
tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ ( tc_bool @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ c_COMBK ) ) @ ( c_Arrow__Order__Mirabelle_OProf @ c_FuncSet_OPi ) ) ) @ ( v_F @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0_01) ).
thf(1337,plain,
tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ ( tc_bool @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ c_COMBK ) ) @ ( c_Arrow__Order__Mirabelle_OProf @ c_FuncSet_OPi ) ) ) @ ( v_F @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(428,axiom,
! [B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__empty__right_0) ).
thf(1718,plain,
! [B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(186,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_INT__extend__simps_I4_J_0) ).
thf(1168,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(679,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( B = D )
| ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ c_Arrow__Order__Mirabelle_Omktop ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__mktop_3) ).
thf(2306,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( B = D )
| ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ c_Arrow__Order__Mirabelle_Omktop ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[679]) ).
thf(3,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( D @ ( C @ ( B @ ( A @ c_FuncSet_Orestrict ) ) ) @ c_Set_Oimage ) ) ) )
= ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__restrict__eq_0) ).
thf(760,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( D @ ( C @ ( B @ ( A @ c_FuncSet_Orestrict ) ) ) @ c_Set_Oimage ) ) ) )
= ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(594,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
!= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__not__empty_0) ).
thf(2109,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
!= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).
thf(558,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( E @ tc_fun ) @ ( F @ ( F @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ ( C @ ( B @ c_COMBB ) ) ) ) @ ( A @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) )
= ( tc_bool @ ( E @ tc_fun ) @ ( D @ ( B @ ( D @ ( F @ ( A @ ( C @ c_Set_Oimage ) ) ) @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UN__extend__simps_I10_J_0) ).
thf(2031,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( E @ tc_fun ) @ ( F @ ( F @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ ( C @ ( B @ c_COMBB ) ) ) ) @ ( A @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) )
= ( tc_bool @ ( E @ tc_fun ) @ ( D @ ( B @ ( D @ ( F @ ( A @ ( C @ c_Set_Oimage ) ) ) @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).
thf(576,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( C @ ( E @ ( B @ c_Set_Oimage ) ) ) @ ( A @ ( C @ ( D @ ( B @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( E @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__Int__subset_0) ).
thf(2072,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( C @ ( E @ ( B @ c_Set_Oimage ) ) ) @ ( A @ ( C @ ( D @ ( B @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( E @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).
thf(449,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ ( A @ ( C @ c_Set_Oinsert ) ) @ hAPP ) @ hBOOL )
| ( C = B )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__code_0) ).
thf(1767,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ ( A @ ( C @ c_Set_Oinsert ) ) @ hAPP ) @ hBOOL )
| ( C = B )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).
thf(215,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__assoc_0) ).
thf(1237,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(46,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( K @ ( J @ ( E @ ( I @ ( H @ ( G @ ( A @ ( F @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
| ( ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ hAPP ) )
= ( C @ ( A @ hAPP ) @ ( B @ ( E @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OSup__insert_0) ).
thf(846,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( K @ ( J @ ( E @ ( I @ ( H @ ( G @ ( A @ ( F @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
| ( ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ hAPP ) )
= ( C @ ( A @ hAPP ) @ ( B @ ( E @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(729,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Complete__Lattice_OInf__class_OInf @ hAPP ) )
= ( C @ ( A @ c_Complete__Lattice_OInf__class_OInf @ hAPP ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Inf__insert_0) ).
thf(2427,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Complete__Lattice_OInf__class_OInf @ hAPP ) )
= ( C @ ( A @ c_Complete__Lattice_OInf__class_OInf @ hAPP ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[729]) ).
thf(149,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Set_Ovimage ) ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__UNIV_0) ).
thf(1083,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Set_Ovimage ) ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(94,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Int__distrib2_0) ).
thf(962,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(355,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( F @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( F @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ ( A @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SUP1__iff_2) ).
thf(1554,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( F @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( F @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ ( A @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(161,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup1CI_1) ).
thf(1110,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(238,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__absorb_0) ).
thf(1290,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(716,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__absorb1_0) ).
thf(2395,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[716]) ).
thf(383,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ ( B @ c_COMBK ) ) @ c_Inductive_Ocomplete__lattice__class_Olfp ) )
= B )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lfp__const_0) ).
thf(1618,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ ( B @ c_COMBK ) ) @ c_Inductive_Ocomplete__lattice__class_Olfp ) )
= B )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(286,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( tc_bool @ ( C @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__eq__subset_2) ).
thf(1401,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( tc_bool @ ( C @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(654,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distrib__sup__le_0) ).
thf(2248,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[654]) ).
thf(145,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( F @ tc_fun ) @ ( D @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) )
= ( tc_bool @ ( F @ tc_fun ) @ ( C @ ( C @ ( tc_bool @ ( F @ tc_fun ) @ ( D @ ( A @ ( E @ c_COMBB ) ) ) ) @ ( B @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UN__simps_I10_J_0) ).
thf(1073,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( F @ tc_fun ) @ ( D @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) )
= ( tc_bool @ ( F @ tc_fun ) @ ( C @ ( C @ ( tc_bool @ ( F @ tc_fun ) @ ( D @ ( A @ ( E @ c_COMBB ) ) ) ) @ ( B @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(551,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( K @ ( J @ ( I @ ( H @ ( G @ ( A @ ( F @ ( B @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
| ~ ( C @ ( D @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OInf__lower_0) ).
thf(2014,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( K @ ( J @ ( I @ ( H @ ( G @ ( A @ ( F @ ( B @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
| ~ ( C @ ( D @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ hAPP ) @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).
thf(710,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ c_SetInterval_Oord_OlessThan ) ) @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ord_OlessThan__iff_0) ).
thf(2380,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ c_SetInterval_Oord_OlessThan ) ) @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[710]) ).
thf(459,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_Orderings_Obot__class_Obot @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_Lattices_Obounded__lattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__bot__left_0) ).
thf(1793,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_Orderings_Obot__class_Obot @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_Lattices_Obounded__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(302,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( H @ ( I @ ( F @ ( G @ ( E @ ( C @ ( A @ ( B @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
| ( D @ ( I @ ( H @ ( G @ ( F @ ( tc_bool @ ( D @ ( D @ ( E @ c_COMBC ) ) ) @ ( tc_bool @ ( D @ ( D @ ( C @ c_COMBC ) ) ) @ ( B @ ( A @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_Odual__complete__lattice_0) ).
thf(1437,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( H @ ( I @ ( F @ ( G @ ( E @ ( C @ ( A @ ( B @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
| ( D @ ( I @ ( H @ ( G @ ( F @ ( tc_bool @ ( D @ ( D @ ( E @ c_COMBC ) ) ) @ ( tc_bool @ ( D @ ( D @ ( C @ c_COMBC ) ) ) @ ( B @ ( A @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(325,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( B @ ( D @ c_Equiv__Relations_Oquotient ) ) @ ( A @ ( A @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( B @ c_Relation_OImage ) ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_quotientI_0) ).
thf(1486,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( B @ ( D @ c_Equiv__Relations_Oquotient ) ) @ ( A @ ( A @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( B @ c_Relation_OImage ) ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(703,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D = E )
| ~ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A = B )
| ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( E @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A = D )
| ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__below_10) ).
thf(2363,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D = E )
| ~ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A = B )
| ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( E @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A = D )
| ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[703]) ).
thf(579,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( K @ ( J @ ( E @ ( I @ ( H @ ( G @ ( A @ ( F @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
| ( ( D @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( B @ c_Set_Oinsert ) ) @ ( A @ hAPP ) )
= ( C @ ( B @ ( E @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OSup__binary_0) ).
thf(2077,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( K @ ( J @ ( E @ ( I @ ( H @ ( G @ ( A @ ( F @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
| ( ( D @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( B @ c_Set_Oinsert ) ) @ ( A @ hAPP ) )
= ( C @ ( B @ ( E @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).
thf(442,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( C @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_psubset__insert__iff_3) ).
thf(1750,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( C @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).
thf(100,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Orderings_Opreorder )
| ( B @ ( A @ tc_fun ) @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Opreorder) ).
thf(977,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Orderings_Opreorder )
| ( B @ ( A @ tc_fun ) @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(680,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( C @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( C @ ( B @ c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1 ) ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__bexI_0) ).
thf(2309,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( C @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( C @ ( B @ c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1 ) ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[680]) ).
thf(4,axiom,
tc_nat @ class_Orderings_Opreorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).
thf(762,plain,
tc_nat @ class_Orderings_Opreorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(514,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( E @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( E @ ( C @ hAPP ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
!= ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ ( B @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UNION__empty__conv_I1_J_0) ).
thf(1924,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( E @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( E @ ( C @ hAPP ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
!= ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ ( B @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).
thf(112,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( A @ ( E @ ( D @ c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 ) ) ) @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( B @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ball__conj__distrib_1) ).
thf(1005,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( A @ ( E @ ( D @ c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 ) ) ) @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( B @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(598,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__Int2_0) ).
thf(2117,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).
thf(288,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insertI2_0) ).
thf(1406,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(592,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( E @ ( D @ ( C @ c_Fun_Obij__betw ) ) ) ) )
| ( B @ ( A @ ( A @ ( tc_bool @ ( B @ tc_fun ) @ ( E @ c_COMBK ) ) @ ( D @ c_FuncSet_OPi ) ) ) @ ( C @ ( B @ ( A @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bij__betw__imp__funcset_0) ).
thf(2104,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( E @ ( D @ ( C @ c_Fun_Obij__betw ) ) ) ) )
| ( B @ ( A @ ( A @ ( tc_bool @ ( B @ tc_fun ) @ ( E @ c_COMBK ) ) @ ( D @ c_FuncSet_OPi ) ) ) @ ( C @ ( B @ ( A @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).
thf(305,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( E @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( tc_bool @ ( A @ tc_fun ) @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__mono_0) ).
thf(1443,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( E @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( tc_bool @ ( A @ tc_fun ) @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(465,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__iff_0) ).
thf(1808,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(589,axiom,
! [B: $i,A: $i] : ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_top1I_0) ).
thf(2099,plain,
! [B: $i,A: $i] : ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).
thf(370,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( E @ ( E @ ( tc_bool @ ( A @ tc_fun ) @ ( D @ c_COMBK ) ) @ ( F @ c_FuncSet_OPi ) ) ) @ ( B @ ( A @ ( E @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( F @ ( C @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ hAPP ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_funcset__mem_0) ).
thf(1591,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( E @ ( E @ ( tc_bool @ ( A @ tc_fun ) @ ( D @ c_COMBK ) ) @ ( F @ c_FuncSet_OPi ) ) ) @ ( B @ ( A @ ( E @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( F @ ( C @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ hAPP ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(175,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I7_J_0) ).
thf(1142,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(229,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__leE_0) ).
thf(1269,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(457,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( D @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__le__trans_0) ).
thf(1788,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( D @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(378,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__left__commute_0) ).
thf(1608,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(173,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Ovimage ) ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__empty_0) ).
thf(1137,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Ovimage ) ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(246,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_1) ).
thf(1310,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(560,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ c_Collect ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__Collect_1) ).
thf(2035,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ c_Collect ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).
thf(435,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D
= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( ( B @ ( C @ ( D @ ( C @ ( B @ ( A @ c_COMBK ) ) @ c_Set_Oimage ) ) ) )
= ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__constant__conv_1) ).
thf(1735,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D
= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( ( B @ ( C @ ( D @ ( C @ ( B @ ( A @ c_COMBK ) ) @ c_Set_Oimage ) ) ) )
= ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(488,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
!= ( A @ ( C @ ( B @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__not__insert_0) ).
thf(1867,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
!= ( A @ ( C @ ( B @ c_Set_Oinsert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).
thf(232,axiom,
! [B: $i,A: $i] :
( ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__UNIV__left_0) ).
thf(1275,plain,
! [B: $i,A: $i] :
( ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(32,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
= ( D @ ( D @ ( C @ ( A @ c_Set_Oinsert ) ) @ ( B @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__commute_0) ).
thf(814,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
= ( D @ ( D @ ( C @ ( A @ c_Set_Oinsert ) ) @ ( B @ c_Set_Oinsert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(612,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D = E )
| ( A = B )
| ~ ( c_Arrow__Order__Mirabelle_OProf @ ( F @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( c_Arrow__Order__Mirabelle_OProf @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( E @ ( A @ ( D @ ( C @ ( F @ v_sko__local__Xpairwise__neutrality__1 ) ) ) ) ) @ ( F @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( E @ ( D @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( E @ ( A @ ( D @ ( C @ ( F @ v_sko__local__Xpairwise__neutrality__1 ) ) ) ) ) @ ( C @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( F @ ( v_F @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( E @ ( D @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( v_F @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pairwise__neutrality_0) ).
thf(2146,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D = E )
| ( A = B )
| ~ ( c_Arrow__Order__Mirabelle_OProf @ ( F @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( c_Arrow__Order__Mirabelle_OProf @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( E @ ( A @ ( D @ ( C @ ( F @ v_sko__local__Xpairwise__neutrality__1 ) ) ) ) ) @ ( F @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( E @ ( D @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( E @ ( A @ ( D @ ( C @ ( F @ v_sko__local__Xpairwise__neutrality__1 ) ) ) ) ) @ ( C @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( F @ ( v_F @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( E @ ( D @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( v_F @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).
thf(334,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( D @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_psubset__insert__iff_0) ).
thf(1507,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( D @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(330,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UnCI_0) ).
thf(1497,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(631,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Complete__Lattice_OSup__class_OSup @ hAPP ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( C @ ( B @ c_ATP__Linkup_Osko__Complete__Lattice__XUnionE__1__1 ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UnionE_1) ).
thf(2195,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Complete__Lattice_OSup__class_OSup @ hAPP ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( C @ ( B @ c_ATP__Linkup_Osko__Complete__Lattice__XUnionE__1__1 ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).
thf(184,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__left__absorb_0) ).
thf(1164,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(23,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( C @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_Oconverse ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_converse__converse_0) ).
thf(797,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( C @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_Oconverse ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(683,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ( D = E )
| ( A = E )
| ( B = D )
| ~ ( c_Arrow__Order__Mirabelle_OProf @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( c_Arrow__Order__Mirabelle_OProf @ ( F @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( B @ ( D @ ( A @ ( F @ ( C @ v_sko__local__X2__1 ) ) ) ) ) @ ( C @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( B @ ( D @ ( A @ ( F @ ( C @ v_sko__local__X2__1 ) ) ) ) ) @ ( F @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( E @ ( D @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( F @ ( v_F @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( E @ ( D @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( v_F @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_2_3) ).
thf(2316,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ( D = E )
| ( A = E )
| ( B = D )
| ~ ( c_Arrow__Order__Mirabelle_OProf @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( c_Arrow__Order__Mirabelle_OProf @ ( F @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( B @ ( D @ ( A @ ( F @ ( C @ v_sko__local__X2__1 ) ) ) ) ) @ ( C @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( B @ ( D @ ( A @ ( F @ ( C @ v_sko__local__X2__1 ) ) ) ) ) @ ( F @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( E @ ( D @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( F @ ( v_F @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( E @ ( D @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( v_F @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[683]) ).
thf(750,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D = E )
| ~ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A = B )
| ( A = E )
| ( B = E )
| ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__above_4) ).
thf(2476,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D = E )
| ~ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A = B )
| ( A = E )
| ( B = E )
| ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[750]) ).
thf(620,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( F @ ( C @ c_FuncSet_OPi ) ) ) @ ( E @ ( D @ ( A @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( F @ hAPP ) @ ( B @ ( E @ hAPP ) @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_PiE_0) ).
thf(2168,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( F @ ( C @ c_FuncSet_OPi ) ) ) @ ( E @ ( D @ ( A @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( F @ hAPP ) @ ( B @ ( E @ hAPP ) @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).
thf(447,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__partition_0) ).
thf(1761,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(260,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__inf_0) ).
thf(1342,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(73,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
!= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_disjoint__iff__not__equal_0) ).
thf(913,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
!= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(440,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( E @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__Un_0) ).
thf(1746,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( E @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).
thf(639,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( E @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( A @ hAPP ) @ hBOOL )
| ~ ( B @ ( D @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_ATP__Linkup_Osko__Set__XbexCI__1__1 ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bexCI_1) ).
thf(2216,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( E @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( A @ hAPP ) @ hBOOL )
| ~ ( B @ ( D @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_ATP__Linkup_Osko__Set__XbexCI__1__1 ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[639]) ).
thf(697,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( A @ ( A @ ( tc_bool @ ( F @ tc_fun ) @ ( H @ c_COMBK ) ) @ ( C @ c_FuncSet_OPi ) ) ) @ ( E @ ( F @ ( A @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( F @ ( F @ ( tc_bool @ ( B @ tc_fun ) @ ( G @ c_COMBK ) ) @ ( H @ c_FuncSet_OPi ) ) ) @ ( D @ ( B @ ( F @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( A @ ( tc_bool @ ( B @ tc_fun ) @ ( G @ c_COMBK ) ) @ ( C @ c_FuncSet_OPi ) ) ) @ ( B @ ( F @ ( A @ ( E @ ( D @ ( C @ c_FuncSet_Ocompose ) ) ) ) ) @ ( B @ ( A @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_funcset__compose_0) ).
thf(2348,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( A @ ( A @ ( tc_bool @ ( F @ tc_fun ) @ ( H @ c_COMBK ) ) @ ( C @ c_FuncSet_OPi ) ) ) @ ( E @ ( F @ ( A @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( F @ ( F @ ( tc_bool @ ( B @ tc_fun ) @ ( G @ c_COMBK ) ) @ ( H @ c_FuncSet_OPi ) ) ) @ ( D @ ( B @ ( F @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( A @ ( tc_bool @ ( B @ tc_fun ) @ ( G @ c_COMBK ) ) @ ( C @ c_FuncSet_OPi ) ) ) @ ( B @ ( F @ ( A @ ( E @ ( D @ ( C @ c_FuncSet_Ocompose ) ) ) ) ) @ ( B @ ( A @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[697]) ).
thf(564,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( E @ c_Equiv__Relations_Oequiv ) ) )
| ~ ( B @ ( A @ ( A @ ( D @ ( C @ c_Pair ) ) ) @ ( A @ ( A @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( A @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ ( B @ c_Relation_OImage ) ) ) @ ( A @ ( A @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( B @ c_Relation_OImage ) ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equiv__class__subset_0) ).
thf(2046,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( E @ c_Equiv__Relations_Oequiv ) ) )
| ~ ( B @ ( A @ ( A @ ( D @ ( C @ c_Pair ) ) ) @ ( A @ ( A @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( A @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ ( B @ c_Relation_OImage ) ) ) @ ( A @ ( A @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( B @ c_Relation_OImage ) ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).
thf(218,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_HOL_Oord )
| ( B @ ( A @ tc_fun ) @ class_HOL_Oord ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__HOL_Oord) ).
thf(1243,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_HOL_Oord )
| ( B @ ( A @ tc_fun ) @ class_HOL_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(282,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( tc_bool @ ( A @ tc_fun ) @ ( E @ ( B @ ( F @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( F @ ( C @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UN__subset__iff_0) ).
thf(1391,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( tc_bool @ ( A @ tc_fun ) @ ( E @ ( B @ ( F @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( F @ ( C @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(44,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( I @ ( C @ ( H @ ( G @ ( F @ ( E @ ( D @ ( A @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
| ( ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ hAPP ) )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OInf__UNIV_0) ).
thf(841,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( I @ ( C @ ( H @ ( G @ ( F @ ( E @ ( D @ ( A @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
| ( ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ hAPP ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(549,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__iff_2) ).
thf(2010,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).
thf(394,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Lattices_Olattice )
| ( B @ ( A @ tc_fun ) @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olattice) ).
thf(1645,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Lattices_Olattice )
| ( B @ ( A @ tc_fun ) @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(267,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__insert__left_0) ).
thf(1359,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ c_Set_Oinsert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(375,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ ( B @ c_Set_Oimage ) ) ) @ ( E @ ( tc_bool @ ( D @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( D @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Hilbert__Choice_Oinv__into ) ) ) @ c_Fun_Oinj__on ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__inv__into_0) ).
thf(1601,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ ( B @ c_Set_Oimage ) ) ) @ ( E @ ( tc_bool @ ( D @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( D @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Hilbert__Choice_Oinv__into ) ) ) @ c_Fun_Oinj__on ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(581,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( E @ ( B @ ( A @ c_SetInterval_Oord_OatLeastAtMost ) ) ) @ ( C @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ord_OatLeastAtMost__iff_0) ).
thf(2082,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( E @ ( B @ ( A @ c_SetInterval_Oord_OatLeastAtMost ) ) ) @ ( C @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).
thf(574,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( F @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( E @ ( B @ ( F @ c_Pair ) ) ) @ ( A @ ( E @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( E @ ( D @ ( C @ c_Relation_OImage ) ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__ImageI_0) ).
thf(2067,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( F @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( E @ ( B @ ( F @ c_Pair ) ) ) @ ( A @ ( E @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( E @ ( D @ ( C @ c_Relation_OImage ) ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).
thf(463,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( C @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__insert__right_0) ).
thf(1803,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( C @ c_Set_Oinsert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(340,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Complete__Lattice_OSup__class_OSup @ hAPP ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UnionI_0) ).
thf(1518,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Complete__Lattice_OSup__class_OSup @ hAPP ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(497,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__greatest_0) ).
thf(1887,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).
thf(15,axiom,
tc_nat @ class_Lattices_Oupper__semilattice,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Lattices_Oupper__semilattice) ).
thf(782,plain,
tc_nat @ class_Lattices_Oupper__semilattice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(304,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( E @ ( D @ ( C @ c_SetInterval_Oord_OatLeastAtMost ) ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ord_OatLeastAtMost__iff_2) ).
thf(1441,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( E @ ( D @ ( C @ c_SetInterval_Oord_OatLeastAtMost ) ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(211,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__left__commute_0) ).
thf(1228,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(323,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( B @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_Set_Oimage ) ) ) )
= ( E @ ( B @ ( D @ ( A @ c_Set_Oimage ) ) ) @ ( E @ ( B @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( E @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__Un_0) ).
thf(1482,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( B @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_Set_Oimage ) ) ) )
= ( E @ ( B @ ( D @ ( A @ c_Set_Oimage ) ) ) @ ( E @ ( B @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( E @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(223,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__imp__le_0) ).
thf(1254,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(137,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( B @ ( A @ ( C @ ( E @ ( D @ c_FuncSet_Osko__FuncSet__Xrestrict__in__funcset__1__1 ) ) ) ) @ ( C @ hAPP ) @ ( B @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( A @ ( tc_bool @ ( B @ tc_fun ) @ ( E @ c_COMBK ) ) @ ( D @ c_FuncSet_OPi ) ) ) @ ( B @ ( A @ ( D @ ( C @ c_FuncSet_Orestrict ) ) ) @ ( B @ ( A @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_restrict__in__funcset_1) ).
thf(1055,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( B @ ( A @ ( C @ ( E @ ( D @ c_FuncSet_Osko__FuncSet__Xrestrict__in__funcset__1__1 ) ) ) ) @ ( C @ hAPP ) @ ( B @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( A @ ( tc_bool @ ( B @ tc_fun ) @ ( E @ c_COMBK ) ) @ ( D @ c_FuncSet_OPi ) ) ) @ ( B @ ( A @ ( D @ ( C @ c_FuncSet_Orestrict ) ) ) @ ( B @ ( A @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(17,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( B @ ( D @ ( C @ ( B @ ( A @ c_FuncSet_Orestrict ) ) ) @ c_Fun_Oinj__on ) ) ) )
| ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__restrict__eq_0) ).
thf(785,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( B @ ( D @ ( C @ ( B @ ( A @ c_FuncSet_Orestrict ) ) ) @ c_Fun_Oinj__on ) ) ) )
| ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(490,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Lattices_Olattice )
| ( B @ ( A @ tc_fun ) @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olower__semilattice) ).
thf(1871,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Lattices_Olattice )
| ( B @ ( A @ tc_fun ) @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).
thf(506,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Set_Oinsert ) ) )
= ( C @ ( B @ ( A @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__Diff__single_0) ).
thf(1907,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Set_Oinsert ) ) )
= ( C @ ( B @ ( A @ c_Set_Oinsert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).
thf(227,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__le_1) ).
thf(1264,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(252,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( C @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_predicate1D_0) ).
thf(1323,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( C @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(26,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( H @ ( A @ ( C @ c_Fun_Obij__betw ) ) ) ) )
| ~ ( F @ ( E @ ( G @ ( H @ ( B @ c_Fun_Obij__betw ) ) ) ) )
| ( F @ ( D @ ( G @ ( A @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_FuncSet_Ocompose ) ) ) ) ) @ c_Fun_Obij__betw ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bij__betw__compose_0) ).
thf(802,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( H @ ( A @ ( C @ c_Fun_Obij__betw ) ) ) ) )
| ~ ( F @ ( E @ ( G @ ( H @ ( B @ c_Fun_Obij__betw ) ) ) ) )
| ( F @ ( D @ ( G @ ( A @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_FuncSet_Ocompose ) ) ) ) ) @ c_Fun_Obij__betw ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(542,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_Orderings_Otop__class_Otop ) )
| ( ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
!= ( A @ c_Orderings_Otop__class_Otop ) )
| ~ ( A @ class_Lattices_Obounded__lattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__eq__top__eq1_0) ).
thf(1992,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_Orderings_Otop__class_Otop ) )
| ( ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
!= ( A @ c_Orderings_Otop__class_Otop ) )
| ~ ( A @ class_Lattices_Obounded__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).
thf(603,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( E @ ( D @ ( A @ ( B @ c_Set_Ovimage ) ) ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ hAPP ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__code_0) ).
thf(2126,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( E @ ( D @ ( A @ ( B @ c_Set_Ovimage ) ) ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ hAPP ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).
thf(171,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_Orderings_Otop__class_Otop ) )
| ( ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
!= ( A @ c_Orderings_Otop__class_Otop ) )
| ~ ( A @ class_Lattices_Obounded__lattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__eq__top__eq2_0) ).
thf(1132,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_Orderings_Otop__class_Otop ) )
| ( ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
!= ( A @ c_Orderings_Otop__class_Otop ) )
| ~ ( A @ class_Lattices_Obounded__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(89,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( E @ ( D @ ( B @ c_Set_Ovimage ) ) ) @ ( C @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ hAPP ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimageE_0) ).
thf(949,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( E @ ( D @ ( B @ c_Set_Ovimage ) ) ) @ ( C @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ hAPP ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(627,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__eqI_1) ).
thf(2185,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[627]) ).
thf(310,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Fun_Oinj__on ) ) ) )
| ~ ( D @ ( A @ ( E @ ( B @ c_Set_Oimage ) ) ) @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( A @ ( C @ ( B @ c_Set_Ovimage ) ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__subsetI_0) ).
thf(1455,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Fun_Oinj__on ) ) ) )
| ~ ( D @ ( A @ ( E @ ( B @ c_Set_Oimage ) ) ) @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( A @ ( C @ ( B @ c_Set_Ovimage ) ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(475,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( G @ ( E @ ( F @ ( D @ ( B @ ( A @ c_Finite__Set_Ofold__graph ) ) ) ) ) )
| ( G @ ( E @ ( F @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( E @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( A @ c_Finite__Set_Ofold__graph ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fold__graph_OinsertI_0) ).
thf(1832,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( G @ ( E @ ( F @ ( D @ ( B @ ( A @ c_Finite__Set_Ofold__graph ) ) ) ) ) )
| ( G @ ( E @ ( F @ ( C @ ( A @ hAPP ) @ hAPP ) @ ( E @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( A @ c_Finite__Set_Ofold__graph ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).
thf(82,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_psubset__subset__trans_0) ).
thf(934,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(196,axiom,
! [B: $i,A: $i] :
( ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__cancel_0) ).
thf(1191,plain,
! [B: $i,A: $i] :
( ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(726,axiom,
c_Arrow__Order__Mirabelle_OLin @ ( v_Lab____ @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0) ).
thf(2420,plain,
c_Arrow__Order__Mirabelle_OLin @ ( v_Lab____ @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[726]) ).
thf(220,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( E @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Set_Ovimage ) ) ) )
= ( tc_bool @ ( E @ tc_fun ) @ ( D @ ( E @ ( C @ ( A @ c_Set_Ovimage ) ) ) @ ( D @ ( E @ ( B @ ( A @ c_Set_Ovimage ) ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__Diff_0) ).
thf(1247,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( E @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Set_Ovimage ) ) ) )
= ( tc_bool @ ( E @ tc_fun ) @ ( D @ ( E @ ( C @ ( A @ c_Set_Ovimage ) ) ) @ ( D @ ( E @ ( B @ ( A @ c_Set_Ovimage ) ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(707,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).
thf(2373,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[707]) ).
thf(361,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Set_Oinsert ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__Diff__if_1) ).
thf(1568,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Set_Oinsert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(451,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Lattices_Odistrib__lattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__inf__distrib1_0) ).
thf(1773,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Lattices_Odistrib__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).
thf(329,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ hAPP ) )
= C )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) )
!= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__idem__iff_0) ).
thf(1494,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ hAPP ) )
= C )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) )
!= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(156,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( E @ ( A @ c_SetInterval_Oord_OatLeastAtMost ) ) ) @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ord_OatLeastAtMost__iff_1) ).
thf(1100,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( E @ ( A @ c_SetInterval_Oord_OatLeastAtMost ) ) ) @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(513,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( C @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__insert_2) ).
thf(1922,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( C @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).
thf(34,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Collect ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Collect__def_0) ).
thf(817,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Collect ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(719,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ hAPP ) @ hBOOL )
| ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
!= ( A @ ( B @ c_Collect ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__Collect__eq_0) ).
thf(2403,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ hAPP ) @ hBOOL )
| ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
!= ( A @ ( B @ c_Collect ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[719]) ).
thf(151,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( E @ ( F @ ( B @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( F @ ( C @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ hAPP ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__subset__iff_0) ).
thf(1087,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( E @ ( F @ ( B @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( F @ ( C @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ hAPP ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(422,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( E @ ( D @ ( B @ c_Set_Oimage ) ) ) @ ( C @ ( B @ hAPP ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__eqI_0) ).
thf(1704,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( E @ ( D @ ( B @ c_Set_Oimage ) ) ) @ ( C @ ( B @ hAPP ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(56,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Lattices_Olattice )
| ( B @ ( A @ tc_fun ) @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Oupper__semilattice) ).
thf(870,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Lattices_Olattice )
| ( B @ ( A @ tc_fun ) @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(116,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__insert_0) ).
thf(1013,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(9,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( G @ ( A @ ( C @ c_Fun_Obij__betw ) ) ) ) )
| ~ ( F @ ( E @ ( G @ ( B @ c_Fun_Oinj__on ) ) ) )
| ( F @ ( D @ ( A @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_FuncSet_Ocompose ) ) ) ) ) @ c_Fun_Oinj__on ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__compose_0) ).
thf(770,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( G @ ( A @ ( C @ c_Fun_Obij__betw ) ) ) ) )
| ~ ( F @ ( E @ ( G @ ( B @ c_Fun_Oinj__on ) ) ) )
| ( F @ ( D @ ( A @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_FuncSet_Ocompose ) ) ) ) ) @ c_Fun_Oinj__on ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(437,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( E @ ( B @ c_Set_Ovimage ) ) ) @ ( D @ ( A @ ( C @ ( B @ c_Set_Ovimage ) ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__mono_0) ).
thf(1741,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( E @ ( B @ c_Set_Ovimage ) ) ) @ ( D @ ( A @ ( C @ ( B @ c_Set_Ovimage ) ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(61,axiom,
! [A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop )
!= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UNIV__not__empty_0) ).
thf(881,plain,
! [A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop )
!= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(492,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__commute_0) ).
thf(1875,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).
thf(453,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_ATP__Linkup_Osko__Complete__Lattice__XInterI__1__1 ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Complete__Lattice_OInf__class_OInf @ hAPP ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_InterI_1) ).
thf(1778,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_ATP__Linkup_Osko__Complete__Lattice__XInterI__1__1 ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Complete__Lattice_OInf__class_OInf @ hAPP ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(548,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( B = C )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_0) ).
thf(2007,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( B = C )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).
thf(642,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Complete__Lattice_OSup__class_OSup @ hAPP ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( C @ ( B @ c_ATP__Linkup_Osko__Complete__Lattice__XUnionE__1__1 ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UnionE_0) ).
thf(2222,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Complete__Lattice_OSup__class_OSup @ hAPP ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( C @ ( B @ c_ATP__Linkup_Osko__Complete__Lattice__XUnionE__1__1 ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[642]) ).
thf(291,axiom,
! [B: $i,A: $i] : ( A @ ( B @ c_Set_OPow ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Pow__top_0) ).
thf(1415,plain,
! [B: $i,A: $i] : ( A @ ( B @ c_Set_OPow ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(523,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Lattices_Odistrib__lattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__distrib2_0) ).
thf(1946,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Lattices_Odistrib__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).
thf(556,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( E @ c_Relation_OImage ) ) ) @ ( D @ ( B @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( B @ ( A @ ( D @ ( C @ c_Pair ) ) ) @ ( B @ ( A @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Image__singleton__iff_0) ).
thf(2027,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( E @ c_Relation_OImage ) ) ) @ ( D @ ( B @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( B @ ( A @ ( D @ ( C @ c_Pair ) ) ) @ ( B @ ( A @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).
thf(19,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = F )
| ( ( E @ ( D @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Fun_Ofun__upd ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ ( E @ ( D @ ( G @ ( F @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Fun_Ofun__upd ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__twist_0) ).
thf(789,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = F )
| ( ( E @ ( D @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Fun_Ofun__upd ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ ( E @ ( D @ ( G @ ( F @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Fun_Ofun__upd ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(308,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( A = B )
| ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ c_Arrow__Order__Mirabelle_Omkbot ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__mkbot_5) ).
thf(1450,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( A = B )
| ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ c_Arrow__Order__Mirabelle_Omkbot ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(585,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( B @ ( A @ ( D @ c_FuncSet_Oextensional ) ) @ ( B @ ( A @ ( D @ ( C @ c_FuncSet_Orestrict ) ) ) @ ( B @ ( A @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_restrict__extensional_0) ).
thf(2090,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( B @ ( A @ ( D @ c_FuncSet_Oextensional ) ) @ ( B @ ( A @ ( D @ ( C @ c_FuncSet_Orestrict ) ) ) @ ( B @ ( A @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).
thf(274,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( K @ ( J @ ( I @ ( E @ ( H @ ( G @ ( F @ ( A @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
| ( ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ hAPP ) )
= ( C @ ( A @ hAPP ) @ ( B @ ( E @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OInf__insert_0) ).
thf(1373,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( K @ ( J @ ( I @ ( E @ ( H @ ( G @ ( F @ ( A @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
| ( ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ hAPP ) )
= ( C @ ( A @ hAPP ) @ ( B @ ( E @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(508,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( C @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert__iff_3) ).
thf(1911,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( C @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).
thf(659,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( A = E )
| ( ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
!= ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ c_Set_Oinsert ) ) @ ( D @ c_Set_Oinsert ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_2) ).
thf(2259,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( A = E )
| ( ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
!= ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ c_Set_Oinsert ) ) @ ( D @ c_Set_Oinsert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[659]) ).
thf(256,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_Equiv__Relations_Oequiv ) ) )
| ( ( A @ ( C @ ( B @ c_Equiv__Relations_Oquotient ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Complete__Lattice_OSup__class_OSup @ hAPP ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Union__quotient_0) ).
thf(1334,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_Equiv__Relations_Oequiv ) ) )
| ( ( A @ ( C @ ( B @ c_Equiv__Relations_Oquotient ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Complete__Lattice_OSup__class_OSup @ hAPP ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(412,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ c_Arrow__Order__Mirabelle_OIIA )
| ~ ( c_Arrow__Order__Mirabelle_OProf @ ( D @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( c_Arrow__Order__Mirabelle_OProf @ ( E @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( D @ ( B @ ( A @ v_sko__Arrow__Order__Mirabelle__XIIA__def__1 ) ) ) @ ( D @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( D @ ( B @ ( A @ v_sko__Arrow__Order__Mirabelle__XIIA__def__1 ) ) ) @ ( E @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( C @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IIA__def_3) ).
thf(1682,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ c_Arrow__Order__Mirabelle_OIIA )
| ~ ( c_Arrow__Order__Mirabelle_OProf @ ( D @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( c_Arrow__Order__Mirabelle_OProf @ ( E @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( D @ ( B @ ( A @ v_sko__Arrow__Order__Mirabelle__XIIA__def__1 ) ) ) @ ( D @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( D @ ( B @ ( A @ v_sko__Arrow__Order__Mirabelle__XIIA__def__1 ) ) ) @ ( E @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( C @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(601,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( E @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( A @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( C @ ( B @ c_ATP__Linkup_Osko__Set__Xbex__Un__1__3 ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bex__Un_7) ).
thf(2122,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( E @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( A @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( C @ ( B @ c_ATP__Linkup_Osko__Set__Xbex__Un__1__3 ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).
thf(410,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( A @ hAPP ) )
= ( B @ ( C @ ( D @ ( A @ ( D @ ( A @ hAPP ) @ c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__2 ) ) ) ) @ ( A @ hAPP ) ) )
| ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Set_Oimage ) ) ) @ ( D @ ( A @ hAPP ) @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_range__ex1__eq_2) ).
thf(1677,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( A @ hAPP ) )
= ( B @ ( C @ ( D @ ( A @ ( D @ ( A @ hAPP ) @ c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__2 ) ) ) ) @ ( A @ hAPP ) ) )
| ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Set_Oimage ) ) ) @ ( D @ ( A @ hAPP ) @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(135,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Orderings_Obot__class_Obot @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Obot ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bot__least_0) ).
thf(1051,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Orderings_Obot__class_Obot @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(70,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Complete__Lattice_OSup__class_OSup @ hAPP ) )
= ( C @ ( A @ c_Complete__Lattice_OSup__class_OSup @ hAPP ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sup__insert_0) ).
thf(905,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Complete__Lattice_OSup__class_OSup @ hAPP ) )
= ( C @ ( A @ c_Complete__Lattice_OSup__class_OSup @ hAPP ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(243,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ ( C @ ( E @ c_Set_Oimage ) ) ) @ ( D @ ( A @ ( B @ ( E @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( D @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__image__iff_2) ).
thf(1302,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ ( C @ ( E @ c_Set_Oimage ) ) ) @ ( D @ ( A @ ( B @ ( E @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( D @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(403,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( D @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D = A )
| ~ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D = B )
| ( B = D )
| ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__below_7) ).
thf(1664,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( D @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D = A )
| ~ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D = B )
| ( B = D )
| ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(129,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_psubsetD_0) ).
thf(1040,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(160,axiom,
tc_bool @ class_Lattices_Obounded__lattice,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Obounded__lattice) ).
thf(1109,plain,
tc_bool @ class_Lattices_Obounded__lattice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(293,axiom,
tc_bool @ class_Lattices_Olattice,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olattice) ).
thf(1418,plain,
tc_bool @ class_Lattices_Olattice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(648,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__subset__conv_1) ).
thf(2236,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[648]) ).
thf(278,axiom,
! [B: $i,A: $i] :
~ ( A @ ( B @ c_Arrow__Order__Mirabelle_Omkbot ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__mkbot_1) ).
thf(1383,plain,
! [B: $i,A: $i] :
~ ( A @ ( B @ c_Arrow__Order__Mirabelle_Omkbot ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(119,axiom,
v_F @ c_Arrow__Order__Mirabelle_OIIA,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_assms_I3_J_0) ).
thf(1020,plain,
v_F @ c_Arrow__Order__Mirabelle_OIIA,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(529,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ c_Arrow__Order__Mirabelle_Omkbot ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B = A )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__mkbot_4) ).
thf(1960,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ c_Arrow__Order__Mirabelle_Omkbot ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B = A )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).
thf(28,axiom,
tc_nat @ class_HOL_Oord,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__HOL_Oord) ).
thf(806,plain,
tc_nat @ class_HOL_Oord,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(366,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E = D )
| ~ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( E @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A = D )
| ( B = D )
| ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__above_3) ).
thf(1581,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E = D )
| ~ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( E @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A = D )
| ( B = D )
| ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(691,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ c_SetInterval_Oord_OatMost ) ) @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ord_OatMost__iff_0) ).
thf(2335,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ c_SetInterval_Oord_OatMost ) ) @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[691]) ).
thf(96,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( C @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( C @ ( B @ c_ATP__Linkup_Osko__Set__XbexE__1__1 ) ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bexE_0) ).
thf(966,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( C @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( C @ ( B @ c_ATP__Linkup_Osko__Set__XbexE__1__1 ) ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(235,axiom,
! [A: $i] :
( ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Complete__Lattice_OSup__class_OSup @ hAPP ) )
= ( A @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sup__empty_0) ).
thf(1283,plain,
! [A: $i] :
( ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Complete__Lattice_OSup__class_OSup @ hAPP ) )
= ( A @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(577,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( c_Arrow__Order__Mirabelle_OLin @ ( B @ ( A @ v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1 ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__Lin_0) ).
thf(2073,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( c_Arrow__Order__Mirabelle_OLin @ ( B @ ( A @ v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1 ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).
thf(569,axiom,
! [B: $i,A: $i] : ( B @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equalityE_0) ).
thf(2058,plain,
! [B: $i,A: $i] : ( B @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[569]) ).
thf(669,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( K @ ( J @ ( I @ ( E @ ( H @ ( G @ ( F @ ( A @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
| ( ( D @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( B @ c_Set_Oinsert ) ) @ ( A @ hAPP ) )
= ( C @ ( B @ ( E @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OInf__binary_0) ).
thf(2281,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( K @ ( J @ ( I @ ( E @ ( H @ ( G @ ( F @ ( A @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
| ( ( D @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( B @ c_Set_Oinsert ) ) @ ( A @ hAPP ) )
= ( C @ ( B @ ( E @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[669]) ).
thf(460,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( A @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
| ( ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ hAPP ) )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OInf__empty_0) ).
thf(1796,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( I @ ( H @ ( G @ ( F @ ( E @ ( D @ ( A @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
| ( ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ hAPP ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).
thf(109,axiom,
! [B: $i,A: $i] :
( ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__empty_0) ).
thf(998,plain,
! [B: $i,A: $i] :
( ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(261,axiom,
! [C: $i,B: $i,A: $i] : ( B @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__upper2_0) ).
thf(1345,plain,
! [C: $i,B: $i,A: $i] : ( B @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(418,axiom,
! [B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__empty__right_0) ).
thf(1696,plain,
! [B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(102,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( A @ ( tc_bool @ ( D @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__diff_0) ).
thf(981,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( A @ ( tc_bool @ ( D @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(7,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( D @ ( C @ ( B @ ( D @ ( C @ ( B @ ( A @ c_FuncSet_Orestrict ) ) ) @ c_Fun_Oinj__on ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__restrict__eq_1) ).
thf(766,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( D @ ( C @ ( B @ ( D @ ( C @ ( B @ ( A @ c_FuncSet_Orestrict ) ) ) @ c_Fun_Oinj__on ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(59,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( D @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__trans_0) ).
thf(877,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( D @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(629,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( C @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_psubset__insert__iff_1) ).
thf(2190,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( C @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[629]) ).
thf(165,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( D @ ( E @ ( B @ c_Set_Oimage ) ) ) @ ( A @ ( D @ ( C @ ( B @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__mono_0) ).
thf(1119,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( D @ ( E @ ( B @ c_Set_Oimage ) ) ) @ ( A @ ( D @ ( C @ ( B @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(728,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( B @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( D @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( C @ ( C @ ( D @ ( B @ c_Pair ) ) ) @ ( C @ ( C @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( E @ c_Equiv__Relations_Oequiv ) ) )
| ( ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) )
!= ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equiv__class__eq__iff_3) ).
thf(2424,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( B @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( D @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( C @ ( C @ ( D @ ( B @ c_Pair ) ) ) @ ( C @ ( C @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( E @ c_Equiv__Relations_Oequiv ) ) )
| ( ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) )
!= ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[728]) ).
thf(706,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ ( D @ c_Set_Oinsert ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__subset_1) ).
thf(2371,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ ( D @ c_Set_Oinsert ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[706]) ).
thf(343,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_Complete__Lattice_OInf__class_OInf @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Inf__lower_0) ).
thf(1526,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_Complete__Lattice_OInf__class_OInf @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(608,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mem__def_1) ).
thf(2137,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).
thf(158,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( E @ tc_fun ) @ ( A @ ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) )
= ( tc_bool @ ( E @ tc_fun ) @ ( A @ ( D @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( tc_bool @ ( E @ tc_fun ) @ ( A @ ( D @ ( B @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( tc_bool @ ( E @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UN__Un_0) ).
thf(1104,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( E @ tc_fun ) @ ( A @ ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) )
= ( tc_bool @ ( E @ tc_fun ) @ ( A @ ( D @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( tc_bool @ ( E @ tc_fun ) @ ( A @ ( D @ ( B @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( tc_bool @ ( E @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(217,axiom,
! [C: $i,B: $i,A: $i] : ( A @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insertI1_0) ).
thf(1242,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(47,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__code_2) ).
thf(849,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(76,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Lattices_Obounded__lattice )
| ( B @ ( A @ tc_fun ) @ class_Lattices_Obounded__lattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Obounded__lattice) ).
thf(920,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Lattices_Obounded__lattice )
| ( B @ ( A @ tc_fun ) @ class_Lattices_Obounded__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(635,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D = B )
| ~ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A = B )
| ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__below_12) ).
thf(2204,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D = B )
| ~ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A = B )
| ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[635]) ).
thf(78,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Diff_0) ).
thf(925,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(200,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( A @ hAPP ) @ ( C @ ( B @ ( A @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) )
= D )
| ~ ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inv__f__eq_0) ).
thf(1199,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( A @ hAPP ) @ ( C @ ( B @ ( A @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) )
= D )
| ~ ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(30,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( E @ ( A @ ( B @ c_Fun_Obij__betw ) ) ) ) )
| ( C @ ( D @ ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Hilbert__Choice_Oinv__into ) ) ) @ c_Fun_Obij__betw ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bij__betw__inv__into_0) ).
thf(810,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( E @ ( A @ ( B @ c_Fun_Obij__betw ) ) ) ) )
| ( C @ ( D @ ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Hilbert__Choice_Oinv__into ) ) ) @ c_Fun_Obij__betw ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(258,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__supI2_0) ).
thf(1338,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(455,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( C @ ( D @ c_FuncSet_Oextensional ) ) @ ( A @ ( E @ ( C @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( C @ ( D @ c_FuncSet_Oextensional ) ) @ ( B @ ( E @ ( C @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( E @ ( C @ ( B @ ( A @ ( D @ c_FuncSet_Osko__FuncSet__XextensionalityI__1__1 ) ) ) ) @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_extensionalityI_0) ).
thf(1783,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( C @ ( D @ c_FuncSet_Oextensional ) ) @ ( A @ ( E @ ( C @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( C @ ( D @ c_FuncSet_Oextensional ) ) @ ( B @ ( E @ ( C @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( E @ ( C @ ( B @ ( A @ ( D @ c_FuncSet_Osko__FuncSet__XextensionalityI__1__1 ) ) ) ) @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(142,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( C = B )
| ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__less__linear_0) ).
thf(1067,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( C = B )
| ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(711,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__subset__iff_1) ).
thf(2382,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[711]) ).
thf(510,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__disjoint_0) ).
thf(1915,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).
thf(424,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Complete__Lattice_OSup__class_OSup @ hAPP ) )
= B )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sup__singleton_0) ).
thf(1708,plain,
! [B: $i,A: $i] :
( ( ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Complete__Lattice_OSup__class_OSup @ hAPP ) )
= B )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(571,axiom,
! [C: $i,B: $i,A: $i] :
~ ( A @ ( C @ c_Arrow__Order__Mirabelle_Omktop ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__mktop_0) ).
thf(2061,plain,
! [C: $i,B: $i,A: $i] :
~ ( A @ ( C @ c_Arrow__Order__Mirabelle_Omktop ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).
thf(545,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = C )
| ~ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( ( B @ ( A @ hAPP ) )
!= ( C @ ( A @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_injD_0) ).
thf(2000,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = C )
| ~ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( ( B @ ( A @ hAPP ) )
!= ( C @ ( A @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).
thf(133,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__rev__mp_0) ).
thf(1047,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(433,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( tc_bool @ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( A @ c_in @ c_COMBC ) ) ) @ hAPP ) @ ( B @ ( tc_bool @ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( A @ c_in @ c_COMBC ) ) ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pred__subset__eq_1) ).
thf(1730,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( tc_bool @ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( A @ c_in @ c_COMBC ) ) ) @ hAPP ) @ ( B @ ( tc_bool @ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( A @ c_in @ c_COMBC ) ) ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(138,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( B = C )
| ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__le_2) ).
thf(1057,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( B = C )
| ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(735,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__greatest_0) ).
thf(2441,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[735]) ).
thf(661,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( A @ ( C @ ( E @ ( D @ c_FuncSet_Osko__FuncSet__XPi__I__1__1 ) ) ) ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( E @ ( D @ c_FuncSet_OPi ) ) ) @ ( C @ ( B @ ( A @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Pi__I_0) ).
thf(2264,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( A @ ( C @ ( E @ ( D @ c_FuncSet_Osko__FuncSet__XPi__I__1__1 ) ) ) ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( E @ ( D @ c_FuncSet_OPi ) ) ) @ ( C @ ( B @ ( A @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[661]) ).
thf(502,axiom,
! [C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insertI_0) ).
thf(1900,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( B @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).
thf(38,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( E @ ( B @ ( A @ c_Fun_Obij__betw ) ) ) ) )
| ( ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) )
= E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bij__betw__def_1) ).
thf(825,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( E @ ( B @ ( A @ c_Fun_Obij__betw ) ) ) ) )
| ( ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) )
= E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(120,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( B @ ( C @ c_Set_Oimage ) ) ) @ ( E @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inv__into__into_0) ).
thf(1021,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( B @ ( C @ c_Set_Oimage ) ) ) @ ( E @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( E @ ( D @ ( A @ ( C @ ( B @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(130,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( B @ ( A @ ( A @ ( tc_bool @ ( B @ tc_fun ) @ ( C @ c_COMBK ) ) @ ( A @ ( B @ ( C @ ( D @ c_Set_Oimage ) ) ) @ c_FuncSet_OPi ) ) ) @ ( B @ ( A @ ( A @ ( B @ ( C @ ( D @ c_Set_Oimage ) ) ) @ ( A @ ( B @ ( D @ ( C @ c_Hilbert__Choice_Oinv__into ) ) ) @ c_FuncSet_Orestrict ) ) ) @ ( B @ ( A @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inv__into__funcset_0) ).
thf(1042,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( B @ ( A @ ( A @ ( tc_bool @ ( B @ tc_fun ) @ ( C @ c_COMBK ) ) @ ( A @ ( B @ ( C @ ( D @ c_Set_Oimage ) ) ) @ c_FuncSet_OPi ) ) ) @ ( B @ ( A @ ( A @ ( B @ ( C @ ( D @ c_Set_Oimage ) ) ) @ ( A @ ( B @ ( D @ ( C @ c_Hilbert__Choice_Oinv__into ) ) ) @ c_FuncSet_Orestrict ) ) ) @ ( B @ ( A @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(409,axiom,
! [A: $i] : ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__empty_1) ).
thf(1676,plain,
! [A: $i] : ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(207,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ ( B @ c_Fun_Oinj__on ) ) ) )
| ~ ( A @ ( E @ ( tc_bool @ ( C @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( C @ ( D @ ( D @ ( C @ ( E @ ( B @ c_Set_Oimage ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Hilbert__Choice_Oinv__into ) ) ) @ c_Set_Oimage ) ) ) )
= E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inv__into__image__cancel_0) ).
thf(1217,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ ( B @ c_Fun_Oinj__on ) ) ) )
| ~ ( A @ ( E @ ( tc_bool @ ( C @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( C @ ( D @ ( D @ ( C @ ( E @ ( B @ c_Set_Oimage ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Hilbert__Choice_Oinv__into ) ) ) @ c_Set_Oimage ) ) ) )
= E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(472,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D = E )
| ~ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A = B )
| ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( D @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( D @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__above_14) ).
thf(1824,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D = E )
| ~ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A = B )
| ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( D @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( D @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).
thf(606,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ ( B @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( D @ ( A @ ( B @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( A @ ( B @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_HOL_Oord ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__fun__def_2) ).
thf(2132,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ ( B @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( D @ ( A @ ( B @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( A @ ( B @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_HOL_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).
thf(92,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_COMBK ) ) @ ( A @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UN__constant_1) ).
thf(957,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_COMBK ) ) @ ( A @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(209,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( E @ ( D @ ( C @ c_SetInterval_Oord_OgreaterThanLessThan ) ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ord_OgreaterThanLessThan__iff_2) ).
thf(1223,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( E @ ( D @ ( C @ c_SetInterval_Oord_OgreaterThanLessThan ) ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(66,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( B @ ( F @ ( A @ c_Fun_Oinj__on ) ) ) )
| ~ ( F @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( F @ ( D @ ( tc_bool @ ( B @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( E @ ( B @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_Set_Oimage ) ) ) )
= ( E @ ( B @ ( D @ ( A @ c_Set_Oimage ) ) ) @ ( E @ ( B @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( E @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__image__Int_0) ).
thf(894,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( B @ ( F @ ( A @ c_Fun_Oinj__on ) ) ) )
| ~ ( F @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( F @ ( D @ ( tc_bool @ ( B @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( E @ ( B @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_Set_Oimage ) ) ) )
= ( E @ ( B @ ( D @ ( A @ c_Set_Oimage ) ) ) @ ( E @ ( B @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( E @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(265,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__asym_H_0) ).
thf(1355,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(667,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bex__empty_0) ).
thf(2277,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[667]) ).
thf(167,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UnCI_1) ).
thf(1123,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(52,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( C @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_psubset__insert__iff_8) ).
thf(862,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( C @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(332,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntI_0) ).
thf(1502,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(36,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( D @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__eqI_1) ).
thf(820,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( D @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(296,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( A @ ( C @ ( E @ ( D @ c_FuncSet_Osko__FuncSet__XPi__I_H__1__1 ) ) ) ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( E @ ( D @ c_FuncSet_OPi ) ) ) @ ( C @ ( B @ ( A @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Pi__I_H_0) ).
thf(1423,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( A @ ( C @ ( E @ ( D @ c_FuncSet_Osko__FuncSet__XPi__I_H__1__1 ) ) ) ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( E @ ( D @ c_FuncSet_OPi ) ) ) @ ( C @ ( B @ ( A @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(125,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__least_0) ).
thf(1032,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(270,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ ( C @ ( D @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert_0) ).
thf(1365,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ ( C @ ( D @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(512,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I8_J_0) ).
thf(1920,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).
thf(732,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
!= B )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__inf_1) ).
thf(2433,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
!= B )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[732]) ).
thf(60,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( E @ ( A @ ( D @ c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 ) ) ) @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( B @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ball__conj__distrib_0) ).
thf(879,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( E @ ( A @ ( D @ c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 ) ) ) @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( B @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(690,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__absorb2_0) ).
thf(2332,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[690]) ).
thf(525,axiom,
! [C: $i,B: $i,A: $i] : ( A @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__code_1) ).
thf(1951,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).
thf(240,axiom,
tc_bool @ class_Lattices_Odistrib__lattice,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Odistrib__lattice) ).
thf(1296,plain,
tc_bool @ class_Lattices_Odistrib__lattice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(40,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = F )
| ( ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) )
!= ( D @ ( C @ ( F @ ( E @ c_Pair ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Pair__eq_1) ).
thf(830,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = F )
| ( ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) )
!= ( D @ ( C @ ( F @ ( E @ c_Pair ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(204,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__commute_0) ).
thf(1210,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(645,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distrib__inf__le_0) ).
thf(2228,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[645]) ).
thf(595,axiom,
! [C: $i,B: $i,A: $i] : ( A @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insertCI_1) ).
thf(2112,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[595]) ).
thf(159,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( E @ ( D @ ( C @ ( tc_bool @ ( E @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ c_Fun_Oinj__on ) ) ) )
| ~ ( A @ ( E @ ( C @ ( B @ c_Fun_Oinj__on ) ) ) )
| ~ ( A @ ( E @ ( D @ ( B @ c_Fun_Oinj__on ) ) ) )
| ( ( A @ ( E @ ( tc_bool @ ( E @ tc_fun ) @ ( C @ ( D @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ c_Set_Oimage ) ) ) @ ( A @ ( E @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
!= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__Un_3) ).
thf(1106,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( E @ ( D @ ( C @ ( tc_bool @ ( E @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ c_Fun_Oinj__on ) ) ) )
| ~ ( A @ ( E @ ( C @ ( B @ c_Fun_Oinj__on ) ) ) )
| ~ ( A @ ( E @ ( D @ ( B @ c_Fun_Oinj__on ) ) ) )
| ( ( A @ ( E @ ( tc_bool @ ( E @ tc_fun ) @ ( C @ ( D @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ c_Set_Oimage ) ) ) @ ( A @ ( E @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
!= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(74,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( D @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__sup__iff_1) ).
thf(916,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( D @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(737,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Fun_Oinj__on ) ) ) )
| ~ ( E @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( D @ ( E @ ( B @ c_Set_Oimage ) ) ) @ ( A @ ( D @ ( C @ ( B @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__image__subset__iff_1) ).
thf(2445,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Fun_Oinj__on ) ) ) )
| ~ ( E @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( D @ ( E @ ( B @ c_Set_Oimage ) ) ) @ ( A @ ( D @ ( C @ ( B @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[737]) ).
thf(414,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Set_Ovimage ) ) ) )
= ( C @ ( B @ ( tc_bool @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( C @ ( tc_bool @ ( tc_bool @ ( D @ tc_fun ) @ tc_fun ) @ ( D @ ( A @ ( D @ c_in @ c_COMBB ) ) ) ) @ c_COMBC ) ) ) @ hAPP ) @ c_Collect ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__def_0) ).
thf(1687,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Set_Ovimage ) ) ) )
= ( C @ ( B @ ( tc_bool @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( C @ ( tc_bool @ ( tc_bool @ ( D @ tc_fun ) @ tc_fun ) @ ( D @ ( A @ ( D @ c_in @ c_COMBB ) ) ) ) @ c_COMBC ) ) ) @ hAPP ) @ c_Collect ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(311,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( F @ c_Equiv__Relations_Oequiv ) ) )
| ~ ( A @ ( A @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( D @ c_Relation_OImage ) ) ) @ ( A @ ( A @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( D @ c_Relation_OImage ) ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( E @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( A @ ( C @ ( B @ c_Pair ) ) ) @ ( A @ ( A @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equiv__class__nondisjoint_0) ).
thf(1457,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( F @ c_Equiv__Relations_Oequiv ) ) )
| ~ ( A @ ( A @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( D @ c_Relation_OImage ) ) ) @ ( A @ ( A @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( D @ c_Relation_OImage ) ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( E @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( A @ ( C @ ( B @ c_Pair ) ) ) @ ( A @ ( A @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(470,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
!= C )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__sup_1) ).
thf(1819,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
!= C )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(385,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__asym_0) ).
thf(1624,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(688,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ~ ( D @ ( C @ ( E @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) )
!= ( D @ ( C @ ( E @ ( A @ c_Set_Oimage ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__Un__image__eq__iff_0) ).
thf(2327,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ~ ( D @ ( C @ ( E @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) )
!= ( D @ ( C @ ( E @ ( A @ c_Set_Oimage ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[688]) ).
thf(638,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D = A )
| ( A = B )
| ( D = B )
| ~ ( c_Arrow__Order__Mirabelle_OProf @ ( E @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( c_Arrow__Order__Mirabelle_OProf @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( D @ ( C @ ( E @ v_sko__local__X4__1 ) ) ) ) @ ( E @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( D @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( D @ ( C @ ( E @ v_sko__local__X4__1 ) ) ) ) @ ( C @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( v_F @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( D @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( v_F @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_4_0) ).
thf(2213,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D = A )
| ( A = B )
| ( D = B )
| ~ ( c_Arrow__Order__Mirabelle_OProf @ ( E @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( c_Arrow__Order__Mirabelle_OProf @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( D @ ( C @ ( E @ v_sko__local__X4__1 ) ) ) ) @ ( E @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( D @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( D @ ( C @ ( E @ v_sko__local__X4__1 ) ) ) ) @ ( C @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( v_F @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( D @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( v_F @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[638]) ).
thf(198,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__least_0) ).
thf(1195,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(637,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Relation_OImage ) ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Image__empty_0) ).
thf(2211,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Relation_OImage ) ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[637]) ).
thf(682,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Fun_Oinj__on ) ) ) )
| ( ( D @ ( B @ hAPP ) @ ( C @ ( A @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) )
= D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inv__f__f_0) ).
thf(2313,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Fun_Oinj__on ) ) ) )
| ( ( D @ ( B @ hAPP ) @ ( C @ ( A @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) )
= D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[682]) ).
thf(169,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( E @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_Set_Ovimage ) ) ) )
= ( B @ ( E @ ( D @ ( A @ c_Set_Ovimage ) ) ) @ ( B @ ( E @ ( C @ ( A @ c_Set_Ovimage ) ) ) @ ( tc_bool @ ( E @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__Un_0) ).
thf(1128,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( E @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_Set_Ovimage ) ) ) )
= ( B @ ( E @ ( D @ ( A @ c_Set_Ovimage ) ) ) @ ( B @ ( E @ ( C @ ( A @ c_Set_Ovimage ) ) ) @ ( tc_bool @ ( E @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(363,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ c_Set_OPow ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Complete__Lattice_OSup__class_OSup @ hAPP ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Union__Pow__eq_0) ).
thf(1573,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ c_Set_OPow ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Complete__Lattice_OSup__class_OSup @ hAPP ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(99,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( B = C )
| ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_psubset__eq_2) ).
thf(974,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( B = C )
| ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(676,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( E @ ( tc_bool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( E @ ( D @ ( C @ ( B @ ( A @ c_COMBB ) ) ) ) @ c_Set_Oimage ) ) ) )
= ( D @ ( C @ ( C @ ( E @ ( tc_bool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Set_Oimage ) ) ) @ ( A @ c_Set_Oimage ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_range__composition_0) ).
thf(2300,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( E @ ( tc_bool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( E @ ( D @ ( C @ ( B @ ( A @ c_COMBB ) ) ) ) @ c_Set_Oimage ) ) ) )
= ( D @ ( C @ ( C @ ( E @ ( tc_bool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Set_Oimage ) ) ) @ ( A @ c_Set_Oimage ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[676]) ).
thf(590,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subsetD_0) ).
thf(2100,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).
thf(225,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( B @ ( A @ v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1 ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__Lin_1) ).
thf(1259,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( B @ ( A @ v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1 ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(709,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( E @ ( tc_bool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( A @ c_Set_Ovimage ) ) ) @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( B @ ( A @ hAPP ) )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__singleton__eq_0) ).
thf(2377,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( E @ ( tc_bool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( A @ c_Set_Ovimage ) ) ) @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( B @ ( A @ hAPP ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[709]) ).
thf(254,axiom,
! [A: $i] :
( ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Complete__Lattice_OInf__class_OInf @ hAPP ) )
= ( A @ c_Orderings_Otop__class_Otop ) )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Inf__empty_0) ).
thf(1328,plain,
! [A: $i] :
( ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Complete__Lattice_OInf__class_OInf @ hAPP ) )
= ( A @ c_Orderings_Otop__class_Otop ) )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(166,axiom,
! [B: $i,A: $i] :
~ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_emptyE_0) ).
thf(1121,plain,
! [B: $i,A: $i] :
~ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(533,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__subset__iff_2) ).
thf(1970,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).
thf(484,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__assoc_0) ).
thf(1856,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).
thf(297,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( D @ hAPP ) @ hBOOL )
| ( A @ ( D @ c_Collect ) @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__Collect_2) ).
thf(1425,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( D @ hAPP ) @ hBOOL )
| ( A @ ( D @ c_Collect ) @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(406,axiom,
! [B: $i,A: $i] :
( ~ ( c_Arrow__Order__Mirabelle_OLin @ ( A @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( c_Arrow__Order__Mirabelle_OLin @ ( B @ ( A @ c_Arrow__Order__Mirabelle_Omkbot ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mkbot__Lin_0) ).
thf(1672,plain,
! [B: $i,A: $i] :
( ~ ( c_Arrow__Order__Mirabelle_OLin @ ( A @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( c_Arrow__Order__Mirabelle_OLin @ ( B @ ( A @ c_Arrow__Order__Mirabelle_Omkbot ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(350,axiom,
! [B: $i,A: $i] :
( ( ( A @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_Lattices_Obounded__lattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__bot__right_0) ).
thf(1540,plain,
! [B: $i,A: $i] :
( ( ( A @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_Lattices_Obounded__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(55,axiom,
! [B: $i,A: $i] : ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UNIV__I_0) ).
thf(869,plain,
! [B: $i,A: $i] : ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(444,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( E @ ( C @ c_Equiv__Relations_Oequiv ) ) )
| ~ ( E @ ( A @ ( A @ ( D @ ( B @ c_Pair ) ) ) @ ( A @ ( A @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equiv__class__eq__iff_1) ).
thf(1755,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( E @ ( C @ c_Equiv__Relations_Oequiv ) ) )
| ~ ( E @ ( A @ ( A @ ( D @ ( B @ c_Pair ) ) ) @ ( A @ ( A @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(16,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( D @ ( C @ ( D @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ ( D @ ( C @ ( A @ ( B @ c_Hilbert__Choice_Oinv__into ) ) ) @ c_FuncSet_Orestrict ) ) ) @ ( A @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_FuncSet_Ocompose ) ) ) ) ) )
= ( D @ ( D @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ ( D @ c_COMBI @ c_FuncSet_Orestrict ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_compose__id__inv__into_0) ).
thf(783,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( D @ ( C @ ( D @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ ( D @ ( C @ ( A @ ( B @ c_Hilbert__Choice_Oinv__into ) ) ) @ c_FuncSet_Orestrict ) ) ) @ ( A @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_FuncSet_Ocompose ) ) ) ) ) )
= ( D @ ( D @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ ( D @ c_COMBI @ c_FuncSet_Orestrict ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(663,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__assoc_0) ).
thf(2268,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[663]) ).
thf(105,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( E @ c_Fun_Oinj__on ) ) ) )
| ~ ( D @ ( A @ ( C @ ( E @ c_Set_Oimage ) ) ) @ ( D @ ( A @ ( B @ ( E @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( D @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__image__subset__iff_0) ).
thf(989,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( E @ c_Fun_Oinj__on ) ) ) )
| ~ ( D @ ( A @ ( C @ ( E @ c_Set_Oimage ) ) ) @ ( D @ ( A @ ( B @ ( E @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( D @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(50,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__mono_0) ).
thf(857,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(152,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( B @ ( tc_bool @ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( A @ c_in @ c_COMBC ) ) ) @ hAPP ) )
!= ( C @ ( tc_bool @ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( A @ c_in @ c_COMBC ) ) ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pred__equals__eq_0) ).
thf(1089,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( B @ ( tc_bool @ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( A @ c_in @ c_COMBC ) ) ) @ hAPP ) )
!= ( C @ ( tc_bool @ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( A @ c_in @ c_COMBC ) ) ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(214,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__absorb_0) ).
thf(1234,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(58,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) )
!= ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_singleton__inject_0) ).
thf(874,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) )
!= ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(616,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( B = C )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_0) ).
thf(2157,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( B = C )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[616]) ).
thf(597,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__assoc_0) ).
thf(2115,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).
thf(347,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_Equiv__Relations_Oquotient ) ) @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( D @ ( C @ ( B @ c_List_Osko__Equiv__Relations__XquotientE__1__1 ) ) ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_quotientE_1) ).
thf(1534,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_Equiv__Relations_Oquotient ) ) @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( D @ ( C @ ( B @ c_List_Osko__Equiv__Relations__XquotientE__1__1 ) ) ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(118,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__absorb1_0) ).
thf(1017,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(62,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( B @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( B @ ( C @ ( D @ ( C @ ( B @ ( A @ c_COMBK ) ) @ c_Set_Ovimage ) ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__const_0) ).
thf(884,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( B @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( B @ ( C @ ( D @ ( C @ ( B @ ( A @ c_COMBK ) ) @ c_Set_Ovimage ) ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(182,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( E @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( F @ ( B @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( F @ ( E @ ( D @ ( C @ c_SetInterval_Oord_OatLeastLessThan ) ) ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ord_OatLeastLessThan__iff_2) ).
thf(1160,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( E @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( F @ ( B @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( F @ ( E @ ( D @ ( C @ c_SetInterval_Oord_OatLeastLessThan ) ) ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(123,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( E @ ( tc_bool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Fun_Oinj__on ) ) ) )
| ~ ( D @ ( C @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( E @ ( D @ ( B @ c_Set_Oimage ) ) ) @ ( C @ ( B @ hAPP ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__image__mem__iff_1) ).
thf(1028,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( E @ ( tc_bool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Fun_Oinj__on ) ) ) )
| ~ ( D @ ( C @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( E @ ( D @ ( B @ c_Set_Oimage ) ) ) @ ( C @ ( B @ hAPP ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(268,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( E @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( C @ hAPP ) @ hBOOL )
| ~ ( B @ ( D @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( C @ ( B @ c_ATP__Linkup_Osko__Set__XbexCI__1__1 ) ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bexCI_0) ).
thf(1361,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( E @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( C @ hAPP ) @ hBOOL )
| ~ ( B @ ( D @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( C @ ( B @ c_ATP__Linkup_Osko__Set__XbexCI__1__1 ) ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(1,negated_conjecture,
~ ( c_Arrow__Order__Mirabelle_OLin @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( v_Lab____ @ c_COMBK ) ) @ ( v_F @ hAPP ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(753,plain,
~ ( c_Arrow__Order__Mirabelle_OLin @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( v_Lab____ @ c_COMBK ) ) @ ( v_F @ hAPP ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(313,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__subset__iff_0) ).
thf(1461,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(146,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_COMBK ) ) @ ( A @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) )
= ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UN__empty2_0) ).
thf(1075,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_COMBK ) ) @ ( A @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) )
= ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(741,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
= B )
| ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
!= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__triv_0) ).
thf(2455,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
= B )
| ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
!= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[741]) ).
thf(580,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__psubset__trans_0) ).
thf(2080,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).
thf(367,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert__iff_2) ).
thf(1584,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(206,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I6_J_0) ).
thf(1214,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(203,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__commute_0) ).
thf(1207,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(498,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_Complete__Lattice_OInf__class_OInf @ hAPP ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_InterD_0) ).
thf(1889,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_Complete__Lattice_OInf__class_OInf @ hAPP ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).
thf(294,axiom,
! [C: $i,B: $i,A: $i] : ( B @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__lower1_0) ).
thf(1419,plain,
! [C: $i,B: $i,A: $i] : ( B @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(743,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( E @ ( B @ ( A @ c_SetInterval_Oord_OgreaterThanLessThan ) ) ) @ ( C @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ord_OgreaterThanLessThan__iff_0) ).
thf(2460,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( E @ ( B @ ( A @ c_SetInterval_Oord_OgreaterThanLessThan ) ) ) @ ( C @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[743]) ).
thf(328,axiom,
v_F @ c_Arrow__Order__Mirabelle_Ounanimity,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_u_0) ).
thf(1493,plain,
v_F @ c_Arrow__Order__Mirabelle_Ounanimity,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(530,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__ge2_0) ).
thf(1964,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).
thf(521,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__supI2_0) ).
thf(1942,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).
thf(401,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__insert__absorb_0) ).
thf(1659,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(567,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_COMBC ) ) ) @ hAPP ) @ hAPP ) )
= ( E @ ( F @ ( A @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBC__def_0) ).
thf(2053,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_COMBC ) ) ) @ hAPP ) @ hAPP ) )
= ( E @ ( F @ ( A @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).
thf(479,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D = E )
| ~ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A = B )
| ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( E @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( E @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__below_14) ).
thf(1842,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D = E )
| ~ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A = B )
| ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( E @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( E @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).
thf(420,axiom,
! [B: $i,A: $i] :
~ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ex__in__conv_0) ).
thf(1700,plain,
! [B: $i,A: $i] :
~ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(519,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( D @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B = D )
| ~ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( B @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__below_1) ).
thf(1937,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( D @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B = D )
| ~ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( B @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).
thf(466,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( E @ tc_fun ) @ ( C @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) )
= ( tc_bool @ ( E @ tc_fun ) @ ( C @ ( D @ ( B @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( A @ ( D @ hAPP ) @ ( tc_bool @ ( E @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UN__insert_0) ).
thf(1810,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( E @ tc_fun ) @ ( C @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) )
= ( tc_bool @ ( E @ tc_fun ) @ ( C @ ( D @ ( B @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( A @ ( D @ hAPP ) @ ( tc_bool @ ( E @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).
thf(622,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( A @ ( B @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( C @ ( A @ ( B @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_HOL_Oord ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__fun__def_1) ).
thf(2172,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( A @ ( B @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( C @ ( A @ ( B @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_HOL_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[622]) ).
thf(380,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__ge1_0) ).
thf(1612,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(748,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D = E )
| ( A = B )
| ( D = B )
| ( E = A )
| ~ ( c_Arrow__Order__Mirabelle_OProf @ ( F @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( c_Arrow__Order__Mirabelle_OProf @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( E @ ( A @ ( D @ ( C @ ( F @ v_sko__local__X2__1 ) ) ) ) ) @ ( F @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( E @ ( D @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( E @ ( A @ ( D @ ( C @ ( F @ v_sko__local__X2__1 ) ) ) ) ) @ ( C @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( F @ ( v_F @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( E @ ( D @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( v_F @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_2_2) ).
thf(2472,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D = E )
| ( A = B )
| ( D = B )
| ( E = A )
| ~ ( c_Arrow__Order__Mirabelle_OProf @ ( F @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( c_Arrow__Order__Mirabelle_OProf @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( E @ ( A @ ( D @ ( C @ ( F @ v_sko__local__X2__1 ) ) ) ) ) @ ( F @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( E @ ( D @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( E @ ( A @ ( D @ ( C @ ( F @ v_sko__local__X2__1 ) ) ) ) ) @ ( C @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( F @ ( v_F @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( E @ ( D @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( v_F @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[748]) ).
thf(180,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__infE_0) ).
thf(1155,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(439,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__Int__distrib_0) ).
thf(1744,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(163,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ c_Arrow__Order__Mirabelle_Omkbot ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A = D )
| ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__mkbot_2) ).
thf(1114,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ c_Arrow__Order__Mirabelle_Omkbot ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A = D )
| ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(452,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ hAPP ) @ hBOOL )
| ~ ( A @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__predicate1D_0) ).
thf(1776,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ hAPP ) @ hBOOL )
| ~ ( A @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(241,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( F @ ( G @ c_Equiv__Relations_Oequiv ) ) )
| ~ ( C @ ( F @ ( G @ c_Equiv__Relations_Oquotient ) ) @ ( A @ ( tc_bool @ ( C @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( F @ ( G @ c_Equiv__Relations_Oquotient ) ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ ( D @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( E @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( F @ ( C @ ( C @ ( E @ ( D @ c_Pair ) ) ) @ ( C @ ( C @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_quotient__eqI_0) ).
thf(1297,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( F @ ( G @ c_Equiv__Relations_Oequiv ) ) )
| ~ ( C @ ( F @ ( G @ c_Equiv__Relations_Oquotient ) ) @ ( A @ ( tc_bool @ ( C @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( F @ ( G @ c_Equiv__Relations_Oquotient ) ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ ( D @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( E @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( F @ ( C @ ( C @ ( E @ ( D @ c_Pair ) ) ) @ ( C @ ( C @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(678,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__le_0) ).
thf(2304,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[678]) ).
thf(651,axiom,
tc_bool @ class_Lattices_Oupper__semilattice,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oupper__semilattice) ).
thf(2243,plain,
tc_bool @ class_Lattices_Oupper__semilattice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[651]) ).
thf(517,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ c_Set_OPow ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_PowD_0) ).
thf(1932,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ c_Set_OPow ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).
thf(461,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
= ( B @ ( C @ ( A @ ( tc_bool @ ( C @ ( C @ ( C @ c_fequal @ c_COMBC ) ) ) @ hAPP ) @ c_Collect ) @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__def_0) ).
thf(1799,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
= ( B @ ( C @ ( A @ ( tc_bool @ ( C @ ( C @ ( C @ c_fequal @ c_COMBC ) ) ) @ hAPP ) @ c_Collect ) @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(539,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert__iff_4) ).
thf(1984,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).
thf(111,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = A )
| ~ ( c_Arrow__Order__Mirabelle_OProf @ ( D @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( c_Arrow__Order__Mirabelle_OProf @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ ( B @ ( C @ ( D @ v_sko__local__X3__1 ) ) ) @ ( D @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( B @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ ( B @ ( C @ ( D @ v_sko__local__X3__1 ) ) ) @ ( C @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( v_F @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( B @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( v_F @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_3_2) ).
thf(1002,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = A )
| ~ ( c_Arrow__Order__Mirabelle_OProf @ ( D @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( c_Arrow__Order__Mirabelle_OProf @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ ( B @ ( C @ ( D @ v_sko__local__X3__1 ) ) ) @ ( D @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( B @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ ( B @ ( C @ ( D @ v_sko__local__X3__1 ) ) ) @ ( C @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( v_F @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( B @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( v_F @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(299,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D = E )
| ~ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A = B )
| ( A = E )
| ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( D @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__above_8) ).
thf(1429,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D = E )
| ~ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A = B )
| ( A = E )
| ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( D @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(427,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Int__assoc__eq_1) ).
thf(1715,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(429,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__irrefl_0) ).
thf(1720,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(739,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ hAPP ) @ hBOOL )
| ~ ( B @ ( D @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( C @ ( B @ c_ATP__Linkup_Osko__Set__XbexCI__1__1 ) ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bexCI_2) ).
thf(2450,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ hAPP ) @ hBOOL )
| ~ ( B @ ( D @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( C @ ( B @ c_ATP__Linkup_Osko__Set__XbexCI__1__1 ) ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[739]) ).
thf(369,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ ( B @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( B @ ( C @ ( D @ ( C @ ( B @ ( A @ c_COMBK ) ) @ c_Set_Ovimage ) ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__const_1) ).
thf(1588,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ ( B @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( B @ ( C @ ( D @ ( C @ ( B @ ( A @ c_COMBK ) ) @ c_Set_Ovimage ) ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(178,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__less_0) ).
thf(1150,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(321,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ~ ( B @ ( D @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_ATP__Linkup_Osko__Set__XbexI__1__1 ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bexI_1) ).
thf(1478,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ~ ( B @ ( D @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_ATP__Linkup_Osko__Set__XbexI__1__1 ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(221,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Lattices_Odistrib__lattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__inf__distrib2_0) ).
thf(1249,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Lattices_Odistrib__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(228,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I5_J_0) ).
thf(1266,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(713,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ( B = D )
| ( A = D )
| ~ ( c_Arrow__Order__Mirabelle_OProf @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( c_Arrow__Order__Mirabelle_OProf @ ( E @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( B @ ( A @ ( E @ ( C @ v_sko__local__X4__1 ) ) ) ) @ ( C @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( B @ ( A @ ( E @ ( C @ v_sko__local__X4__1 ) ) ) ) @ ( E @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( D @ ( B @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( v_F @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( D @ ( B @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( v_F @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_4_3) ).
thf(2387,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ( B = D )
| ( A = D )
| ~ ( c_Arrow__Order__Mirabelle_OProf @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( c_Arrow__Order__Mirabelle_OProf @ ( E @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( B @ ( A @ ( E @ ( C @ v_sko__local__X4__1 ) ) ) ) @ ( C @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( B @ ( A @ ( E @ ( C @ v_sko__local__X4__1 ) ) ) ) @ ( E @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( D @ ( B @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( v_F @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( D @ ( B @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( v_F @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[713]) ).
thf(213,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( B = D )
| ( ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
!= ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ c_Set_Oinsert ) ) @ ( D @ c_Set_Oinsert ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_1) ).
thf(1231,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( B = D )
| ( ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
!= ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ c_Set_Oinsert ) ) @ ( D @ c_Set_Oinsert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(404,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( G @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( G @ ( C @ hAPP ) @ ( F @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( F @ ( D @ hAPP ) @ hBOOL )
| ( tc_bool @ ( A @ tc_fun ) @ ( E @ ( C @ ( B @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( A @ ( E @ ( D @ ( C @ ( B @ c_ATP__Linkup_Osko__Complete__Lattice__Xbex__UN__1__3 ) ) ) ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bex__UN_3) ).
thf(1668,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( G @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( G @ ( C @ hAPP ) @ ( F @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( F @ ( D @ hAPP ) @ hBOOL )
| ( tc_bool @ ( A @ tc_fun ) @ ( E @ ( C @ ( B @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( A @ ( E @ ( D @ ( C @ ( B @ c_ATP__Linkup_Osko__Complete__Lattice__Xbex__UN__1__3 ) ) ) ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(535,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B = A )
| ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( B @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_notin__Lin__iff_0) ).
thf(1974,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B = A )
| ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( B @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).
thf(745,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Complete__Lattice_OInf__class_OInf @ hAPP ) )
= ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Inf__binary_0) ).
thf(2465,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Complete__Lattice_OInf__class_OInf @ hAPP ) )
= ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[745]) ).
thf(139,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( B @ c_Set_Oinsert ) ) @ ( A @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__inter__insert_0) ).
thf(1060,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( B @ c_Set_Oinsert ) ) @ ( A @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ c_Set_Oinsert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(103,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( E @ c_Equiv__Relations_Oequiv ) ) )
| ~ ( E @ ( D @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( C @ ( C @ ( D @ ( B @ c_Pair ) ) ) @ ( C @ ( C @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) )
!= ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__equiv__class_0) ).
thf(984,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( E @ c_Equiv__Relations_Oequiv ) ) )
| ~ ( E @ ( D @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( C @ ( C @ ( D @ ( B @ c_Pair ) ) ) @ ( C @ ( C @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) )
!= ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(72,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_DiffI_0) ).
thf(911,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(752,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( C @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_psubset__insert__iff_6) ).
thf(2482,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( C @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[752]) ).
thf(374,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Complete__Lattice_OInf__class_OInf @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Inter__lower_0) ).
thf(1599,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Complete__Lattice_OInf__class_OInf @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(537,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( A @ hAPP ) @ ( B @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( C @ ( B @ ( A @ c_Set_Ovimage ) ) ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__code_1) ).
thf(1979,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( A @ hAPP ) @ ( B @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( C @ ( B @ ( A @ c_Set_Ovimage ) ) ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).
thf(14,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__eqI_0) ).
thf(779,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(446,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
= C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__same_0) ).
thf(1759,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(283,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( B @ ( A @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
!= ( C @ ( D @ ( A @ c_Set_Oinsert ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__ident_0) ).
thf(1393,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( B @ ( A @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
!= ( C @ ( D @ ( A @ c_Set_Oinsert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(301,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I3_J_0) ).
thf(1434,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(468,axiom,
! [B: $i,A: $i] :
( ~ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( tc_bool @ ( B @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( A
= ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__empty_0) ).
thf(1814,plain,
! [B: $i,A: $i] :
( ~ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ ( tc_bool @ ( B @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( A
= ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
thf(636,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__absorb1_0) ).
thf(2208,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[636]) ).
thf(359,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_ATP__Linkup_Osko__Set__XballE__1__1 ) ) @ ( D @ hAPP ) @ hBOOL )
| ( B @ ( D @ hAPP ) @ hBOOL )
| ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ballE_1) ).
thf(1563,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_ATP__Linkup_Osko__Set__XballE__1__1 ) ) @ ( D @ hAPP ) @ hBOOL )
| ( B @ ( D @ hAPP ) @ hBOOL )
| ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(721,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
!= ( A @ ( D @ ( C @ ( B @ c_Set_Oimage ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__is__image_0) ).
thf(2408,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
!= ( A @ ( D @ ( C @ ( B @ c_Set_Oimage ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[721]) ).
thf(338,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__diff_0) ).
thf(1515,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(122,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ hAPP ) @ hBOOL )
| ~ ( D @ ( C @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf1I_0) ).
thf(1026,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ hAPP ) @ hBOOL )
| ~ ( D @ ( C @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(382,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ c_Arrow__Order__Mirabelle_OIIA )
| ~ ( c_Arrow__Order__Mirabelle_OProf @ ( D @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( c_Arrow__Order__Mirabelle_OProf @ ( E @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( B @ ( A @ v_sko__Arrow__Order__Mirabelle__XIIA__def__1 ) ) ) @ ( D @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( B @ ( A @ v_sko__Arrow__Order__Mirabelle__XIIA__def__1 ) ) ) @ ( E @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( C @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IIA__def_1) ).
thf(1616,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ c_Arrow__Order__Mirabelle_OIIA )
| ~ ( c_Arrow__Order__Mirabelle_OProf @ ( D @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( c_Arrow__Order__Mirabelle_OProf @ ( E @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( B @ ( A @ v_sko__Arrow__Order__Mirabelle__XIIA__def__1 ) ) ) @ ( D @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( B @ ( A @ v_sko__Arrow__Order__Mirabelle__XIIA__def__1 ) ) ) @ ( E @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( C @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(434,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__Diff1_0) ).
thf(1732,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(201,axiom,
! [B: $i,A: $i] :
( ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__empty__left_0) ).
thf(1202,plain,
! [B: $i,A: $i] :
( ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(20,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( F @ ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Fun_Ofun__upd ) ) ) ) )
= ( E @ ( D @ ( F @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__upd_0) ).
thf(792,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( F @ ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Fun_Ofun__upd ) ) ) ) )
= ( E @ ( D @ ( F @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(578,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Finite__Set_Ofold__graph ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fold__graph_OemptyI_0) ).
thf(2076,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Finite__Set_Ofold__graph ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).
thf(187,axiom,
! [B: $i,A: $i] :
( ( A @ c_Orderings_Otop__class_Otop @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Otop ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_top__greatest_0) ).
thf(1170,plain,
! [B: $i,A: $i] :
( ( A @ c_Orderings_Otop__class_Otop @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Otop ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(236,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__mono_0) ).
thf(1286,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(705,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ( B = D )
| ( A = D )
| ~ ( c_Arrow__Order__Mirabelle_OProf @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( c_Arrow__Order__Mirabelle_OProf @ ( E @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( B @ ( A @ ( E @ ( C @ v_sko__local__X4__1 ) ) ) ) @ ( C @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( B @ ( A @ ( E @ ( C @ v_sko__local__X4__1 ) ) ) ) @ ( E @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( D @ ( B @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( v_F @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( D @ ( B @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( v_F @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_4_1) ).
thf(2368,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ( B = D )
| ( A = D )
| ~ ( c_Arrow__Order__Mirabelle_OProf @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( c_Arrow__Order__Mirabelle_OProf @ ( E @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( B @ ( A @ ( E @ ( C @ v_sko__local__X4__1 ) ) ) ) @ ( C @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( B @ ( A @ ( E @ ( C @ v_sko__local__X4__1 ) ) ) ) @ ( E @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( D @ ( B @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( v_F @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( D @ ( B @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( v_F @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[705]) ).
thf(316,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( D @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__supE_1) ).
thf(1466,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( D @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(144,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Complete__Lattice_OSup__class_OSup @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Union__upper_0) ).
thf(1071,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Complete__Lattice_OSup__class_OSup @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(11,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_FuncSet_Ocompose ) ) ) ) ) )
= ( F @ ( D @ ( A @ ( D @ ( F @ ( E @ ( C @ ( B @ c_COMBB ) ) ) ) @ c_FuncSet_Orestrict ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_compose__def_0) ).
thf(773,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_FuncSet_Ocompose ) ) ) ) ) )
= ( F @ ( D @ ( A @ ( D @ ( F @ ( E @ ( C @ ( B @ c_COMBB ) ) ) ) @ c_FuncSet_Orestrict ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(21,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
= ( C @ ( B @ ( A @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__absorb2_0) ).
thf(794,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
= ( C @ ( B @ ( A @ c_Set_Oinsert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(611,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( E @ ( C @ c_Equiv__Relations_Oequiv ) ) )
| ~ ( E @ ( A @ ( A @ ( B @ ( D @ c_Pair ) ) ) @ ( A @ ( A @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equiv__class__eq__iff_2) ).
thf(2144,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( E @ ( C @ c_Equiv__Relations_Oequiv ) ) )
| ~ ( E @ ( A @ ( A @ ( B @ ( D @ c_Pair ) ) ) @ ( A @ ( A @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).
thf(172,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).
thf(1135,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(673,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( D @ ( C @ c_SetInterval_Oord_OatMost ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ord_OatMost__iff_1) ).
thf(2292,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( D @ ( C @ c_SetInterval_Oord_OatMost ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[673]) ).
thf(411,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
= ( A @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oimage ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__is__image_1) ).
thf(1680,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
= ( A @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oimage ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(419,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__trans_0) ).
thf(1698,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(372,axiom,
! [A: $i] :
( ~ ( c_Arrow__Order__Mirabelle_OLin @ ( A @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( c_Arrow__Order__Mirabelle_OLin @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ c_Relation_Oconverse ) ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_converse__in__Lin_1) ).
thf(1595,plain,
! [A: $i] :
( ~ ( c_Arrow__Order__Mirabelle_OLin @ ( A @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( c_Arrow__Order__Mirabelle_OLin @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ c_Relation_Oconverse ) ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(388,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__Int__distrib2_0) ).
thf(1631,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(432,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__idem_0) ).
thf(1727,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(336,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_COMBK ) ) @ hAPP ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBK__def_0) ).
thf(1510,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_COMBK ) ) @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(448,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ ( B @ c_Set_Oimage ) ) ) @ ( E @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( C @ ( A @ ( B @ c_Set_Oimage ) ) ) @ ( F @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( E = F )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) )
!= ( F @ ( D @ ( C @ ( B @ ( A @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inv__into__injective_0) ).
thf(1764,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ ( B @ c_Set_Oimage ) ) ) @ ( E @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( C @ ( A @ ( B @ c_Set_Oimage ) ) ) @ ( F @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( E = F )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) )
!= ( F @ ( D @ ( C @ ( B @ ( A @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).
thf(723,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( D @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D = B )
| ~ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A = D )
| ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__below_9) ).
thf(2413,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( D @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D = B )
| ~ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A = D )
| ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[723]) ).
thf(656,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_COMBK ) ) @ hAPP ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ATP__Linkup_OCOMBK__def_0) ).
thf(2253,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_COMBK ) ) @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[656]) ).
thf(666,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insertCI_0) ).
thf(2275,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[666]) ).
thf(559,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( F @ ( C @ c_Product__Type_OSigma ) ) ) @ ( D @ ( A @ ( E @ ( B @ c_Pair ) ) ) @ ( D @ ( A @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SigmaD1_0) ).
thf(2033,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( F @ ( C @ c_Product__Type_OSigma ) ) ) @ ( D @ ( A @ ( E @ ( B @ c_Pair ) ) ) @ ( D @ ( A @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).
thf(613,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_Set_Oinsert ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B = D )
| ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insertE_0) ).
thf(2149,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_Set_Oinsert ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B = D )
| ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).
thf(353,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( c_Arrow__Order__Mirabelle_OProf @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( c_Arrow__Order__Mirabelle_OProf @ ( D @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( A @ ( D @ ( C @ v_sko__local__X3__1 ) ) ) @ ( C @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( A @ ( D @ ( C @ v_sko__local__X3__1 ) ) ) @ ( D @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( B @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( v_F @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( B @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( v_F @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_3_3) ).
thf(1548,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( c_Arrow__Order__Mirabelle_OProf @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( c_Arrow__Order__Mirabelle_OProf @ ( D @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( A @ ( D @ ( C @ v_sko__local__X3__1 ) ) ) @ ( C @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( A @ ( D @ ( C @ v_sko__local__X3__1 ) ) ) @ ( D @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( B @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( v_F @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( B @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( v_F @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(515,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( E @ ( E @ ( tc_bool @ ( F @ tc_fun ) @ ( I @ c_COMBK ) ) @ ( A @ c_FuncSet_OPi ) ) ) @ ( D @ ( F @ ( E @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( G @ ( F @ ( F @ ( tc_bool @ ( G @ tc_fun ) @ ( J @ c_COMBK ) ) @ ( I @ c_FuncSet_OPi ) ) ) @ ( C @ ( G @ ( F @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( H @ ( G @ ( G @ ( tc_bool @ ( H @ tc_fun ) @ ( K @ c_COMBK ) ) @ ( J @ c_FuncSet_OPi ) ) ) @ ( B @ ( H @ ( G @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( H @ ( G @ ( E @ ( G @ ( F @ ( E @ ( D @ ( C @ ( A @ c_FuncSet_Ocompose ) ) ) ) ) @ ( B @ ( A @ c_FuncSet_Ocompose ) ) ) ) ) )
= ( H @ ( F @ ( E @ ( D @ ( H @ ( G @ ( F @ ( C @ ( B @ ( I @ c_FuncSet_Ocompose ) ) ) ) ) @ ( A @ c_FuncSet_Ocompose ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_compose__assoc_0) ).
thf(1927,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( E @ ( E @ ( tc_bool @ ( F @ tc_fun ) @ ( I @ c_COMBK ) ) @ ( A @ c_FuncSet_OPi ) ) ) @ ( D @ ( F @ ( E @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( G @ ( F @ ( F @ ( tc_bool @ ( G @ tc_fun ) @ ( J @ c_COMBK ) ) @ ( I @ c_FuncSet_OPi ) ) ) @ ( C @ ( G @ ( F @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( H @ ( G @ ( G @ ( tc_bool @ ( H @ tc_fun ) @ ( K @ c_COMBK ) ) @ ( J @ c_FuncSet_OPi ) ) ) @ ( B @ ( H @ ( G @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( H @ ( G @ ( E @ ( G @ ( F @ ( E @ ( D @ ( C @ ( A @ c_FuncSet_Ocompose ) ) ) ) ) @ ( B @ ( A @ c_FuncSet_Ocompose ) ) ) ) ) )
= ( H @ ( F @ ( E @ ( D @ ( H @ ( G @ ( F @ ( C @ ( B @ ( I @ c_FuncSet_Ocompose ) ) ) ) ) @ ( A @ c_FuncSet_Ocompose ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).
thf(35,axiom,
tc_nat @ class_Lattices_Odistrib__lattice,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Lattices_Odistrib__lattice) ).
thf(819,plain,
tc_nat @ class_Lattices_Odistrib__lattice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(113,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( D @ ( C @ c_ATP__Linkup_Osko__Set__XballE__1__1 ) ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( D @ hAPP ) @ hBOOL )
| ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ballE_0) ).
thf(1007,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( D @ ( C @ c_ATP__Linkup_Osko__Set__XballE__1__1 ) ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( D @ hAPP ) @ hBOOL )
| ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(565,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( C @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__single__insert_0) ).
thf(2048,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( C @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).
thf(496,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( C @ c_Equiv__Relations_Oquotient ) ) @ ( A @ ( tc_bool @ ( D @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A
= ( D @ ( D @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ ( B @ ( A @ ( C @ c_List_Osko__Equiv__Relations__XquotientE__1__1 ) ) ) @ c_Set_Oinsert ) ) @ ( B @ c_Relation_OImage ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_quotientE_0) ).
thf(1884,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( C @ c_Equiv__Relations_Oquotient ) ) @ ( A @ ( tc_bool @ ( D @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A
= ( D @ ( D @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ ( B @ ( A @ ( C @ c_List_Osko__Equiv__Relations__XquotientE__1__1 ) ) ) @ c_Set_Oinsert ) ) @ ( B @ c_Relation_OImage ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).
thf(281,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ c_Complete__Lattice_OSup__class_OSup @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sup__upper_0) ).
thf(1389,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ c_Complete__Lattice_OSup__class_OSup @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(168,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__left__commute_0) ).
thf(1125,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(397,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__le__not__le_1) ).
thf(1652,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(552,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ c_COMBI @ hAPP ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBI__def_0) ).
thf(2016,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_COMBI @ hAPP ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).
thf(280,axiom,
! [B: $i,A: $i] : ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__UNIV_0) ).
thf(1388,plain,
! [B: $i,A: $i] : ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(717,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_Orderings_Obot__class_Obot ) )
| ( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
!= ( A @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Lattices_Obounded__lattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__eq__bot__eq1_0) ).
thf(2398,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_Orderings_Obot__class_Obot ) )
| ( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
!= ( A @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Lattices_Obounded__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[717]) ).
thf(341,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( B @ ( D @ ( A @ c_Pair ) ) ) @ ( B @ ( B @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( C @ ( E @ c_Equiv__Relations_Oequiv ) ) )
| ~ ( E @ ( A @ ( B @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( D @ ( B @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( B @ ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ c_Equiv__Relations_Oquotient ) ) )
!= ( B @ ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ c_Equiv__Relations_Oquotient ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__equiv__class__iff2_0) ).
thf(1520,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( B @ ( D @ ( A @ c_Pair ) ) ) @ ( B @ ( B @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( C @ ( E @ c_Equiv__Relations_Oequiv ) ) )
| ~ ( E @ ( A @ ( B @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( D @ ( B @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( B @ ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ c_Equiv__Relations_Oquotient ) ) )
!= ( B @ ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ c_Equiv__Relations_Oquotient ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(607,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = E )
| ~ ( B @ ( F @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( C @ ( D @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_COMBK ) ) @ ( A @ c_Product__Type_OSigma ) ) ) )
!= ( C @ ( D @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_COMBK ) ) @ ( E @ c_Product__Type_OSigma ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Times__eq__cancel2_0) ).
thf(2134,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = E )
| ~ ( B @ ( F @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( C @ ( D @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_COMBK ) ) @ ( A @ c_Product__Type_OSigma ) ) ) )
!= ( C @ ( D @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_COMBK ) ) @ ( E @ c_Product__Type_OSigma ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).
thf(628,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( E @ ( D @ ( B @ c_Set_Oimage ) ) ) @ ( C @ ( B @ hAPP ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_imageI_0) ).
thf(2188,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( E @ ( D @ ( B @ c_Set_Oimage ) ) ) @ ( C @ ( B @ hAPP ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[628]) ).
thf(10,axiom,
! [B: $i,A: $i] : ( A @ ( A @ ( B @ ( A @ c_COMBI @ c_Fun_Oinj__on ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__id2_0) ).
thf(772,plain,
! [B: $i,A: $i] : ( A @ ( A @ ( B @ ( A @ c_COMBI @ c_Fun_Oinj__on ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(715,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( C @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( F @ hAPP ) @ ( D @ ( B @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( F @ ( E @ c_Product__Type_OSigma ) ) ) @ ( B @ ( A @ ( D @ ( C @ c_Pair ) ) ) @ ( B @ ( A @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SigmaI_0) ).
thf(2393,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( C @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( F @ hAPP ) @ ( D @ ( B @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( F @ ( E @ c_Product__Type_OSigma ) ) ) @ ( B @ ( A @ ( D @ ( C @ c_Pair ) ) ) @ ( B @ ( A @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[715]) ).
thf(443,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ~ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) )
!= ( D @ ( C @ ( E @ ( A @ c_Set_Oimage ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__image__eq__iff_0) ).
thf(1752,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ~ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) )
!= ( D @ ( C @ ( E @ ( A @ c_Set_Oimage ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(224,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( C @ ( D @ ( B @ c_Pair ) ) ) @ ( C @ ( C @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( E @ c_Equiv__Relations_Oequiv ) ) )
| ~ ( E @ ( B @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( D @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) )
!= ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__equiv__class__iff_0) ).
thf(1256,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( C @ ( D @ ( B @ c_Pair ) ) ) @ ( C @ ( C @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( E @ c_Equiv__Relations_Oequiv ) ) )
| ~ ( E @ ( B @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( D @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) )
!= ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(326,axiom,
! [B: $i,A: $i] :
( ( ( A @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Lattices_Obounded__lattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__bot__right_0) ).
thf(1488,plain,
! [B: $i,A: $i] :
( ( ( A @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Lattices_Obounded__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(174,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( B @ ( C @ c_ATP__Linkup_Osko__Complete__Lattice__XUnion__disjoint__1__1 ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Complete__Lattice_OSup__class_OSup @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Union__disjoint_1) ).
thf(1139,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( B @ ( C @ c_ATP__Linkup_Osko__Complete__Lattice__XUnion__disjoint__1__1 ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Complete__Lattice_OSup__class_OSup @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(456,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( E @ c_Fun_Oinj__on ) ) ) )
| ~ ( D @ ( A @ ( C @ ( E @ c_Set_Oimage ) ) ) @ ( B @ ( E @ hAPP ) @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__image__mem__iff_0) ).
thf(1786,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( E @ c_Fun_Oinj__on ) ) ) )
| ~ ( D @ ( A @ ( C @ ( E @ c_Set_Oimage ) ) ) @ ( B @ ( E @ hAPP ) @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).
thf(83,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( I @ ( C @ ( H @ ( G @ ( F @ ( E @ ( A @ ( D @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
| ( ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ hAPP ) )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OSup__empty_0) ).
thf(936,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( I @ ( C @ ( H @ ( G @ ( F @ ( E @ ( A @ ( D @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
| ( ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ hAPP ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(641,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ c_Arrow__Order__Mirabelle_OIIA )
| ~ ( c_Arrow__Order__Mirabelle_OProf @ ( E @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( c_Arrow__Order__Mirabelle_OProf @ ( D @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( E @ ( B @ ( A @ v_sko__Arrow__Order__Mirabelle__XIIA__def__1 ) ) ) @ ( E @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( E @ ( B @ ( A @ v_sko__Arrow__Order__Mirabelle__XIIA__def__1 ) ) ) @ ( D @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( C @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IIA__def_2) ).
thf(2220,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ c_Arrow__Order__Mirabelle_OIIA )
| ~ ( c_Arrow__Order__Mirabelle_OProf @ ( E @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( c_Arrow__Order__Mirabelle_OProf @ ( D @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( E @ ( B @ ( A @ v_sko__Arrow__Order__Mirabelle__XIIA__def__1 ) ) ) @ ( E @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( E @ ( B @ ( A @ v_sko__Arrow__Order__Mirabelle__XIIA__def__1 ) ) ) @ ( D @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( C @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[641]) ).
thf(557,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( E @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Ovimage ) ) ) )
= ( D @ ( E @ ( C @ ( A @ c_Set_Ovimage ) ) ) @ ( D @ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Ovimage ) ) ) @ ( tc_bool @ ( E @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__insert_0) ).
thf(2029,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( E @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Ovimage ) ) ) )
= ( D @ ( E @ ( C @ ( A @ c_Set_Ovimage ) ) ) @ ( D @ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Ovimage ) ) ) @ ( tc_bool @ ( E @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).
thf(247,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mem__def_0) ).
thf(1312,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(18,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( D @ ( A @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_FuncSet_Ocompose ) ) ) ) ) @ c_Set_Oimage ) ) ) )
= ( F @ ( E @ ( E @ ( D @ ( A @ ( C @ c_Set_Oimage ) ) ) @ ( B @ c_Set_Oimage ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_surj__compose_0) ).
thf(787,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( D @ ( A @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_FuncSet_Ocompose ) ) ) ) ) @ c_Set_Oimage ) ) ) )
= ( F @ ( E @ ( E @ ( D @ ( A @ ( C @ c_Set_Oimage ) ) ) @ ( B @ c_Set_Oimage ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(487,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_DiffE_0) ).
thf(1865,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).
thf(390,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( B @ ( E @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__Un_1) ).
thf(1635,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( B @ ( E @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(619,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( A @ ( C @ ( E @ ( D @ c_FuncSet_Osko__FuncSet__Xrestrict__in__funcset__1__1 ) ) ) ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( A @ ( tc_bool @ ( B @ tc_fun ) @ ( E @ c_COMBK ) ) @ ( D @ c_FuncSet_OPi ) ) ) @ ( B @ ( A @ ( D @ ( C @ c_FuncSet_Orestrict ) ) ) @ ( B @ ( A @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_restrict__in__funcset_0) ).
thf(2166,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( A @ ( C @ ( E @ ( D @ c_FuncSet_Osko__FuncSet__Xrestrict__in__funcset__1__1 ) ) ) ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( A @ ( tc_bool @ ( B @ tc_fun ) @ ( E @ c_COMBK ) ) @ ( D @ c_FuncSet_OPi ) ) ) @ ( B @ ( A @ ( D @ ( C @ c_FuncSet_Orestrict ) ) ) @ ( B @ ( A @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[619]) ).
thf(315,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UN__extend__simps_I3_J_0) ).
thf(1464,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(684,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( D @ ( B @ c_Set_Oinsert ) ) @ ( A @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__mono_0) ).
thf(2319,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( D @ ( B @ c_Set_Oinsert ) ) @ ( A @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[684]) ).
thf(408,axiom,
tc_bool @ class_Complete__Lattice_Ocomplete__lattice,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Complete__Lattice_Ocomplete__lattice) ).
thf(1675,plain,
tc_bool @ class_Complete__Lattice_Ocomplete__lattice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(230,axiom,
tc_bool @ class_Orderings_Obot,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Obot) ).
thf(1271,plain,
tc_bool @ class_Orderings_Obot,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(273,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ ( E @ ( D @ c_FuncSet_Osko__FuncSet__XPi__I__1__1 ) ) ) ) @ ( E @ hAPP ) @ ( B @ ( A @ ( C @ ( E @ ( D @ c_FuncSet_Osko__FuncSet__XPi__I__1__1 ) ) ) ) @ ( C @ hAPP ) @ ( B @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( E @ ( D @ c_FuncSet_OPi ) ) ) @ ( C @ ( B @ ( A @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Pi__I_1) ).
thf(1371,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ ( E @ ( D @ c_FuncSet_Osko__FuncSet__XPi__I__1__1 ) ) ) ) @ ( E @ hAPP ) @ ( B @ ( A @ ( C @ ( E @ ( D @ c_FuncSet_Osko__FuncSet__XPi__I__1__1 ) ) ) ) @ ( C @ hAPP ) @ ( B @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( E @ ( D @ c_FuncSet_OPi ) ) ) @ ( C @ ( B @ ( A @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(216,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__left__commute_0) ).
thf(1239,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(544,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( A = E )
| ( ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
!= ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ c_Set_Oinsert ) ) @ ( D @ c_Set_Oinsert ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_0) ).
thf(1997,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( A = E )
| ( ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
!= ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ c_Set_Oinsert ) ) @ ( D @ c_Set_Oinsert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).
thf(568,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= C )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__absorb2_0) ).
thf(2055,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= C )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).
thf(153,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( C @ ( B @ c_ATP__Linkup_Osko__Complete__Lattice__XInterI__1__1 ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Complete__Lattice_OInf__class_OInf @ hAPP ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_InterI_0) ).
thf(1092,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( C @ ( B @ c_ATP__Linkup_Osko__Complete__Lattice__XInterI__1__1 ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Complete__Lattice_OInf__class_OInf @ hAPP ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(501,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( B = C )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__antisym_0) ).
thf(1897,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( B = C )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).
thf(27,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( A @ c_COMBI @ c_Set_Ovimage ) ) ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__ident_0) ).
thf(804,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( A @ c_COMBI @ c_Set_Ovimage ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(696,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( H @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( G @ ( F @ ( H @ ( B @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( G @ ( F @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ tc_fun ) @ ( C @ ( B @ ( A @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SUP2__iff_2) ).
thf(2346,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( H @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( G @ ( F @ ( H @ ( B @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( G @ ( F @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ tc_fun ) @ ( C @ ( B @ ( A @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[696]) ).
thf(599,axiom,
tc_bool @ class_HOL_Oord,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__HOL_Oord) ).
thf(2119,plain,
tc_bool @ class_HOL_Oord,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).
thf(582,axiom,
! [B: $i,A: $i] :
( ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__empty__left_0) ).
thf(2084,plain,
! [B: $i,A: $i] :
( ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).
thf(500,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
!= ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Int__assoc__eq_0) ).
thf(1894,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
!= ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).
thf(164,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( tc_bool @ ( A @ ( A @ ( A @ c_fequal @ c_COMBC ) ) ) @ hAPP ) @ c_Collect ) )
= ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_singleton__conv_0) ).
thf(1117,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( tc_bool @ ( A @ ( A @ ( A @ c_fequal @ c_COMBC ) ) ) @ hAPP ) @ c_Collect ) )
= ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(115,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ ( A @ c_COMBK ) ) @ c_Set_Oimage ) ) ) )
= ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__constant__conv_0) ).
thf(1011,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ ( A @ c_COMBK ) ) @ c_Set_Oimage ) ) ) )
= ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(263,axiom,
! [C: $i,B: $i,A: $i] :
( ( C = B )
| ( B @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neqE_0) ).
thf(1349,plain,
! [C: $i,B: $i,A: $i] :
( ( C = B )
| ( B @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(430,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = A )
| ~ ( c_Arrow__Order__Mirabelle_OProf @ ( D @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( c_Arrow__Order__Mirabelle_OProf @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( B @ ( C @ ( D @ v_sko__local__X3__1 ) ) ) @ ( D @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( B @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( B @ ( C @ ( D @ v_sko__local__X3__1 ) ) ) @ ( C @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( v_F @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( B @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( v_F @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_3_0) ).
thf(1722,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = A )
| ~ ( c_Arrow__Order__Mirabelle_OProf @ ( D @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( c_Arrow__Order__Mirabelle_OProf @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( B @ ( C @ ( D @ v_sko__local__X3__1 ) ) ) @ ( D @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( B @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( B @ ( C @ ( D @ v_sko__local__X3__1 ) ) ) @ ( C @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( v_F @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( B @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( v_F @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(416,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = C )
| ~ ( F @ ( D @ ( E @ ( A @ c_Fun_Oinj__on ) ) ) )
| ~ ( E @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( C @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( B @ ( A @ hAPP ) )
!= ( C @ ( A @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__def_0) ).
thf(1690,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = C )
| ~ ( F @ ( D @ ( E @ ( A @ c_Fun_Oinj__on ) ) ) )
| ~ ( E @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( C @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( B @ ( A @ hAPP ) )
!= ( C @ ( A @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(6,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( C @ ( B @ ( E @ ( D @ ( B @ ( A @ c_FuncSet_Orestrict ) ) ) @ c_Fun_Obij__betw ) ) ) ) )
| ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Obij__betw ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bij__betw__restrict__eq_0) ).
thf(764,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( C @ ( B @ ( E @ ( D @ ( B @ ( A @ c_FuncSet_Orestrict ) ) ) @ c_Fun_Obij__betw ) ) ) ) )
| ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Obij__betw ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(101,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( C @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_psubset__insert__iff_4) ).
thf(979,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( C @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(702,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( B @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_Relation_OImage ) ) ) )
= ( E @ ( B @ ( D @ ( A @ c_Relation_OImage ) ) ) @ ( E @ ( B @ ( C @ ( A @ c_Relation_OImage ) ) ) @ ( tc_bool @ ( E @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Image__Un_0) ).
thf(2361,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( B @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_Relation_OImage ) ) ) )
= ( E @ ( B @ ( D @ ( A @ c_Relation_OImage ) ) ) @ ( E @ ( B @ ( C @ ( A @ c_Relation_OImage ) ) ) @ ( tc_bool @ ( E @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[702]) ).
thf(681,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( A @ ( B @ ( C @ ( D @ c_Pair ) ) ) @ ( A @ ( B @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( B @ ( E @ c_Relation_Oconverse ) ) @ ( B @ ( A @ ( D @ ( C @ c_Pair ) ) ) @ ( B @ ( A @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_converse__iff_1) ).
thf(2311,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( A @ ( B @ ( C @ ( D @ c_Pair ) ) ) @ ( A @ ( B @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( B @ ( E @ c_Relation_Oconverse ) ) @ ( B @ ( A @ ( D @ ( C @ c_Pair ) ) ) @ ( B @ ( A @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[681]) ).
thf(483,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__inf__absorb_0) ).
thf(1853,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).
thf(289,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A = D )
| ~ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A = B )
| ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__above_12) ).
thf(1408,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A = D )
| ~ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A = B )
| ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(658,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__iff_2) ).
thf(2257,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[658]) ).
thf(108,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( tc_bool @ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( A @ c_in @ c_COMBC ) ) ) @ hAPP ) @ ( B @ ( tc_bool @ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( A @ c_in @ c_COMBC ) ) ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pred__subset__eq_0) ).
thf(996,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( tc_bool @ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( A @ c_in @ c_COMBC ) ) ) @ hAPP ) @ ( B @ ( tc_bool @ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( A @ c_in @ c_COMBC ) ) ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(670,axiom,
! [B: $i,A: $i] :
( ( ( A @ c_Orderings_Otop__class_Otop @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_Lattices_Obounded__lattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__top__right_0) ).
thf(2284,plain,
! [B: $i,A: $i] :
( ( ( A @ c_Orderings_Otop__class_Otop @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_Lattices_Obounded__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[670]) ).
thf(653,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
= ( B @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__is__Un_0) ).
thf(2246,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
= ( B @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[653]) ).
thf(376,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( B @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_Inductive_Ocomplete__lattice__class_Olfp ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lfp__lowerbound_0) ).
thf(1603,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( B @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_Inductive_Ocomplete__lattice__class_Olfp ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(131,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( C @ hAPP ) @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( A @ ( D @ ( C @ c_Set_Ovimage ) ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__eq_1) ).
thf(1043,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( C @ hAPP ) @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( A @ ( D @ ( C @ c_Set_Ovimage ) ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(462,axiom,
! [B: $i,A: $i] :
( ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__UNIV_0) ).
thf(1801,plain,
! [B: $i,A: $i] :
( ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).
thf(362,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__iff_2) ).
thf(1571,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(275,axiom,
! [B: $i,A: $i] :
~ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bot1E_0) ).
thf(1376,plain,
! [B: $i,A: $i] :
~ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(303,axiom,
! [B: $i,A: $i] :
~ ( B @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_psubset__eq_1) ).
thf(1439,plain,
! [B: $i,A: $i] :
~ ( B @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(632,axiom,
! [B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__Diff_0) ).
thf(2197,plain,
! [B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[632]) ).
thf(532,axiom,
! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_fequal @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ATP__Linkup_Oequal__imp__fequal_0) ).
thf(1969,plain,
! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_fequal @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).
thf(245,axiom,
! [C: $i,B: $i,A: $i] :
( ( C = B )
| ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I12_J_0) ).
thf(1307,plain,
! [C: $i,B: $i,A: $i] :
( ( C = B )
| ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(573,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__le_1) ).
thf(2065,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).
thf(189,axiom,
! [B: $i,A: $i] :
~ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__iff_0) ).
thf(1175,plain,
! [B: $i,A: $i] :
~ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(626,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( E @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_Set_Oinsert ) ) )
= ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__image_0) ).
thf(2182,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( E @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_Set_Oinsert ) ) )
= ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).
thf(695,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D = E )
| ~ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A = B )
| ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( D @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B = E )
| ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__above_10) ).
thf(2343,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D = E )
| ~ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A = B )
| ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( D @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B = E )
| ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[695]) ).
thf(33,axiom,
tc_nat @ class_Orderings_Oorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).
thf(816,plain,
tc_nat @ class_Orderings_Oorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(486,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( ( E @ ( B @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_Set_Oimage ) ) ) )
= ( E @ ( B @ ( D @ ( A @ c_Set_Oimage ) ) ) @ ( E @ ( B @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( E @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__Int_0) ).
thf(1862,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( ( E @ ( B @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_Set_Oimage ) ) ) )
= ( E @ ( B @ ( D @ ( A @ c_Set_Oimage ) ) ) @ ( E @ ( B @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( E @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).
thf(95,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( C @ hAPP ) @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( A @ ( D @ ( C @ c_Set_Ovimage ) ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimageI2_0) ).
thf(964,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( C @ hAPP ) @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( A @ ( D @ ( C @ c_Set_Ovimage ) ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(356,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( ( D @ ( C @ ( B @ ( A @ ( B @ ( A @ hAPP ) @ c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__2 ) ) ) ) )
!= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_range__ex1__eq_3) ).
thf(1556,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( ( D @ ( C @ ( B @ ( A @ ( B @ ( A @ hAPP ) @ c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__2 ) ) ) ) )
!= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(239,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( G @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_FuncSet_Ocompose ) ) ) ) ) @ hAPP ) )
= ( G @ ( C @ hAPP ) @ ( B @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_compose__eq_0) ).
thf(1293,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( G @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_FuncSet_Ocompose ) ) ) ) ) @ hAPP ) )
= ( G @ ( C @ hAPP ) @ ( B @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(526,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( B = C )
| ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__neq__trans_0) ).
thf(1952,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( B = C )
| ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).
thf(162,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__Un_0) ).
thf(1112,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(64,axiom,
c_Arrow__Order__Mirabelle_OLin @ ( v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1 @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linear__alt_0) ).
thf(890,plain,
c_Arrow__Order__Mirabelle_OLin @ ( v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1 @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(625,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_Set_Ovimage ) ) ) @ ( A @ c_Set_Oimage ) ) ) )
= ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( tc_bool @ ( D @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__vimage__eq_0) ).
thf(2180,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_Set_Ovimage ) ) ) @ ( A @ c_Set_Oimage ) ) ) )
= ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( tc_bool @ ( D @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).
thf(493,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ ( E @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( D @ hAPP ) @ ( C @ ( B @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_HOL_Oord ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__funD_0) ).
thf(1877,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ ( E @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( D @ hAPP ) @ ( C @ ( B @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_HOL_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).
thf(318,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( D @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert__iff_1) ).
thf(1471,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( D @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(555,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf1E_1) ).
thf(2025,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).
thf(148,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ ( B @ c_Fun_Oinj__on ) ) ) )
| ~ ( A @ ( E @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( E @ ( B @ hAPP ) @ ( D @ ( C @ ( B @ ( A @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) )
= E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inv__into__f__f_0) ).
thf(1080,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ ( B @ c_Fun_Oinj__on ) ) ) )
| ~ ( A @ ( E @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( E @ ( B @ hAPP ) @ ( D @ ( C @ ( B @ ( A @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) )
= E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(24,axiom,
tc_nat @ class_Lattices_Olattice,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Lattices_Olattice) ).
thf(799,plain,
tc_nat @ class_Lattices_Olattice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(507,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ ( C @ ( E @ c_Set_Oimage ) ) ) @ ( B @ ( E @ hAPP ) @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__image__eqI_0) ).
thf(1909,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ ( C @ ( E @ c_Set_Oimage ) ) ) @ ( B @ ( E @ hAPP ) @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).
thf(183,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( D @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_DiffE_1) ).
thf(1162,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( D @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(477,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__left__absorb_0) ).
thf(1838,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).
thf(253,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D = E )
| ( A = B )
| ~ ( c_Arrow__Order__Mirabelle_OProf @ ( F @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( c_Arrow__Order__Mirabelle_OProf @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( E @ ( A @ ( D @ ( C @ ( F @ v_sko__local__Xpairwise__neutrality__1 ) ) ) ) ) @ ( F @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( E @ ( D @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( E @ ( A @ ( D @ ( C @ ( F @ v_sko__local__Xpairwise__neutrality__1 ) ) ) ) ) @ ( C @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( F @ ( v_F @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( E @ ( D @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( v_F @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pairwise__neutrality_2) ).
thf(1325,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D = E )
| ( A = B )
| ~ ( c_Arrow__Order__Mirabelle_OProf @ ( F @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( c_Arrow__Order__Mirabelle_OProf @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( E @ ( A @ ( D @ ( C @ ( F @ v_sko__local__Xpairwise__neutrality__1 ) ) ) ) ) @ ( F @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( E @ ( D @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( E @ ( A @ ( D @ ( C @ ( F @ v_sko__local__Xpairwise__neutrality__1 ) ) ) ) ) @ ( C @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( F @ ( v_F @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( E @ ( D @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( v_F @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(190,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I10_J_0) ).
thf(1177,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(277,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( A @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_COMBK ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UN__constant_0) ).
thf(1381,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( A @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_COMBK ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(725,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__inf__iff_0) ).
thf(2418,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[725]) ).
thf(284,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_fequal @ hAPP ) @ hAPP ) @ hBOOL )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ATP__Linkup_Ofequal__imp__equal_0) ).
thf(1396,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_fequal @ hAPP ) @ hAPP ) @ hBOOL )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(698,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Diff__cancel2_0) ).
thf(2350,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[698]) ).
thf(718,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__infI2_0) ).
thf(2401,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[718]) ).
thf(8,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( E @ ( B @ ( A @ c_Fun_Obij__betw ) ) ) ) )
| ( D @ ( C @ ( E @ ( B @ ( D @ ( C @ ( B @ ( A @ c_FuncSet_Orestrict ) ) ) @ c_Fun_Obij__betw ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bij__betw__restrict__eq_1) ).
thf(768,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( E @ ( B @ ( A @ c_Fun_Obij__betw ) ) ) ) )
| ( D @ ( C @ ( E @ ( B @ ( D @ ( C @ ( B @ ( A @ c_FuncSet_Orestrict ) ) ) @ c_Fun_Obij__betw ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(219,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( E @ ( A @ c_Fun_Oinj__on ) ) ) )
| ~ ( E @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__inj__on_0) ).
thf(1245,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( E @ ( A @ c_Fun_Oinj__on ) ) ) )
| ~ ( E @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(583,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( C @ c_Set_OPow ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_PowI_0) ).
thf(2086,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( C @ c_Set_OPow ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).
thf(609,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__idem_0) ).
thf(2139,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).
thf(117,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( E @ ( A @ ( D @ c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 ) ) ) @ ( A @ hAPP ) @ hBOOL )
| ~ ( C @ ( E @ ( A @ ( D @ c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 ) ) ) @ ( E @ hAPP ) @ hBOOL )
| ~ ( D @ ( B @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ball__conj__distrib_2) ).
thf(1015,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( E @ ( A @ ( D @ c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 ) ) ) @ ( A @ hAPP ) @ hBOOL )
| ~ ( C @ ( E @ ( A @ ( D @ c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 ) ) ) @ ( E @ hAPP ) @ hBOOL )
| ~ ( D @ ( B @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(554,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ ( E @ hAPP ) @ hAPP ) )
= ( C @ ( D @ ( E @ hAPP ) @ hAPP ) ) )
| ~ ( G @ ( F @ ( B @ ( E @ c_Record_Oiso__tuple__update__accessor__cong__assist ) ) ) )
| ( ( C @ ( B @ hAPP ) @ ( A @ hAPP ) )
!= ( C @ ( B @ hAPP ) @ ( D @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_update__accessor__congruence__foldE_0) ).
thf(2022,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ ( E @ hAPP ) @ hAPP ) )
= ( C @ ( D @ ( E @ hAPP ) @ hAPP ) ) )
| ~ ( G @ ( F @ ( B @ ( E @ c_Record_Oiso__tuple__update__accessor__cong__assist ) ) ) )
| ( ( C @ ( B @ hAPP ) @ ( A @ hAPP ) )
!= ( C @ ( B @ hAPP ) @ ( D @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).
thf(714,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( D @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B = D )
| ~ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( B @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( B @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__below_2) ).
thf(2390,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( D @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B = D )
| ~ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( B @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( B @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[714]) ).
thf(77,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( E @ c_Equiv__Relations_Oequiv ) ) )
| ~ ( E @ ( A @ ( B @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( D @ ( B @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( B @ ( B @ ( D @ ( A @ c_Pair ) ) ) @ ( B @ ( B @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( B @ ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ c_Equiv__Relations_Oquotient ) ) )
= ( B @ ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ c_Equiv__Relations_Oquotient ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__equiv__class__iff2_1) ).
thf(922,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( E @ c_Equiv__Relations_Oequiv ) ) )
| ~ ( E @ ( A @ ( B @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( D @ ( B @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( B @ ( B @ ( D @ ( A @ c_Pair ) ) ) @ ( B @ ( B @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( B @ ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ c_Equiv__Relations_Oquotient ) ) )
= ( B @ ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ c_Equiv__Relations_Oquotient ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(464,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( E @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_FuncSet_Orestrict ) ) ) @ hAPP ) )
= ( D @ c_HOL_Oundefined ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_restrict__apply_1) ).
thf(1805,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( E @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_FuncSet_Orestrict ) ) ) @ hAPP ) )
= ( D @ c_HOL_Oundefined ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(575,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( B = C )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__iff_2) ).
thf(2069,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( B = C )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).
thf(306,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ ( E @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( E @ ( D @ ( C @ ( A @ ( B @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) @ ( A @ hAPP ) )
= E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_f__inv__into__f_0) ).
thf(1445,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ ( E @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( E @ ( D @ ( C @ ( A @ ( B @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) @ ( A @ hAPP ) )
= E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(344,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
!= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Ononempty__iff_2) ).
thf(1528,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
!= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(652,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ ( E @ ( D @ c_FuncSet_Osko__FuncSet__XrestrictI__1__1 ) ) ) ) @ ( E @ hAPP ) @ ( B @ ( A @ ( C @ ( E @ ( D @ c_FuncSet_Osko__FuncSet__XrestrictI__1__1 ) ) ) ) @ ( C @ hAPP ) @ ( B @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( E @ ( D @ c_FuncSet_OPi ) ) ) @ ( B @ ( A @ ( D @ ( C @ c_FuncSet_Orestrict ) ) ) @ ( B @ ( A @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_restrictI_1) ).
thf(2244,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ ( E @ ( D @ c_FuncSet_Osko__FuncSet__XrestrictI__1__1 ) ) ) ) @ ( E @ hAPP ) @ ( B @ ( A @ ( C @ ( E @ ( D @ c_FuncSet_Osko__FuncSet__XrestrictI__1__1 ) ) ) ) @ ( C @ hAPP ) @ ( B @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( E @ ( D @ c_FuncSet_OPi ) ) ) @ ( B @ ( A @ ( D @ ( C @ c_FuncSet_Orestrict ) ) ) @ ( B @ ( A @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[652]) ).
thf(110,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ hAPP ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__triv_0) ).
thf(1000,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ hAPP ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(48,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A = B )
| ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( B @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_notin__Lin__iff_1) ).
thf(851,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A = B )
| ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( B @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(157,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( B @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Lin__irrefl_0) ).
thf(1102,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( B @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(547,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( tc_bool @ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( A @ c_in @ c_COMBC ) ) ) @ hAPP ) @ c_Collect ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Collect__mem__eq_0) ).
thf(2005,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( tc_bool @ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( A @ c_in @ c_COMBC ) ) ) @ hAPP ) @ c_Collect ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).
thf(386,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_Orderings_Otop__class_Otop @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ c_Orderings_Otop__class_Otop ) )
| ~ ( A @ class_Lattices_Obounded__lattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__top__left_0) ).
thf(1626,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_Orderings_Otop__class_Otop @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ c_Orderings_Otop__class_Otop ) )
| ~ ( A @ class_Lattices_Obounded__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(126,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_psubset__insert__iff_9) ).
thf(1034,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(185,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__Int_0) ).
thf(1166,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( B @ tc_fun ) @ ( D @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(87,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( E @ ( C @ ( F @ c_Product__Type_OSigma ) ) ) @ ( A @ ( E @ ( B @ ( D @ c_Pair ) ) ) @ ( A @ ( E @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ hAPP ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SigmaD2_0) ).
thf(944,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( E @ ( C @ ( F @ c_Product__Type_OSigma ) ) ) @ ( A @ ( E @ ( B @ ( D @ c_Pair ) ) ) @ ( A @ ( E @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ hAPP ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(664,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( G @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( G @ ( C @ hAPP ) @ ( F @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( F @ ( A @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( A @ ( C @ ( B @ c_ATP__Linkup_Osko__Complete__Lattice__Xbex__UN__1__3 ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bex__UN_4) ).
thf(2271,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( G @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( G @ ( C @ hAPP ) @ ( F @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( F @ ( A @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( A @ ( C @ ( B @ c_ATP__Linkup_Osko__Complete__Lattice__Xbex__UN__1__3 ) ) ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[664]) ).
thf(413,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
!= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__empty_0) ).
thf(1684,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
!= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(634,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_Equiv__Relations_Oequiv ) ) )
| ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( A @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( C @ c_Relation_OImage ) ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equiv__class__self_0) ).
thf(2202,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_Equiv__Relations_Oequiv ) ) )
| ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( A @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( C @ c_Relation_OImage ) ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[634]) ).
thf(176,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Set_Oimage ) ) ) )
= ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( E @ ( D @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__set__diff_0) ).
thf(1145,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Set_Oimage ) ) ) )
= ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( E @ ( D @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(134,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( F @ ( B @ ( E @ ( A @ c_SetInterval_Oord_OatLeastLessThan ) ) ) ) @ ( C @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ord_OatLeastLessThan__iff_0) ).
thf(1049,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( F @ ( B @ ( E @ ( A @ c_SetInterval_Oord_OatLeastLessThan ) ) ) ) @ ( C @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(402,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ c_COMBI @ hAPP ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ATP__Linkup_OCOMBI__def_0) ).
thf(1662,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_COMBI @ hAPP ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(588,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Complete__Lattice_OSup__class_OSup @ hAPP ) )
= ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sup__binary_0) ).
thf(2096,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Complete__Lattice_OSup__class_OSup @ hAPP ) )
= ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).
thf(244,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( A @ ( A @ ( B @ ( D @ c_Pair ) ) ) @ ( A @ ( A @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ ( F @ ( E @ c_Equiv__Relations_Oequiv ) ) )
| ~ ( A @ ( F @ ( E @ c_Equiv__Relations_Oquotient ) ) @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ ( F @ ( E @ c_Equiv__Relations_Oquotient ) ) @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( D @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_quotient__eq__iff_0) ).
thf(1304,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( A @ ( A @ ( B @ ( D @ c_Pair ) ) ) @ ( A @ ( A @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ ( F @ ( E @ c_Equiv__Relations_Oequiv ) ) )
| ~ ( A @ ( F @ ( E @ c_Equiv__Relations_Oquotient ) ) @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ ( F @ ( E @ c_Equiv__Relations_Oquotient ) ) @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( D @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(491,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Orderings_Oorder )
| ( B @ ( A @ tc_fun ) @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Oorder) ).
thf(1873,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Orderings_Oorder )
| ( B @ ( A @ tc_fun ) @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).
thf(505,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Complete__Lattice_Ocomplete__lattice )
| ( B @ ( A @ tc_fun ) @ class_Complete__Lattice_Ocomplete__lattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Complete__Lattice_Ocomplete__lattice) ).
thf(1905,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Complete__Lattice_Ocomplete__lattice )
| ( B @ ( A @ tc_fun ) @ class_Complete__Lattice_Ocomplete__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).
thf(295,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Lattices_Odistrib__lattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__distrib1_0) ).
thf(1420,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Lattices_Odistrib__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(79,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__absorb_0) ).
thf(927,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(561,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Complete__Lattice_OInf__class_OInf @ hAPP ) )
= B )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Inf__singleton_0) ).
thf(2037,plain,
! [B: $i,A: $i] :
( ( ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Complete__Lattice_OInf__class_OInf @ hAPP ) )
= B )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).
thf(233,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( D @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D = A )
| ~ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D = B )
| ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( D @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__below_13) ).
thf(1277,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( D @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D = A )
| ~ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D = B )
| ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( D @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(602,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ball__empty_0) ).
thf(2124,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).
thf(31,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ c_Fun_Obij__betw ) ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bij__betw__def_2) ).
thf(812,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ c_Fun_Obij__betw ) ) ) ) )
| ~ ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(335,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( A @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( C @ hAPP ) @ c_Set_Oinsert ) ) @ ( C @ c_Set_Ovimage ) ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__singleton__eq_1) ).
thf(1509,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( A @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( C @ hAPP ) @ c_Set_Oinsert ) ) @ ( C @ c_Set_Ovimage ) ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(84,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( E @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( D @ ( E @ ( B @ c_Set_Oimage ) ) ) @ ( A @ ( D @ ( C @ ( B @ c_Set_Oimage ) ) ) @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__diff__subset_0) ).
thf(939,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( E @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( D @ ( E @ ( B @ c_Set_Oimage ) ) ) @ ( A @ ( D @ ( C @ ( B @ c_Set_Oimage ) ) ) @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(259,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntE_0) ).
thf(1340,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(97,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A = B )
| ~ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A = B )
| ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__above_11) ).
thf(968,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A = B )
| ~ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A = B )
| ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(192,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( A = D )
| ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ c_Arrow__Order__Mirabelle_Omkbot ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__mkbot_3) ).
thf(1181,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( A = D )
| ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ c_Arrow__Order__Mirabelle_Omkbot ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(37,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( C @ ( B @ ( E @ c_Set_Oinsert ) ) @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__insert_0) ).
thf(823,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( C @ ( B @ ( E @ c_Set_Oinsert ) ) @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(42,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( E @ c_Equiv__Relations_Oequiv ) ) )
| ~ ( A @ ( C @ ( C @ ( D @ ( B @ c_Pair ) ) ) @ ( C @ ( C @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) )
= ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equiv__class__eq__iff_0) ).
thf(836,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( E @ c_Equiv__Relations_Oequiv ) ) )
| ~ ( A @ ( C @ ( C @ ( D @ ( B @ c_Pair ) ) ) @ ( C @ ( C @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) )
= ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(354,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I4_J_0) ).
thf(1551,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(480,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( B = D )
| ( ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
!= ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ c_Set_Oinsert ) ) @ ( D @ c_Set_Oinsert ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_3) ).
thf(1845,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( B = D )
| ( ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
!= ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ c_Set_Oinsert ) ) @ ( D @ c_Set_Oinsert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).
thf(441,axiom,
! [A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__empty_2) ).
thf(1748,plain,
! [A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).
thf(450,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D = E )
| ~ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A = B )
| ( B = D )
| ( A = D )
| ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__below_4) ).
thf(1770,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D = E )
| ~ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A = B )
| ( B = D )
| ( A = D )
| ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(708,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__supE_0) ).
thf(2375,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[708]) ).
thf(550,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( E @ ( D @ ( B @ c_Set_Ovimage ) ) ) @ ( C @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ hAPP ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimageD_0) ).
thf(2012,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( E @ ( D @ ( B @ c_Set_Ovimage ) ) ) @ ( C @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ hAPP ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).
thf(377,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ( D = E )
| ~ ( c_Arrow__Order__Mirabelle_OProf @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( c_Arrow__Order__Mirabelle_OProf @ ( F @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( B @ ( D @ ( A @ ( F @ ( C @ v_sko__local__Xpairwise__neutrality__1 ) ) ) ) ) @ ( C @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( B @ ( D @ ( A @ ( F @ ( C @ v_sko__local__Xpairwise__neutrality__1 ) ) ) ) ) @ ( F @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( E @ ( D @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( F @ ( v_F @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( E @ ( D @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( v_F @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pairwise__neutrality_1) ).
thf(1605,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ( D = E )
| ~ ( c_Arrow__Order__Mirabelle_OProf @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( c_Arrow__Order__Mirabelle_OProf @ ( F @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( B @ ( D @ ( A @ ( F @ ( C @ v_sko__local__Xpairwise__neutrality__1 ) ) ) ) ) @ ( C @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( B @ ( D @ ( A @ ( F @ ( C @ v_sko__local__Xpairwise__neutrality__1 ) ) ) ) ) @ ( F @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( E @ ( D @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( F @ ( v_F @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( E @ ( D @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( v_F @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(395,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_1) ).
thf(1647,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(272,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( B = C )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_0) ).
thf(1368,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( B = C )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(454,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D = E )
| ~ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B = D )
| ( A = D )
| ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__below_3) ).
thf(1780,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D = E )
| ~ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B = D )
| ( A = D )
| ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).
thf(345,axiom,
! [C: $i,B: $i,A: $i] : ( B @ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__subset_0) ).
thf(1531,plain,
! [C: $i,B: $i,A: $i] : ( B @ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(107,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( tc_bool @ ( A @ tc_fun ) @ ( E @ ( B @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( C @ ( B @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( tc_bool @ ( A @ tc_fun ) @ ( E @ ( B @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UN__absorb_0) ).
thf(993,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( tc_bool @ ( A @ tc_fun ) @ ( E @ ( B @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( C @ ( B @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( tc_bool @ ( A @ tc_fun ) @ ( E @ ( B @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(143,axiom,
! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__lower2_0) ).
thf(1070,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(57,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ hAPP ) @ hBOOL )
| ~ ( B @ ( D @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( C @ ( B @ c_ATP__Linkup_Osko__Set__XbexI__1__1 ) ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bexI_0) ).
thf(872,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ hAPP ) @ hBOOL )
| ~ ( B @ ( D @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( C @ ( B @ c_ATP__Linkup_Osko__Set__XbexI__1__1 ) ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(210,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__commute_0) ).
thf(1225,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(438,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( C @ ( A @ ( D @ ( A @ ( D @ ( C @ ( B @ c_Set_Ovimage ) ) ) @ ( B @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__vimage__subset_0) ).
thf(1743,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( C @ ( A @ ( D @ ( A @ ( D @ ( C @ ( B @ c_Set_Ovimage ) ) ) @ ( B @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).
thf(630,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F = B )
| ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
= ( F @ ( A @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__apply_1) ).
thf(2192,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F = B )
| ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
= ( F @ ( A @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[630]) ).
thf(63,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
!= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__empty_1) ).
thf(887,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
!= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(91,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( A = B )
| ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ c_Arrow__Order__Mirabelle_Omktop ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__mktop_5) ).
thf(954,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( A = B )
| ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ c_Arrow__Order__Mirabelle_Omktop ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(222,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( A @ c_Set_Oinsert ) ) )
= ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UN__extend__simps_I1_J_0) ).
thf(1252,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( A @ c_Set_Oinsert ) ) )
= ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(212,axiom,
! [B: $i,A: $i] : ( A @ ( B @ c_Set_OPow ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Pow__bottom_0) ).
thf(1230,plain,
! [B: $i,A: $i] : ( A @ ( B @ c_Set_OPow ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(324,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Lattices_Odistrib__lattice )
| ( B @ ( A @ tc_fun ) @ class_Lattices_Odistrib__lattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Odistrib__lattice) ).
thf(1484,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Lattices_Odistrib__lattice )
| ( B @ ( A @ tc_fun ) @ class_Lattices_Odistrib__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(617,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( E @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__eqI_1) ).
thf(2160,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( E @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).
thf(300,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__ord_I2_J_0) ).
thf(1432,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(194,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( F @ ( A @ c_Fun_Oinj__on ) ) ) )
| ~ ( F @ ( B @ ( tc_bool @ ( D @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( F @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Set_Oimage ) ) ) )
= ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( E @ ( D @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__image__set__diff_0) ).
thf(1186,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( F @ ( A @ c_Fun_Oinj__on ) ) ) )
| ~ ( F @ ( B @ ( tc_bool @ ( D @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( F @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Set_Oimage ) ) ) )
= ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( E @ ( D @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(128,axiom,
! [C: $i,B: $i,A: $i] :
~ ( B @ ( C @ c_Arrow__Order__Mirabelle_Omkbot ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__mkbot_0) ).
thf(1038,plain,
! [C: $i,B: $i,A: $i] :
~ ( B @ ( C @ c_Arrow__Order__Mirabelle_Omkbot ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(226,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Orderings_Obot )
| ( B @ ( A @ tc_fun ) @ class_Orderings_Obot ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Obot) ).
thf(1262,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Orderings_Obot )
| ( B @ ( A @ tc_fun ) @ class_Orderings_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(692,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( E @ ( D @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Set_Oimage ) ) ) )
= ( E @ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( F @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Set_Oimage ) ) ) @ ( C @ c_Set_Oinsert ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__image_0) ).
thf(2337,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( E @ ( D @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Set_Oimage ) ) ) )
= ( E @ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( F @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Set_Oimage ) ) ) @ ( C @ c_Set_Oinsert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[692]) ).
thf(604,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( C @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( F @ hAPP ) @ ( D @ ( B @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( F @ ( E @ c_Product__Type_OSigma ) ) ) @ ( B @ ( A @ ( D @ ( C @ c_Pair ) ) ) @ ( B @ ( A @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mem__Sigma__iff_2) ).
thf(2128,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( C @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( F @ hAPP ) @ ( D @ ( B @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( F @ ( E @ c_Product__Type_OSigma ) ) ) @ ( B @ ( A @ ( D @ ( C @ c_Pair ) ) ) @ ( B @ ( A @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).
thf(503,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__infI_0) ).
thf(1901,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).
thf(563,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ~ ( B @ ( D @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_ATP__Linkup_Osko__Set__XbexCI__1__1 ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bexCI_3) ).
thf(2044,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ~ ( B @ ( D @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_ATP__Linkup_Osko__Set__XbexCI__1__1 ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).
thf(170,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ hAPP ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__idem__iff_1) ).
thf(1130,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ hAPP ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(436,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( E @ ( C @ ( A @ c_Record_Oiso__tuple__update__accessor__cong__assist ) ) ) )
| ( ( D @ ( E @ ( E @ ( D @ ( C @ hAPP ) @ ( B @ hAPP ) @ c_COMBK ) ) @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_iso__tuple__update__accessor__cong__assist__def_0) ).
thf(1738,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( E @ ( C @ ( A @ c_Record_Oiso__tuple__update__accessor__cong__assist ) ) ) )
| ( ( D @ ( E @ ( E @ ( D @ ( C @ hAPP ) @ ( B @ hAPP ) @ c_COMBK ) ) @ ( A @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( A @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(700,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ ( A @ c_Set_Ovimage ) ) ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__vimage__image__eq_0) ).
thf(2354,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ ( A @ c_Set_Ovimage ) ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[700]) ).
thf(425,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__mp_0) ).
thf(1711,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(136,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntE_1) ).
thf(1053,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(331,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D = A )
| ( A = B )
| ( D = B )
| ~ ( c_Arrow__Order__Mirabelle_OProf @ ( E @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( c_Arrow__Order__Mirabelle_OProf @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( A @ ( D @ ( C @ ( E @ v_sko__local__X4__1 ) ) ) ) @ ( E @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( D @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( A @ ( D @ ( C @ ( E @ v_sko__local__X4__1 ) ) ) ) @ ( C @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( v_F @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( D @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( v_F @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_4_2) ).
thf(1499,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D = A )
| ( A = B )
| ( D = B )
| ~ ( c_Arrow__Order__Mirabelle_OProf @ ( E @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( c_Arrow__Order__Mirabelle_OProf @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( A @ ( D @ ( C @ ( E @ v_sko__local__X4__1 ) ) ) ) @ ( E @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( D @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( A @ ( D @ ( C @ ( E @ v_sko__local__X4__1 ) ) ) ) @ ( C @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( v_F @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( D @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( v_F @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(458,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( E @ c_COMBK ) ) @ ( A @ c_FuncSet_OPi ) ) ) @ ( B @ ( D @ ( C @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( C @ ( A @ c_FuncSet_Oextensional ) ) @ ( B @ ( D @ ( C @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( D @ ( C @ ( C @ ( C @ ( C @ ( A @ ( C @ c_COMBI @ c_FuncSet_Orestrict ) ) ) @ ( B @ ( A @ c_FuncSet_Ocompose ) ) ) ) ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_compose__Id_0) ).
thf(1790,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( E @ c_COMBK ) ) @ ( A @ c_FuncSet_OPi ) ) ) @ ( B @ ( D @ ( C @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( C @ ( A @ c_FuncSet_Oextensional ) ) @ ( B @ ( D @ ( C @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( D @ ( C @ ( C @ ( C @ ( C @ ( A @ ( C @ c_COMBI @ c_FuncSet_Orestrict ) ) ) @ ( B @ ( A @ c_FuncSet_Ocompose ) ) ) ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).
thf(643,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__supI_0) ).
thf(2224,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[643]) ).
thf(242,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( E @ ( A @ c_SetInterval_Oord_OgreaterThanLessThan ) ) ) @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ord_OgreaterThanLessThan__iff_1) ).
thf(1300,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( E @ ( A @ c_SetInterval_Oord_OgreaterThanLessThan ) ) ) @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(391,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( E @ c_Relation_Oconverse ) ) @ ( A @ ( B @ ( C @ ( D @ c_Pair ) ) ) @ ( A @ ( B @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( B @ ( A @ ( D @ ( C @ c_Pair ) ) ) @ ( B @ ( A @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_converseD_0) ).
thf(1637,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( E @ c_Relation_Oconverse ) ) @ ( A @ ( B @ ( C @ ( D @ c_Pair ) ) ) @ ( A @ ( B @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( B @ ( A @ ( D @ ( C @ c_Pair ) ) ) @ ( B @ ( A @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(250,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A = B )
| ~ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A = B )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__above_5) ).
thf(1317,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A = B )
| ~ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(474,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ hAPP ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__idem_0) ).
thf(1830,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ hAPP ) @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(150,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I6_J_0) ).
thf(1085,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(400,axiom,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Fun_Oinj__on ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__empty_0) ).
thf(1658,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Fun_Oinj__on ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(686,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B
= ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( ( A @ ( D @ ( D @ ( A @ ( C @ c_COMBK ) ) @ ( B @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) )
= C )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SUP__const_0) ).
thf(2322,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B
= ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( ( A @ ( D @ ( D @ ( A @ ( C @ c_COMBK ) ) @ ( B @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) )
= C )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[686]) ).
thf(349,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( A @ ( C @ ( E @ ( D @ c_FuncSet_Osko__FuncSet__XrestrictI__1__1 ) ) ) ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( E @ ( D @ c_FuncSet_OPi ) ) ) @ ( B @ ( A @ ( D @ ( C @ c_FuncSet_Orestrict ) ) ) @ ( B @ ( A @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_restrictI_0) ).
thf(1538,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( A @ ( C @ ( E @ ( D @ c_FuncSet_Osko__FuncSet__XrestrictI__1__1 ) ) ) ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( E @ ( D @ c_FuncSet_OPi ) ) ) @ ( B @ ( A @ ( D @ ( C @ c_FuncSet_Orestrict ) ) ) @ ( B @ ( A @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(90,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( E @ ( D @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Set_Oimage ) ) ) )
= ( E @ ( D @ ( F @ ( A @ c_Set_Oimage ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__image_1) ).
thf(951,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( E @ ( D @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Set_Oimage ) ) ) )
= ( E @ ( D @ ( F @ ( A @ c_Set_Oimage ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(746,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( D @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( D @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_psubset__insert__iff_2) ).
thf(2468,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( D @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( D @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[746]) ).
thf(208,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ( D = E )
| ( A = E )
| ( B = D )
| ~ ( c_Arrow__Order__Mirabelle_OProf @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( c_Arrow__Order__Mirabelle_OProf @ ( F @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( B @ ( D @ ( A @ ( F @ ( C @ v_sko__local__X2__1 ) ) ) ) ) @ ( C @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( B @ ( D @ ( A @ ( F @ ( C @ v_sko__local__X2__1 ) ) ) ) ) @ ( F @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( E @ ( D @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( F @ ( v_F @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( E @ ( D @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( v_F @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_2_1) ).
thf(1220,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ( D = E )
| ( A = E )
| ( B = D )
| ~ ( c_Arrow__Order__Mirabelle_OProf @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( c_Arrow__Order__Mirabelle_OProf @ ( F @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( B @ ( D @ ( A @ ( F @ ( C @ v_sko__local__X2__1 ) ) ) ) ) @ ( C @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( B @ ( D @ ( A @ ( F @ ( C @ v_sko__local__X2__1 ) ) ) ) ) @ ( F @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( E @ ( D @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( F @ ( v_F @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( E @ ( D @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( v_F @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(287,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__le__not__le_2) ).
thf(1404,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(518,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( D @ hAPP ) @ ( E @ ( A @ ( D @ ( C @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) )
= B )
| ~ ( E @ ( A @ ( C @ ( D @ c_Fun_Oinj__on ) ) ) )
| ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inv__into__f__eq_0) ).
thf(1934,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( D @ hAPP ) @ ( E @ ( A @ ( D @ ( C @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) )
= B )
| ~ ( E @ ( A @ ( C @ ( D @ c_Fun_Oinj__on ) ) ) )
| ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).
thf(722,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( C @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_psubset__insert__iff_7) ).
thf(2411,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( C @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[722]) ).
thf(351,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( E @ c_Equiv__Relations_Oequiv ) ) )
| ~ ( E @ ( B @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( D @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ ( C @ ( C @ ( D @ ( B @ c_Pair ) ) ) @ ( C @ ( C @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) )
= ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__equiv__class__iff_1) ).
thf(1543,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( E @ c_Equiv__Relations_Oequiv ) ) )
| ~ ( E @ ( B @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( D @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ ( C @ ( C @ ( D @ ( B @ c_Pair ) ) ) @ ( C @ ( C @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) )
= ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(596,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( E @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( D @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ ( D @ ( C @ ( B @ c_ATP__Linkup_Osko__Set__Xbex__Un__1__3 ) ) ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bex__Un_4) ).
thf(2113,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( E @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( D @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ ( D @ ( C @ ( B @ c_ATP__Linkup_Osko__Set__Xbex__Un__1__3 ) ) ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).
thf(121,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( E @ c_FuncSet_Oextensional ) ) @ ( A @ ( C @ ( D @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( B @ ( A @ hAPP ) )
= ( C @ c_HOL_Oundefined ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_extensional__arb_0) ).
thf(1023,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( E @ c_FuncSet_Oextensional ) ) @ ( A @ ( C @ ( D @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( B @ ( A @ hAPP ) )
= ( C @ c_HOL_Oundefined ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(421,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ c_fequal @ hAPP ) @ c_Collect ) )
= ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_singleton__conv2_0) ).
thf(1702,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ c_fequal @ hAPP ) @ c_Collect ) )
= ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(534,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_psubset__insert__iff_5) ).
thf(1972,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).
thf(53,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( D @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A = D )
| ~ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D = B )
| ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__above_9) ).
thf(864,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( D @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A = D )
| ~ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D = B )
| ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(298,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ hAPP ) @ hBOOL )
| ( A @ ( C @ c_Collect ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CollectI_0) ).
thf(1427,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ hAPP ) @ hBOOL )
| ( A @ ( C @ c_Collect ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(333,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I2_J_0) ).
thf(1504,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(154,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= C )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__sup_0) ).
thf(1094,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= C )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(405,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( F @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( F @ ( D @ hAPP ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( tc_bool @ ( A @ tc_fun ) @ ( E @ ( D @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UN__I_0) ).
thf(1670,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( F @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( F @ ( D @ hAPP ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( tc_bool @ ( A @ tc_fun ) @ ( E @ ( D @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(662,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ ( B @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( A @ ( B @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_HOL_Oord ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__fun__def_0) ).
thf(2266,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ ( B @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( A @ ( B @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_HOL_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[662]) ).
thf(51,axiom,
! [B: $i,A: $i] :
( ( ( A @ c_Orderings_Otop__class_Otop @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ c_Orderings_Otop__class_Otop ) )
| ~ ( A @ class_Lattices_Obounded__lattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__top__right_0) ).
thf(859,plain,
! [B: $i,A: $i] :
( ( ( A @ c_Orderings_Otop__class_Otop @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( A @ c_Orderings_Otop__class_Otop ) )
| ~ ( A @ class_Lattices_Obounded__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(106,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__subset_2) ).
thf(991,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(348,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( E @ c_Equiv__Relations_Oequiv ) ) )
| ~ ( A @ ( A @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( D @ c_Relation_OImage ) ) ) @ ( A @ ( A @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( D @ c_Relation_OImage ) ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( C @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( A @ ( C @ ( B @ c_Pair ) ) ) @ ( A @ ( A @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__equiv__class_0) ).
thf(1536,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( E @ c_Equiv__Relations_Oequiv ) ) )
| ~ ( A @ ( A @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( D @ c_Relation_OImage ) ) ) @ ( A @ ( A @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( D @ c_Relation_OImage ) ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( C @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( A @ ( C @ ( B @ c_Pair ) ) ) @ ( A @ ( A @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(538,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_singletonE_0) ).
thf(1981,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).
thf(668,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__infE_1) ).
thf(2279,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[668]) ).
thf(701,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( C @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( B @ ( D @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( C @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B = A )
| ~ ( c_Arrow__Order__Mirabelle_OLin @ ( D @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C = A )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__below_6) ).
thf(2357,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( C @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( B @ ( D @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( C @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B = A )
| ~ ( c_Arrow__Order__Mirabelle_OLin @ ( D @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C = A )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[701]) ).
thf(527,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_psubset__trans_0) ).
thf(1955,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).
thf(495,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_Orderings_Obot__class_Obot @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Lattices_Obounded__lattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__bot__left_0) ).
thf(1881,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_Orderings_Obot__class_Obot @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Lattices_Obounded__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).
thf(231,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( c_Arrow__Order__Mirabelle_OProf @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( c_Arrow__Order__Mirabelle_OProf @ ( D @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( D @ ( C @ v_sko__local__X3__1 ) ) ) @ ( C @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( D @ ( C @ v_sko__local__X3__1 ) ) ) @ ( D @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( B @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( v_F @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( B @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( v_F @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_3_1) ).
thf(1272,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( c_Arrow__Order__Mirabelle_OProf @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( c_Arrow__Order__Mirabelle_OProf @ ( D @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( D @ ( C @ v_sko__local__X3__1 ) ) ) @ ( C @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( D @ ( C @ v_sko__local__X3__1 ) ) ) @ ( D @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( B @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( v_F @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( B @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( v_F @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(520,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ ( E @ c_COMBK ) ) @ ( C @ c_FuncSet_OPi ) ) ) @ ( B @ ( A @ ( D @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( A @ ( D @ ( C @ ( B @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_funcset__image_0) ).
thf(1940,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ ( E @ c_COMBK ) ) @ ( C @ c_FuncSet_OPi ) ) ) @ ( B @ ( A @ ( D @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( A @ ( D @ ( C @ ( B @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).
thf(742,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( E @ ( B @ ( D @ c_Pair ) ) ) @ ( A @ ( E @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( E @ ( E @ ( tc_bool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ ( C @ c_Relation_OImage ) ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Image__singleton__iff_1) ).
thf(2458,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( E @ ( B @ ( D @ c_Pair ) ) ) @ ( A @ ( E @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( E @ ( E @ ( tc_bool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ ( C @ c_Relation_OImage ) ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[742]) ).
thf(751,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( E @ c_Equiv__Relations_Oequiv ) ) )
| ~ ( A @ ( C @ ( C @ ( D @ ( B @ c_Pair ) ) ) @ ( C @ ( C @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) )
= ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equiv__class__eq_0) ).
thf(2479,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( E @ c_Equiv__Relations_Oequiv ) ) )
| ~ ( A @ ( C @ ( C @ ( D @ ( B @ c_Pair ) ) ) @ ( C @ ( C @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) )
= ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[751]) ).
thf(584,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I7_J_0) ).
thf(2088,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).
thf(312,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ ( A @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf1E_0) ).
thf(1459,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ ( A @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(531,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( A @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( C @ c_Finite__Set_Ofold__graph ) ) ) ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__fold__graphE_0) ).
thf(1966,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( A @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( C @ c_Finite__Set_Ofold__graph ) ) ) ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).
thf(81,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B
= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) )
!= ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__is__empty_0) ).
thf(931,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B
= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) )
!= ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(524,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__insert2_0) ).
thf(1949,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).
thf(469,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__subset__iff_0) ).
thf(1817,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).
thf(69,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( B @ ( A @ ( C @ ( E @ ( D @ c_FuncSet_Osko__FuncSet__XfuncsetI__1__1 ) ) ) ) @ ( C @ hAPP ) @ ( B @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( A @ ( tc_bool @ ( B @ tc_fun ) @ ( E @ c_COMBK ) ) @ ( D @ c_FuncSet_OPi ) ) ) @ ( C @ ( B @ ( A @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_funcsetI_1) ).
thf(903,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( B @ ( A @ ( C @ ( E @ ( D @ c_FuncSet_Osko__FuncSet__XfuncsetI__1__1 ) ) ) ) @ ( C @ hAPP ) @ ( B @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( A @ ( tc_bool @ ( B @ tc_fun ) @ ( E @ c_COMBK ) ) @ ( D @ c_FuncSet_OPi ) ) ) @ ( C @ ( B @ ( A @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(339,axiom,
! [C: $i,B: $i,A: $i] : ( A @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__iff_1) ).
thf(1517,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(687,axiom,
! [B: $i,A: $i] :
~ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__psubset__empty_0) ).
thf(2325,plain,
! [B: $i,A: $i] :
~ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[687]) ).
thf(65,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( E @ ( D @ c_Equiv__Relations_Oequiv ) ) )
| ~ ( A @ ( E @ ( D @ c_Equiv__Relations_Oquotient ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ ( E @ ( D @ c_Equiv__Relations_Oquotient ) ) @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B = C )
| ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_quotient__disj_0) ).
thf(891,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( E @ ( D @ c_Equiv__Relations_Oequiv ) ) )
| ~ ( A @ ( E @ ( D @ c_Equiv__Relations_Oquotient ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ ( E @ ( D @ c_Equiv__Relations_Oquotient ) ) @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B = C )
| ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(249,axiom,
! [B: $i,A: $i] : ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_singleton__iff_1) ).
thf(1316,plain,
! [B: $i,A: $i] : ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(396,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( tc_bool @ ( C @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equalityI_0) ).
thf(1649,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( tc_bool @ ( C @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(699,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( E @ ( D @ ( F @ c_FuncSet_OPi ) ) ) @ ( B @ ( A @ ( E @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( F @ ( C @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( D @ hAPP ) @ ( C @ ( B @ hAPP ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Pi__mem_0) ).
thf(2352,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( E @ ( D @ ( F @ c_FuncSet_OPi ) ) ) @ ( B @ ( A @ ( E @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( F @ ( C @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( D @ hAPP ) @ ( C @ ( B @ hAPP ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[699]) ).
thf(181,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( E @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__eqI_0) ).
thf(1157,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( E @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(251,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
= C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__apply_0) ).
thf(1321,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(476,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( B @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B = A )
| ~ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B = A )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__below_5) ).
thf(1834,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( B @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B = A )
| ~ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B = A )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).
thf(509,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( E @ ( D @ c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 ) ) ) @ ( E @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( E @ ( D @ c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 ) ) ) @ ( A @ hAPP ) @ hBOOL )
| ~ ( D @ ( B @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ball__conj__distrib_3) ).
thf(1913,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( E @ ( D @ c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 ) ) ) @ ( E @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( E @ ( D @ c_ATP__Linkup_Osko__Complete__Lattice__Xball__conj__distrib__1__1 ) ) ) @ ( A @ hAPP ) @ hBOOL )
| ~ ( D @ ( B @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).
thf(398,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( I @ ( H @ ( G @ ( F @ ( E @ ( A @ ( D @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
| ( ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ hAPP ) )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OSup__UNIV_0) ).
thf(1654,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( I @ ( H @ ( G @ ( F @ ( E @ ( A @ ( D @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
| ( ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ hAPP ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(290,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( tc_nat @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Finite__Set_Osetsum ) ) ) )
= ( tc_nat @ ( D @ ( B @ ( A @ c_Finite__Set_Osetsum ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_setsum__diff1__nat_1) ).
thf(1412,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( tc_nat @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Finite__Set_Osetsum ) ) ) )
= ( tc_nat @ ( D @ ( B @ ( A @ c_Finite__Set_Osetsum ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(307,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ ( C @ ( E @ c_Set_Oimage ) ) ) @ ( B @ ( E @ hAPP ) @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__iff_2) ).
thf(1448,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ ( C @ ( E @ c_Set_Oimage ) ) ) @ ( B @ ( E @ hAPP ) @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(195,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__le2_0) ).
thf(1189,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(694,axiom,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__upper1_0) ).
thf(2342,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[694]) ).
thf(364,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( D @ ( A @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ c_Set_Oinsert ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__insert__left_0) ).
thf(1575,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( D @ ( A @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ c_Set_Oinsert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(45,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( F @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( F @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ ( A @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SUP1__I_0) ).
thf(844,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( F @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( F @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ ( A @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(644,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Diff__cancel_0) ).
thf(2226,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[644]) ).
thf(309,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__ord_I4_J_0) ).
thf(1453,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(736,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( E @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( D @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ ( D @ ( C @ ( B @ c_ATP__Linkup_Osko__Set__Xbex__Un__1__3 ) ) ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bex__Un_6) ).
thf(2443,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( E @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( D @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ ( D @ ( C @ ( B @ c_ATP__Linkup_Osko__Set__Xbex__Un__1__3 ) ) ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[736]) ).
thf(279,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__neq__le__trans_0) ).
thf(1385,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(665,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Int__distrib_0) ).
thf(2273,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[665]) ).
thf(672,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( A @ ( B @ ( C @ ( D @ c_Pair ) ) ) @ ( A @ ( B @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( B @ ( E @ c_Relation_Oconverse ) ) @ ( B @ ( A @ ( D @ ( C @ c_Pair ) ) ) @ ( B @ ( A @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_converseI_0) ).
thf(2290,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( A @ ( B @ ( C @ ( D @ c_Pair ) ) ) @ ( A @ ( B @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( B @ ( E @ c_Relation_Oconverse ) ) @ ( B @ ( A @ ( D @ ( C @ c_Pair ) ) ) @ ( B @ ( A @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[672]) ).
thf(140,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D = E )
| ( A = B )
| ( D = B )
| ( E = A )
| ~ ( c_Arrow__Order__Mirabelle_OProf @ ( F @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( c_Arrow__Order__Mirabelle_OProf @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( E @ ( A @ ( D @ ( C @ ( F @ v_sko__local__X2__1 ) ) ) ) ) @ ( F @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( E @ ( D @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( E @ ( A @ ( D @ ( C @ ( F @ v_sko__local__X2__1 ) ) ) ) ) @ ( C @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( F @ ( v_F @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( E @ ( D @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( v_F @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_2_0) ).
thf(1062,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D = E )
| ( A = B )
| ( D = B )
| ( E = A )
| ~ ( c_Arrow__Order__Mirabelle_OProf @ ( F @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( c_Arrow__Order__Mirabelle_OProf @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( E @ ( A @ ( D @ ( C @ ( F @ v_sko__local__X2__1 ) ) ) ) ) @ ( F @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( E @ ( D @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( E @ ( A @ ( D @ ( C @ ( F @ v_sko__local__X2__1 ) ) ) ) ) @ ( C @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( F @ ( v_F @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( E @ ( D @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( v_F @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(88,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ~ ( c_Arrow__Order__Mirabelle_OLin @ ( A @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( B @ ( A @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_below__Lin_0) ).
thf(946,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ~ ( c_Arrow__Order__Mirabelle_OLin @ ( A @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( B @ ( A @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(387,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).
thf(1629,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(731,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__sup__iff_2) ).
thf(2431,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[731]) ).
thf(471,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__less_1) ).
thf(1822,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
thf(724,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__le1_0) ).
thf(2416,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[724]) ).
thf(623,axiom,
! [A: $i] :
( ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Complete__Lattice_OSup__class_OSup @ hAPP ) )
= ( A @ c_Orderings_Otop__class_Otop ) )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sup__UNIV_0) ).
thf(2174,plain,
! [A: $i] :
( ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Complete__Lattice_OSup__class_OSup @ hAPP ) )
= ( A @ c_Orderings_Otop__class_Otop ) )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[623]) ).
thf(320,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_psubset__eq_0) ).
thf(1476,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(407,axiom,
! [B: $i,A: $i] : ( A @ ( A @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ ( B @ c_COMBK ) ) @ ( B @ c_FuncSet_OPi ) ) ) @ ( A @ c_COMBI @ ( A @ ( A @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_funcset__id_0) ).
thf(1674,plain,
! [B: $i,A: $i] : ( A @ ( A @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ ( B @ c_COMBK ) ) @ ( B @ c_FuncSet_OPi ) ) ) @ ( A @ c_COMBI @ ( A @ ( A @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(392,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( D @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D = B )
| ~ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__above_2) ).
thf(1639,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( D @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D = B )
| ~ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(504,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ c_Arrow__Order__Mirabelle_OIIA )
| ~ ( c_Arrow__Order__Mirabelle_OProf @ ( E @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( c_Arrow__Order__Mirabelle_OProf @ ( D @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( E @ ( B @ ( A @ v_sko__Arrow__Order__Mirabelle__XIIA__def__1 ) ) ) @ ( E @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( E @ ( B @ ( A @ v_sko__Arrow__Order__Mirabelle__XIIA__def__1 ) ) ) @ ( D @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( C @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IIA__def_0) ).
thf(1903,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ c_Arrow__Order__Mirabelle_OIIA )
| ~ ( c_Arrow__Order__Mirabelle_OProf @ ( E @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( c_Arrow__Order__Mirabelle_OProf @ ( D @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( E @ ( B @ ( A @ v_sko__Arrow__Order__Mirabelle__XIIA__def__1 ) ) ) @ ( E @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( E @ ( B @ ( A @ v_sko__Arrow__Order__Mirabelle__XIIA__def__1 ) ) ) @ ( D @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( C @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).
thf(720,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Diff__Int_0) ).
thf(2406,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[720]) ).
thf(342,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I1_J_0) ).
thf(1523,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( B @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(605,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( C @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup1E_0) ).
thf(2130,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( C @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).
thf(614,axiom,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_Orderings_Otop__class_Otop @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_Lattices_Obounded__lattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__top__left_0) ).
thf(2152,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ c_Orderings_Otop__class_Otop @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= B )
| ~ ( A @ class_Lattices_Obounded__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[614]) ).
thf(660,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__Un__distrib2_0) ).
thf(2262,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[660]) ).
thf(738,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( A @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__insert__right_1) ).
thf(2447,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( A @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[738]) ).
thf(415,axiom,
! [B: $i,A: $i] : ( B @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__refl_0) ).
thf(1689,plain,
! [B: $i,A: $i] : ( B @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(744,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__absorb2_0) ).
thf(2462,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[744]) ).
thf(147,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ ( tc_bool @ ( C @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( A
= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( A
= ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__singletonD_0) ).
thf(1077,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ ( tc_bool @ ( C @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( A
= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( A
= ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(205,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( tc_bool @ ( A @ tc_fun ) @ ( E @ ( B @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( C @ ( B @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UN__upper_0) ).
thf(1212,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( tc_bool @ ( A @ tc_fun ) @ ( E @ ( B @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( C @ ( B @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(5,axiom,
tc_nat @ class_Orderings_Obot,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Obot) ).
thf(763,plain,
tc_nat @ class_Orderings_Obot,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(68,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( D @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B = D )
| ~ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A = D )
| ( A = D )
| ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__above_7) ).
thf(899,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( D @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B = D )
| ~ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A = D )
| ( A = D )
| ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(600,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_ATP__Linkup_Osko__Set__XbexE__1__1 ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bexE_1) ).
thf(2120,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_ATP__Linkup_Osko__Set__XbexE__1__1 ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).
thf(132,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__idemp_0) ).
thf(1045,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(124,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( D @ ( C @ c_SetInterval_Oord_OgreaterThan ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ord_OgreaterThan__iff_1) ).
thf(1030,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( D @ ( C @ c_SetInterval_Oord_OgreaterThan ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(327,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
= ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( B @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_4) ).
thf(1491,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
= ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( B @ c_Set_Oinsert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(712,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( C @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Complete__Lattice_OSup__class_OSup @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
!= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Union__disjoint_0) ).
thf(2384,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( C @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Complete__Lattice_OSup__class_OSup @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
!= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[712]) ).
thf(749,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( B @ ( A @ ( C @ c_FuncSet_Oextensional ) ) @ ( B @ ( F @ ( A @ ( E @ ( D @ ( C @ c_FuncSet_Ocompose ) ) ) ) ) @ ( B @ ( A @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_compose__extensional_0) ).
thf(2475,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( B @ ( A @ ( C @ c_FuncSet_Oextensional ) ) @ ( B @ ( F @ ( A @ ( E @ ( D @ ( C @ c_FuncSet_Ocompose ) ) ) ) ) @ ( B @ ( A @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[749]) ).
thf(80,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( D @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__trans_0) ).
thf(929,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( D @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(689,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( E @ ( B @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( C @ ( B @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__SUPI_0) ).
thf(2330,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( E @ ( B @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( C @ ( B @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[689]) ).
thf(423,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( D @ c_Fun_Oinj__on ) ) ) )
| ~ ( E @ ( C @ ( D @ ( A @ c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1 ) ) ) @ ( E @ ( C @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__transfer_1) ).
thf(1706,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( D @ c_Fun_Oinj__on ) ) ) )
| ~ ( E @ ( C @ ( D @ ( A @ c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1 ) ) ) @ ( E @ ( C @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(197,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup1CI_0) ).
thf(1193,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(646,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( A @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ c_Set_Oinsert ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__insert__right_0) ).
thf(2230,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( A @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ c_Set_Oinsert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[646]) ).
thf(674,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( E @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( E @ ( B @ hAPP ) )
= ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ ( A @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) )
!= ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UNION__empty__conv_I2_J_0) ).
thf(2294,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( E @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( E @ ( B @ hAPP ) )
= ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ ( A @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) )
!= ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[674]) ).
thf(381,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( A @ ( C @ ( E @ ( D @ c_FuncSet_Osko__FuncSet__XfuncsetI__1__1 ) ) ) ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( A @ ( tc_bool @ ( B @ tc_fun ) @ ( E @ c_COMBK ) ) @ ( D @ c_FuncSet_OPi ) ) ) @ ( C @ ( B @ ( A @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_funcsetI_0) ).
thf(1614,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( A @ ( C @ ( E @ ( D @ c_FuncSet_Osko__FuncSet__XfuncsetI__1__1 ) ) ) ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( A @ ( tc_bool @ ( B @ tc_fun ) @ ( E @ c_COMBK ) ) @ ( D @ c_FuncSet_OPi ) ) ) @ ( C @ ( B @ ( A @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(727,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_Orderings_Obot__class_Obot ) )
| ( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
!= ( A @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Lattices_Obounded__lattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__eq__bot__eq2_0) ).
thf(2421,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_Orderings_Obot__class_Obot ) )
| ( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
!= ( A @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Lattices_Obounded__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[727]) ).
thf(25,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( A @ c_COMBI @ c_Set_Oimage ) ) ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__ident_0) ).
thf(800,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( A @ c_COMBI @ c_Set_Oimage ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(640,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__subset__iff_2) ).
thf(2218,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[640]) ).
thf(671,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( D @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B = D )
| ~ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A = D )
| ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( D @ ( B @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__above_13) ).
thf(2287,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( D @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B = D )
| ~ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A = D )
| ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( D @ ( B @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[671]) ).
thf(337,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__left__idem_0) ).
thf(1512,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(677,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( B @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Int__crazy_0) ).
thf(2302,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( B @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[677]) ).
thf(647,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Complete__Lattice_OSup__class_OSup @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( ( B @ ( A @ ( C @ ( B @ c_ATP__Linkup_Osko__Complete__Lattice__XUnion__disjoint__1__1 ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
!= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Union__disjoint_2) ).
thf(2233,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Complete__Lattice_OSup__class_OSup @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( ( B @ ( A @ ( C @ ( B @ c_ATP__Linkup_Osko__Complete__Lattice__XUnion__disjoint__1__1 ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
!= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[647]) ).
thf(352,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( F @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( E @ ( D @ ( F @ ( A @ c_Set_Oimage ) ) ) @ ( C @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Fun_Oinj__on ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__fun__updI_0) ).
thf(1546,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( F @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( E @ ( D @ ( F @ ( A @ c_Set_Oimage ) ) ) @ ( C @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ c_Fun_Oinj__on ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(371,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__sup__iff_0) ).
thf(1593,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(177,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UnE_0) ).
thf(1148,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(566,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( A @ ( D @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
| ( ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ hAPP ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OSup__singleton_0) ).
thf(2050,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( J @ ( I @ ( H @ ( G @ ( F @ ( E @ ( A @ ( D @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
| ( ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ hAPP ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).
thf(322,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1 ) ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__bexI_1) ).
thf(1480,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ( C @ ( A @ ( B @ c_ATP__Linkup_Osko__Set__Xrev__bexI__1__1 ) ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(546,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__ord_I1_J_0) ).
thf(2003,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).
thf(610,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( D @ ( B @ c_Set_Oinsert ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__subset_0) ).
thf(2142,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( D @ ( B @ c_Set_Oinsert ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).
thf(393,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( D @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D = A )
| ~ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__above_1) ).
thf(1642,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( D @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D = A )
| ~ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(591,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).
thf(2102,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).
thf(431,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( C @ hAPP ) @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( A @ ( D @ ( C @ c_Set_Ovimage ) ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimageI_0) ).
thf(1725,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( C @ hAPP ) @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( A @ ( D @ ( C @ c_Set_Ovimage ) ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(234,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = C )
| ~ ( F @ ( D @ ( E @ ( A @ c_Fun_Oinj__on ) ) ) )
| ~ ( E @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( C @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( B @ ( A @ hAPP ) )
!= ( C @ ( A @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__iff_0) ).
thf(1280,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = C )
| ~ ( F @ ( D @ ( E @ ( A @ c_Fun_Oinj__on ) ) ) )
| ~ ( E @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( C @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( B @ ( A @ hAPP ) )
!= ( C @ ( A @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(365,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( C @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B = C )
| ~ ( F @ ( E @ ( D @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( ( B @ ( A @ hAPP ) )
!= ( C @ ( A @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__onD_0) ).
thf(1578,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( C @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B = C )
| ~ ( F @ ( E @ ( D @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( ( B @ ( A @ hAPP ) )
!= ( C @ ( A @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(528,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C = B )
| ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I11_J_0) ).
thf(1957,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C = B )
| ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).
thf(615,axiom,
! [B: $i,A: $i] :
( ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__UNIV__left_0) ).
thf(2155,plain,
! [B: $i,A: $i] :
( ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[615]) ).
thf(657,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert_1) ).
thf(2255,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[657]) ).
thf(155,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( E @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_FuncSet_Orestrict ) ) ) @ hAPP ) )
= ( E @ ( A @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_restrict__apply_0) ).
thf(1097,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( E @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_FuncSet_Orestrict ) ) ) @ hAPP ) )
= ( E @ ( A @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(41,axiom,
tc_nat @ class_Lattices_Olower__semilattice,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Lattices_Olower__semilattice) ).
thf(835,plain,
tc_nat @ class_Lattices_Olower__semilattice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(49,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( B = C )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv3_0) ).
thf(854,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( B = C )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(540,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__eqI_0) ).
thf(1986,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).
thf(54,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__infI2_0) ).
thf(867,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(445,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__absorb_0) ).
thf(1757,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(485,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F = B )
| ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
= ( F @ ( A @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_fun__upd__other_0) ).
thf(1859,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F = B )
| ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofun__upd ) ) ) ) @ hAPP ) )
= ( F @ ( A @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).
thf(399,axiom,
tc_bool @ class_Lattices_Olower__semilattice,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olower__semilattice) ).
thf(1657,plain,
tc_bool @ class_Lattices_Olower__semilattice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(29,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( E @ ( A @ ( B @ c_Fun_Obij__betw ) ) ) ) )
| ( ( C @ ( D @ ( C @ ( B @ ( C @ ( D @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Hilbert__Choice_Oinv__into ) ) ) @ c_FuncSet_Orestrict ) ) ) @ ( A @ c_FuncSet_Ocompose ) ) ) ) ) )
= ( C @ ( C @ ( A @ ( C @ c_COMBI @ c_FuncSet_Orestrict ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_compose__inv__into__id_0) ).
thf(807,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( E @ ( A @ ( B @ c_Fun_Obij__betw ) ) ) ) )
| ( ( C @ ( D @ ( C @ ( B @ ( C @ ( D @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Hilbert__Choice_Oinv__into ) ) ) @ c_FuncSet_Orestrict ) ) ) @ ( A @ c_FuncSet_Ocompose ) ) ) ) ) )
= ( C @ ( C @ ( A @ ( C @ c_COMBI @ c_FuncSet_Orestrict ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(417,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Fun_Oinj__on ) ) ) )
| ( ( A @ ( C @ ( C @ ( A @ ( D @ ( B @ c_Set_Oimage ) ) ) @ ( C @ ( A @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Hilbert__Choice_Oinv__into ) ) ) @ c_Set_Oimage ) ) ) )
= D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__inv__f__f_0) ).
thf(1693,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Fun_Oinj__on ) ) ) )
| ( ( A @ ( C @ ( C @ ( A @ ( D @ ( B @ c_Set_Oimage ) ) ) @ ( C @ ( A @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Hilbert__Choice_Oinv__into ) ) ) @ c_Set_Oimage ) ) ) )
= D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(358,axiom,
! [A: $i] :
( ~ ( c_Arrow__Order__Mirabelle_OLin @ ( A @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( c_Arrow__Order__Mirabelle_OProf @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( A @ c_COMBK ) ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_const__Lin__Prof_0) ).
thf(1561,plain,
! [A: $i] :
( ~ ( c_Arrow__Order__Mirabelle_OLin @ ( A @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( c_Arrow__Order__Mirabelle_OProf @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( A @ c_COMBK ) ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(704,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( E @ ( E @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ c_Fun_Oinj__on ) ) ) )
| ~ ( A @ ( E @ ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( tc_bool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( D @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ c_Set_Oimage ) ) ) @ ( C @ ( B @ hAPP ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__insert_1) ).
thf(2366,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( E @ ( E @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ c_Fun_Oinj__on ) ) ) )
| ~ ( A @ ( E @ ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( tc_bool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( D @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ c_Set_Oimage ) ) ) @ ( C @ ( B @ hAPP ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[704]) ).
thf(586,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( B = C )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__less_0) ).
thf(2091,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( B = C )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).
thf(499,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( D @ ( E @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( B = C )
| ~ ( E @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( C @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( B @ ( A @ hAPP ) )
!= ( C @ ( A @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__contraD_0) ).
thf(1891,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( D @ ( E @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( B = C )
| ~ ( E @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( C @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( B @ ( A @ hAPP ) )
!= ( C @ ( A @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).
thf(39,axiom,
! [A: $i] :
( ( A @ ( A @ c_Orderings_Obot__class_Obot @ ( A @ c_Orderings_Otop__class_Otop @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ ( tc_bool @ ( A @ ( A @ ( A @ c_HOL_Oord__class_Oless @ c_COMBC ) ) ) @ ( tc_bool @ ( A @ ( A @ ( A @ c_lessequals @ c_COMBC ) ) ) @ ( A @ c_Complete__Lattice_OInf__class_OInf @ ( A @ c_Complete__Lattice_OSup__class_OSup @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_dual__complete__lattice_0) ).
thf(828,plain,
! [A: $i] :
( ( A @ ( A @ c_Orderings_Obot__class_Obot @ ( A @ c_Orderings_Otop__class_Otop @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ ( tc_bool @ ( A @ ( A @ ( A @ c_HOL_Oord__class_Oless @ c_COMBC ) ) ) @ ( tc_bool @ ( A @ ( A @ ( A @ c_lessequals @ c_COMBC ) ) ) @ ( A @ c_Complete__Lattice_OInf__class_OInf @ ( A @ c_Complete__Lattice_OSup__class_OSup @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(141,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( F @ ( A @ ( E @ c_SetInterval_Oord_OatLeastLessThan ) ) ) ) @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ord_OatLeastLessThan__iff_1) ).
thf(1065,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( F @ ( A @ ( E @ c_SetInterval_Oord_OatLeastLessThan ) ) ) ) @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(562,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( C @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( D @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( C @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A = B )
| ~ ( c_Arrow__Order__Mirabelle_OLin @ ( D @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A = C )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__above_6) ).
thf(2040,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( C @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ ( D @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( C @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A = B )
| ~ ( c_Arrow__Order__Mirabelle_OLin @ ( D @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A = C )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).
thf(693,axiom,
! [A: $i] :
( ~ ( c_Arrow__Order__Mirabelle_OLin @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ c_Relation_Oconverse ) ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( c_Arrow__Order__Mirabelle_OLin @ ( A @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_converse__in__Lin_0) ).
thf(2340,plain,
! [A: $i] :
( ~ ( c_Arrow__Order__Mirabelle_OLin @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ c_Relation_Oconverse ) ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( c_Arrow__Order__Mirabelle_OLin @ ( A @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[693]) ).
thf(22,axiom,
tc_nat @ class_Orderings_Olinorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
thf(796,plain,
tc_nat @ class_Orderings_Olinorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(75,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( K @ ( J @ ( I @ ( H @ ( G @ ( A @ ( C @ ( F @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
| ~ ( D @ ( B @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__lattice_OSup__upper_0) ).
thf(918,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( K @ ( J @ ( I @ ( H @ ( G @ ( A @ ( C @ ( F @ c_Complete__Lattice_Ocomplete__lattice ) ) ) ) ) ) ) ) )
| ~ ( D @ ( B @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ hAPP ) @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(541,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( D @ ( A @ ( B @ ( C @ ( B @ hAPP ) @ c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__1 ) ) ) ) )
| ~ ( A @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Fun_Oinj__on ) ) ) )
| ~ ( A @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Set_Oimage ) ) ) @ ( C @ ( B @ hAPP ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_range__ex1__eq_1) ).
thf(1989,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( D @ ( A @ ( B @ ( C @ ( B @ hAPP ) @ c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__1 ) ) ) ) )
| ~ ( A @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Fun_Oinj__on ) ) ) )
| ~ ( A @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Set_Oimage ) ) ) @ ( C @ ( B @ hAPP ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).
thf(269,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__supI1_0) ).
thf(1363,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(248,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__inf__iff_1) ).
thf(1314,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(188,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ( D = E )
| ~ ( c_Arrow__Order__Mirabelle_OProf @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( c_Arrow__Order__Mirabelle_OProf @ ( F @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( B @ ( D @ ( A @ ( F @ ( C @ v_sko__local__Xpairwise__neutrality__1 ) ) ) ) ) @ ( C @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( B @ ( D @ ( A @ ( F @ ( C @ v_sko__local__Xpairwise__neutrality__1 ) ) ) ) ) @ ( F @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( E @ ( D @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( F @ ( v_F @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( E @ ( D @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( v_F @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pairwise__neutrality_3) ).
thf(1172,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ( D = E )
| ~ ( c_Arrow__Order__Mirabelle_OProf @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( c_Arrow__Order__Mirabelle_OProf @ ( F @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( B @ ( D @ ( A @ ( F @ ( C @ v_sko__local__Xpairwise__neutrality__1 ) ) ) ) ) @ ( C @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( B @ ( D @ ( A @ ( F @ ( C @ v_sko__local__Xpairwise__neutrality__1 ) ) ) ) ) @ ( F @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( E @ ( D @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( F @ ( v_F @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( E @ ( D @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( v_F @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(67,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( H @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( G @ ( F @ ( H @ ( B @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( G @ ( F @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ tc_fun ) @ ( C @ ( B @ ( A @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SUP2__I_0) ).
thf(897,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( H @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( G @ ( F @ ( H @ ( B @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( G @ ( F @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ tc_fun ) @ ( C @ ( B @ ( A @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(237,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__supI1_0) ).
thf(1288,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(199,axiom,
! [B: $i,A: $i] :
~ ( A @ ( B @ c_Arrow__Order__Mirabelle_Omktop ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__mktop_1) ).
thf(1197,plain,
! [B: $i,A: $i] :
~ ( A @ ( B @ c_Arrow__Order__Mirabelle_Omktop ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(93,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oimage ) ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__empty_0) ).
thf(960,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oimage ) ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(319,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ c_Arrow__Order__Mirabelle_Omktop ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B = D )
| ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__mktop_2) ).
thf(1473,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ c_Arrow__Order__Mirabelle_Omktop ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B = D )
| ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(262,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ~ ( c_Arrow__Order__Mirabelle_OLin @ ( B @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( C @ ( B @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__below_0) ).
thf(1346,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ~ ( c_Arrow__Order__Mirabelle_OLin @ ( B @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( C @ ( B @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(572,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( E @ ( tc_bool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( D @ c_Fun_Oinj__on ) ) ) )
| ( C @ ( E @ ( tc_bool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( D @ c_Set_Oimage ) ) ) @ ( C @ ( E @ ( D @ ( A @ c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1 ) ) ) @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__transfer_0) ).
thf(2063,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( E @ ( tc_bool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( D @ c_Fun_Oinj__on ) ) ) )
| ( C @ ( E @ ( tc_bool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( D @ c_Set_Oimage ) ) ) @ ( C @ ( E @ ( D @ ( A @ c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1 ) ) ) @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).
thf(379,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__less_1) ).
thf(1610,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(264,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Set_Oinsert ) ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__Diff_0) ).
thf(1352,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Set_Oinsert ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(536,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ c_Collect ) @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__Collect_0) ).
thf(1977,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ c_Collect ) @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).
thf(473,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ ( D @ hAPP ) @ hAPP ) )
= C )
| ~ ( F @ ( E @ ( B @ ( D @ c_Record_Oiso__tuple__update__accessor__cong__assist ) ) ) )
| ( ( C @ ( B @ hAPP ) @ ( A @ hAPP ) )
!= ( C @ ( B @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_update__accessor__noopE_0) ).
thf(1827,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ ( D @ hAPP ) @ hAPP ) )
= C )
| ~ ( F @ ( E @ ( B @ ( D @ c_Record_Oiso__tuple__update__accessor__cong__assist ) ) ) )
| ( ( C @ ( B @ hAPP ) @ ( A @ hAPP ) )
!= ( C @ ( B @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).
thf(730,axiom,
tc_bool @ class_Orderings_Oorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Oorder) ).
thf(2430,plain,
tc_bool @ class_Orderings_Oorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[730]) ).
thf(179,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ~ ( c_Arrow__Order__Mirabelle_OLin @ ( B @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( C @ ( B @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__above_0) ).
thf(1152,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ~ ( c_Arrow__Order__Mirabelle_OLin @ ( B @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( C @ ( B @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(346,axiom,
! [B: $i,A: $i] :
( ~ ( c_Arrow__Order__Mirabelle_OLin @ ( A @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( c_Arrow__Order__Mirabelle_OLin @ ( B @ ( A @ c_Arrow__Order__Mirabelle_Omktop ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mktop__Lin_0) ).
thf(1532,plain,
! [B: $i,A: $i] :
( ~ ( c_Arrow__Order__Mirabelle_OLin @ ( A @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( c_Arrow__Order__Mirabelle_OLin @ ( B @ ( A @ c_Arrow__Order__Mirabelle_Omktop ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(276,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( E @ ( E @ ( tc_bool @ ( B @ tc_fun ) @ ( C @ c_COMBK ) ) @ ( A @ c_FuncSet_OPi ) ) ) @ ( D @ ( B @ ( E @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( E @ ( A @ c_FuncSet_Oextensional ) ) @ ( D @ ( B @ ( E @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( B @ ( B @ ( E @ ( D @ ( B @ ( B @ ( C @ ( B @ c_COMBI @ c_FuncSet_Orestrict ) ) ) @ ( A @ c_FuncSet_Ocompose ) ) ) ) ) )
= D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Id__compose_0) ).
thf(1378,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( E @ ( E @ ( tc_bool @ ( B @ tc_fun ) @ ( C @ c_COMBK ) ) @ ( A @ c_FuncSet_OPi ) ) ) @ ( D @ ( B @ ( E @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( E @ ( A @ c_FuncSet_Oextensional ) ) @ ( D @ ( B @ ( E @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( B @ ( B @ ( E @ ( D @ ( B @ ( B @ ( C @ ( B @ c_COMBI @ c_FuncSet_Orestrict ) ) ) @ ( A @ c_FuncSet_Ocompose ) ) ) ) ) )
= D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(266,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( G @ ( F @ ( E @ ( tc_bool @ ( F @ tc_fun ) @ ( F @ ( tc_bool @ ( F @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ ( A @ c_Finite__Set_Ofold__graph ) ) ) ) ) )
| ~ ( C @ ( D @ ( F @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( G @ ( F @ ( E @ ( D @ ( A @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Finite__Set_Ofold__graph ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff1__fold__graph_0) ).
thf(1357,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( G @ ( F @ ( E @ ( tc_bool @ ( F @ tc_fun ) @ ( F @ ( tc_bool @ ( F @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ ( A @ c_Finite__Set_Ofold__graph ) ) ) ) ) )
| ~ ( C @ ( D @ ( F @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( G @ ( F @ ( E @ ( D @ ( A @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( A @ c_Finite__Set_Ofold__graph ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(71,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I8_J_0) ).
thf(908,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(426,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( F @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( E @ ( B @ ( F @ c_Pair ) ) ) @ ( A @ ( E @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( E @ ( D @ ( C @ c_Relation_OImage ) ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Image__iff_2) ).
thf(1713,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( F @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( A @ ( E @ ( B @ ( F @ c_Pair ) ) ) @ ( A @ ( E @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( E @ ( D @ ( C @ c_Relation_OImage ) ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(373,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Orderings_Otop )
| ( B @ ( A @ tc_fun ) @ class_Orderings_Otop ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Otop) ).
thf(1597,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Orderings_Otop )
| ( B @ ( A @ tc_fun ) @ class_Orderings_Otop ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(516,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( F @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( F @ ( D @ hAPP ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( tc_bool @ ( A @ tc_fun ) @ ( E @ ( D @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UN__iff_2) ).
thf(1930,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( F @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( F @ ( D @ hAPP ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( tc_bool @ ( A @ tc_fun ) @ ( E @ ( D @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).
thf(43,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__linear_0) ).
thf(839,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(650,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__inf__iff_2) ).
thf(2241,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[650]) ).
thf(104,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_1) ).
thf(987,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(285,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__Diff_0) ).
thf(1399,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(384,axiom,
! [C: $i,B: $i,A: $i] :
( ( C = B )
| ( B @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neqE__ordered__idom_0) ).
thf(1621,plain,
! [C: $i,B: $i,A: $i] :
( ( C = B )
| ( B @ ( C @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(255,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( E @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( B @ ( C @ ( D @ ( C @ ( B @ ( A @ c_COMBK ) ) @ c_Set_Oimage ) ) ) )
= ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__constant_0) ).
thf(1331,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( E @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( B @ ( C @ ( D @ ( C @ ( B @ ( A @ c_COMBK ) ) @ c_Set_Oimage ) ) ) )
= ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(114,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( D @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__le__less__trans_0) ).
thf(1009,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( D @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_HOL_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(193,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__ord_I3_J_0) ).
thf(1184,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(553,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A = B )
| ~ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A = B )
| ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__below_11) ).
thf(2018,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A = B )
| ~ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A = B )
| ~ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).
thf(733,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= D ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UN__extend__simps_I2_J_0) ).
thf(2436,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= D ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[733]) ).
thf(292,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__Un__distrib_0) ).
thf(1416,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( D @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(621,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_COMBB ) ) ) ) @ hAPP ) )
= ( F @ ( B @ hAPP ) @ ( A @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBB__def_0) ).
thf(2170,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_COMBB ) ) ) ) @ hAPP ) )
= ( F @ ( B @ hAPP ) @ ( A @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[621]) ).
thf(593,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
!= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__Un__eq_1) ).
thf(2106,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
!= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).
thf(624,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( E @ ( D @ ( C @ ( tc_bool @ ( E @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ c_Fun_Oinj__on ) ) ) )
| ( ( A @ ( E @ ( tc_bool @ ( E @ tc_fun ) @ ( C @ ( D @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ c_Set_Oimage ) ) ) @ ( A @ ( E @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__Un_2) ).
thf(2177,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( E @ ( D @ ( C @ ( tc_bool @ ( E @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ c_Fun_Oinj__on ) ) ) )
| ( ( A @ ( E @ ( tc_bool @ ( E @ tc_fun ) @ ( C @ ( D @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ c_Set_Oimage ) ) ) @ ( A @ ( E @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[624]) ).
thf(685,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Set_Oimage ) ) ) @ ( C @ ( B @ hAPP ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rangeI_0) ).
thf(2321,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( A @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Set_Oimage ) ) ) @ ( C @ ( B @ hAPP ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[685]) ).
thf(522,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__subset__conv_0) ).
thf(1944,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).
thf(271,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( C @ ( E @ ( B @ c_Relation_OImage ) ) ) @ ( A @ ( C @ ( D @ ( B @ c_Relation_OImage ) ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( E @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ c_Relation_OImage ) ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Image__Int__subset_0) ).
thf(1367,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( A @ ( C @ ( E @ ( B @ c_Relation_OImage ) ) ) @ ( A @ ( C @ ( D @ ( B @ c_Relation_OImage ) ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( E @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( B @ c_Relation_OImage ) ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(85,axiom,
! [B: $i,A: $i] : ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__subsetI_0) ).
thf(940,plain,
! [B: $i,A: $i] : ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(314,axiom,
tc_bool @ class_Orderings_Opreorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Opreorder) ).
thf(1463,plain,
tc_bool @ class_Orderings_Opreorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(360,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ~ ( c_Arrow__Order__Mirabelle_OLin @ ( A @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( B @ ( A @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_above__Lin_0) ).
thf(1565,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ~ ( c_Arrow__Order__Mirabelle_OLin @ ( A @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( B @ ( A @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(481,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( D @ ( C @ c_SetInterval_Oord_OlessThan ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ord_OlessThan__iff_1) ).
thf(1848,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( D @ ( C @ c_SetInterval_Oord_OlessThan ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).
thf(570,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ c_Arrow__Order__Mirabelle_Ounanimity )
| ~ ( c_Arrow__Order__Mirabelle_OProf @ ( D @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( B @ ( A @ v_sko__Arrow__Order__Mirabelle__Xunanimity__def__1 ) ) @ ( D @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_unanimity__def_0) ).
thf(2059,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ c_Arrow__Order__Mirabelle_Ounanimity )
| ~ ( c_Arrow__Order__Mirabelle_OProf @ ( D @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( B @ ( A @ v_sko__Arrow__Order__Mirabelle__Xunanimity__def__1 ) ) @ ( D @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).
thf(675,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( B = C )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__antisym__conv_0) ).
thf(2297,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( B = C )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[675]) ).
thf(12,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( E @ ( D @ ( C @ ( B @ c_Set_Oimage ) ) ) @ ( A @ c_Set_Oimage ) ) ) )
= ( F @ ( D @ ( C @ ( D @ ( F @ ( E @ ( B @ ( A @ c_COMBB ) ) ) ) @ c_Set_Oimage ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__image_0) ).
thf(775,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( E @ ( D @ ( C @ ( B @ c_Set_Oimage ) ) ) @ ( A @ c_Set_Oimage ) ) ) )
= ( F @ ( D @ ( C @ ( D @ ( F @ ( E @ ( B @ ( A @ c_COMBB ) ) ) ) @ c_Set_Oimage ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(734,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Fun_Oinj__on ) ) ) )
| ( ( A @ ( C @ ( C @ ( A @ ( D @ ( B @ c_Set_Oimage ) ) ) @ ( C @ ( A @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Hilbert__Choice_Oinv__into ) ) ) @ c_Set_Oimage ) ) ) )
= D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inv__image__comp_0) ).
thf(2438,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Fun_Oinj__on ) ) ) )
| ( ( A @ ( C @ ( C @ ( A @ ( D @ ( B @ c_Set_Oimage ) ) ) @ ( C @ ( A @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Hilbert__Choice_Oinv__into ) ) ) @ c_Set_Oimage ) ) ) )
= D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[734]) ).
thf(649,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__left__idem_0) ).
thf(2238,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( C @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[649]) ).
thf(511,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ~ ( E @ ( D @ ( B @ c_FuncSet_Oextensional ) ) @ ( A @ ( E @ ( D @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( D @ ( B @ c_FuncSet_Oextensional ) ) @ ( C @ ( E @ ( D @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( E @ ( D @ ( C @ ( A @ ( B @ c_FuncSet_Osko__FuncSet__XextensionalityI__1__1 ) ) ) ) @ ( A @ hAPP ) )
!= ( E @ ( D @ ( C @ ( A @ ( B @ c_FuncSet_Osko__FuncSet__XextensionalityI__1__1 ) ) ) ) @ ( C @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_extensionalityI_1) ).
thf(1917,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = C )
| ~ ( E @ ( D @ ( B @ c_FuncSet_Oextensional ) ) @ ( A @ ( E @ ( D @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( D @ ( B @ c_FuncSet_Oextensional ) ) @ ( C @ ( E @ ( D @ tc_fun ) @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( E @ ( D @ ( C @ ( A @ ( B @ c_FuncSet_Osko__FuncSet__XextensionalityI__1__1 ) ) ) ) @ ( A @ hAPP ) )
!= ( E @ ( D @ ( C @ ( A @ ( B @ c_FuncSet_Osko__FuncSet__XextensionalityI__1__1 ) ) ) ) @ ( C @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).
thf(2,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = E )
| ( ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) )
!= ( D @ ( C @ ( F @ ( E @ c_Pair ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Pair__eq_0) ).
thf(755,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = E )
| ( ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) )
!= ( D @ ( C @ ( F @ ( E @ c_Pair ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(202,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( D @ ( A @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__insert__left_1) ).
thf(1204,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( D @ ( A @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) )
= ( D @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(467,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__infI1_0) ).
thf(1812,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf @ hAPP ) @ hAPP ) @ ( A @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).
thf(317,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Fun_Oinj__on ) ) ) )
| ~ ( C @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Set_Oimage ) ) ) @ ( A @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A
= ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__1 ) ) ) @ ( B @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_range__ex1__eq_0) ).
thf(1468,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Fun_Oinj__on ) ) ) )
| ~ ( C @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Set_Oimage ) ) ) @ ( A @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A
= ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__1 ) ) ) @ ( B @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(747,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( C @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert__iff_0) ).
thf(2470,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( C @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_lessequals @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[747]) ).
thf(489,axiom,
tc_bool @ class_Orderings_Otop,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Otop) ).
thf(1870,plain,
tc_bool @ class_Orderings_Otop,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).
thf(98,axiom,
! [B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__UNIV__right_0) ).
thf(972,plain,
! [B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Lattices_Oupper__semilattice__class_Osup @ hAPP ) @ hAPP ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(3167,plain,
$false,
inference(e,[status(thm)],[2163,2199,1036,2094,1633,1995,1559,1840,1850,941,1179,777,2250,1586,2452,1879,1337,1718,1168,2306,760,2109,2031,2072,1767,1237,846,2427,1083,962,1554,1110,1290,2395,1618,1401,2248,1073,2014,2380,1793,1437,1486,2363,2077,1750,977,2309,762,1924,1005,2117,1406,2104,1443,1808,2099,1591,1142,1269,1788,1608,1137,1310,2035,1735,1867,1275,814,2146,1507,1497,2195,1164,797,2316,2476,2168,1761,1342,913,1746,2216,2348,2046,1243,1391,841,2010,1645,1359,1601,2082,2067,1803,1518,1887,782,1441,1228,1482,1254,1055,785,1871,1907,1264,1323,802,1992,2126,1132,949,2185,1455,1832,934,1191,2420,1247,2373,1568,1773,1494,1100,1922,817,2403,1087,1704,870,1013,770,1741,881,1875,1778,2007,2222,1415,1946,2027,789,1450,2090,1373,1911,2259,1334,1682,2122,1677,1051,905,1302,1664,1040,1109,1418,2236,1383,1020,1960,806,1581,2335,966,1283,2073,2058,2281,1796,998,1345,1696,981,766,877,2190,1119,2424,2371,1526,2137,1104,1242,849,920,2204,925,1199,810,1338,1783,1067,2382,1915,1708,2061,2000,1047,1730,1057,2441,2264,1900,825,1021,1042,1676,1217,1824,2132,957,1223,894,1355,2277,1123,862,1502,820,1423,1032,1365,1920,2433,879,2332,1951,1296,830,1210,2228,2112,1106,916,2445,1687,1457,1819,1624,2327,2213,1195,2211,2313,1128,1573,974,2300,2100,1259,2377,1328,1121,1970,1856,1425,1672,1540,869,1755,783,2268,989,857,1089,1234,874,2157,2115,1534,1017,884,1160,1028,1361,753,1461,1075,2455,2080,1584,1214,1207,1889,1419,2460,1493,1964,1942,1659,2053,1842,1700,1937,1810,2172,1612,2472,1155,1744,1114,1776,1297,2304,2243,1932,1799,1984,1002,1429,1715,1720,2450,1588,1150,1478,1249,1266,2387,1231,1668,1974,2465,1060,984,911,2482,1599,1979,779,1759,1393,1434,1814,2208,1563,2408,1515,1026,1616,1732,1202,792,2076,1170,1286,2368,1466,1071,773,794,2144,1135,2292,1680,1698,1595,1631,1727,1510,1764,2413,2253,2275,2033,2149,1548,1927,819,1007,2048,1884,1389,1125,1652,2016,1388,2398,1520,2134,2188,772,2393,1752,1256,1488,1139,1786,936,2220,2029,1312,787,1865,1635,2166,1464,2319,1675,1271,1371,1239,1997,2055,1092,1897,804,2346,2119,2084,1894,1117,1011,1349,1722,1690,764,979,2361,2311,1853,1408,2257,996,2284,2246,1603,1043,1801,1571,1376,1439,2197,1969,1307,2065,1175,2182,2343,816,1862,964,1556,1293,1952,1112,890,2180,1877,1471,2025,1080,799,1909,1162,1838,1325,1177,1381,2418,1396,2350,2401,768,1245,2086,2139,1015,2022,2390,922,1805,2069,1445,1528,2244,1000,851,1102,2005,1626,1034,1166,944,2271,1684,2202,1145,1049,1662,2096,1304,1873,1905,1420,927,2037,1277,2124,812,1509,939,1340,968,1181,823,836,1551,1845,1748,1770,2375,2012,1605,1647,1368,1780,1531,993,1070,872,1225,1743,2192,887,954,1252,1230,1484,2160,1432,1186,1038,1262,2337,2128,1901,2044,1130,1738,2354,1711,1053,1499,1790,2224,1300,1637,1317,1830,1085,1658,2322,1538,951,2468,1220,1404,1934,2411,1543,2113,1023,1702,1972,864,1427,1504,1094,1670,2266,859,991,1536,1981,2279,2357,1955,1881,1272,1940,2458,2479,2088,1459,1966,931,1949,1817,903,1517,2325,891,1316,1649,2352,1157,1321,1834,1913,1654,1412,1448,1189,2342,1575,844,2226,1453,2443,1385,2273,2290,1062,946,1629,2431,1822,2416,2174,1476,1674,1639,1903,2406,1523,2130,2152,2262,2447,1689,2462,1077,1212,763,899,2120,1045,1030,1491,2384,2475,929,2330,1706,1193,2230,2294,1614,2421,800,2218,2287,1512,2302,2233,1546,1593,1148,2050,1480,2003,2142,1642,2102,1725,1280,1578,1957,2155,2255,1097,835,854,1986,867,1757,1859,1657,807,1693,1561,2366,2091,1891,828,1065,2040,2340,796,918,1989,1363,1314,1172,897,1288,1197,960,1473,1346,2063,1610,1352,1977,1827,2430,1152,1532,1378,1357,908,1713,1597,1930,839,2241,987,1399,1621,1331,1009,1184,2018,2436,1416,2170,2106,2177,2321,1944,1367,940,1463,1565,1848,2059,2297,775,2438,2238,1917,755,1204,1812,1468,2470,1870,972]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SCT083-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.12 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.27/0.51 % Computer : n014.cluster.edu
% 0.27/0.51 % Model : x86_64 x86_64
% 0.27/0.51 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.27/0.51 % Memory : 8046.5625MB
% 0.27/0.51 % OS : Linux 6.8.0-71-generic
% 0.27/0.51 % CPULimit : 300
% 0.27/0.51 % WCLimit : 300
% 0.27/0.51 % DateTime : Sat Sep 26 06:25:47 UTC 2026
% 0.11/0.52 % CPUTime :
% 0.11/0.52 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 1.48/1.42 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 3.43/2.14 % [INFO] Parsing done (712ms).
% 3.43/2.15 % [INFO] Running in sequential loop mode.
% 4.86/2.71 % [INFO] eprover registered as external prover.
% 4.86/2.72 % [INFO] Scanning for conjecture ...
% 6.00/3.11 % [INFO] Found a conjecture (or negated_conjecture) and 751 axioms. Running axiom selection ...
% 7.66/3.40 % [INFO] Axiom selection finished. Selected 751 axioms (removed 0 axioms).
% 9.58/3.87 % [INFO] Problem is propositional (TPTP CNF).
% 10.03/3.90 % [INFO] Type checking passed.
% 10.03/3.91 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 46.90/11.78 % External prover 'e' found a proof!
% 46.90/11.78 % [INFO] Killing All external provers ...
% 46.90/11.78 % Time passed: 11043ms (effective reasoning time: 9621ms)
% 47.16/11.80 % Axioms used in derivation (751): cls_inf__sup__aci_I2_J_0, cls_in__mktop_1, cls_xt1_I9_J_0, cls_linorder__antisym__conv2_1, cls_Diff1__fold__graph_0, cls_inj__image__mem__iff_1, cls_inf__sup__absorb_0, clsarity_nat__HOL_Oord, cls_vimage__code_0, cls_Int__Un__distrib_0, clsarity_fun__Lattices_Olower__semilattice, cls_Diff__cancel_0, cls_INT__extend__simps_I4_J_0, cls_PiE_0, cls_Int__absorb2_0, cls_subset__insert_1, cls_2_0, cls_Diff__iff_2, cls_bij__betw__compose_0, cls_Inter__lower_0, cls_order__le__less__trans_0, cls_equiv__class__eq__iff_0, cls_sup__ge1_0, cls_image__constant_0, cls_in__above_11, cls_insertE_0, cls_Un__Diff_0, cls_in__below_14, cls_Un__subset__iff_0, cls_ball__conj__distrib_3, cls_insert__inter__insert_0, cls_u_0, cls_less__fun__def_1, cls_Pi__I_0, cls_order__less__le__trans_0, cls_order__eq__iff_0, cls_inj__on__restrict__eq_0, cls_converseI_0, cls_InterI_1, cls_equalityI_0, cls_sup__top__left_0, cls_inj__on__Un_2, cls_COMBC__def_0, cls_subset__image__iff_2, cls_range__ex1__eq_0, cls_Image__singleton__iff_0, cls_empty__is__image_1, cls_inj__image__eq__iff_0, cls_range__ex1__eq_3, cls_image__mono_0, cls_Un__empty__left_0, cls_update__accessor__congruence__foldE_0, cls_le__funD_0, cls_fun__upd__image_1, cls_xt1_I12_J_0, cls_funcsetI_0, cls_subset__empty_1, cls_Pi__mem_0, cls_funcset__image_0, cls_inj__on__image__Int_0, cls_sup__bot__right_0, cls_insert__code_1, cls_fun__upd__apply_1, clsarity_nat__Lattices_Odistrib__lattice, clsarity_bool__Lattices_Olower__semilattice, cls_le__SUPI_0, cls_bexCI_0, cls_Un__upper1_0, cls_UN__extend__simps_I10_J_0, cls_Un__commute_0, clsarity_fun__Orderings_Oorder, cls_UnCI_1, cls_distrib__sup__le_0, cls_Int__mono_0, cls_bij__betw__def_0, cls_linorder__neqE_0, cls_mkbot__Lin_0, cls_vimage__Diff_0, cls_restrict__in__funcset_0, cls_le__iff__inf_1, cls_complete__lattice_OSup__singleton_0, cls_inf__sup__aci_I6_J_0, cls_lfp__const_0, cls_CHAINED_0, cls_image__restrict__eq_0, cls_update__accessor__noopE_0, cls_4_2, cls_COMBK__def_0, cls_ord_OgreaterThan__iff_0, cls_in__below_3, cls_image__Int_0, cls_Diff__Un_0, cls_Int__insert__left_0, cls_empty__iff_0, cls_in__above_7, cls_le__inf__iff_1, cls_bij__betw__imp__funcset_0, cls_Diff__subset__conv_0, cls_Int__Un__distrib2_0, cls_mem__def_1, cls_bexE_1, cls_fun__upd__image_0, clsarity_nat__Orderings_Olinorder, cls_Int__Collect_1, cls_Inf__lower_0, cls_insert__absorb_0, cls_equiv__class__self_0, cls_Int__subset__iff_2, cls_in__below_2, cls_image__vimage__subset_0, cls_inj__on__image__set__diff_0, cls_less__supI1_0, cls_setsum__diff1__nat_1, cls_inf1E_1, cls_Diff__triv_0, cls_insert__iff_1, cls_insert__subset_0, cls_bex__UN_3, cls_inj__transfer_1, cls_Int__absorb1_0, cls_sup__inf__distrib2_0, cls_in__above_4, cls_inj__image__subset__iff_0, cls_le__sup__iff_0, cls_inj__on__Un__image__eq__iff_0, cls_Image__Un_0, cls_in__mkbot_4, cls_inf__sup__distrib1_0, cls_vimage__UNIV_0, cls_order__less__trans_0, cls_surj__compose_0, clsarity_fun__Lattices_Oupper__semilattice, cls_in__below_7, cls_ballE_0, cls_Diff__insert_0, cls_set__rev__mp_0, cls_insert__Diff__if_1, cls_inf__left__commute_0, cls_pred__equals__eq_0, cls_ord_OatLeastAtMost__iff_2, cls_COMBB__def_0, cls_CollectI_0, cls_inf__commute_0, cls_compose__assoc_0, cls_inj__image__mem__iff_0, cls_subset__insert__iff_2, cls_Un__left__commute_0, cls_Pi__I_H_1, clsarity_fun__Orderings_Otop, cls_f__inv__into__f_0, clsarity_bool__HOL_Oord, cls_set__mp_0, cls_bij__betw__inv__into_0, cls_IIA__def_2, cls_Un__Int__distrib2_0, cls_Int__empty__right_0, cls_Collect__empty__eq_0, cls_equiv__class__eq__iff_3, cls_le__supI_0, cls_UN__extend__simps_I1_J_0, cls_psubset__insert__iff_8, cls_CollectD_0, cls_in__below_11, cls_extensionalityI_0, cls_not__psubset__empty_0, cls_vimage__insert_0, cls_Un__empty_2, cls_le__iff__sup_1, cls_order__less__asym_0, cls_Union__disjoint_0, cls_linorder__not__less_0, cls_Inf__singleton_0, cls_Un__subset__iff_1, cls_Inf__binary_0, cls_SUP__const_0, cls_order__le__less_0, cls_rangeI_0, cls_order__less__asym_H_0, cls_inj__on__Un_3, cls_rev__image__eqI_0, cls_linorder__antisym__conv1_0, cls_eq__equiv__class__iff2_1, cls_Diff__UNIV_0, cls_UN__iff_2, cls_linorder__antisym__conv2_0, cls_le__iff__sup_0, cls_empty__is__image_0, cls_psubset__eq_1, cls_UN__extend__simps_I3_J_0, cls_order__eq__refl_0, cls_ord_OatLeastLessThan__iff_0, cls_4_3, cls_inj__on__insert_0, cls_Image__empty_0, cls_range__composition_0, cls_SUP1__I_0, cls_UN__absorb_0, clsarity_fun__Orderings_Obot, cls_bij__betw__def_1, cls_in__mktop_3, cls_le__supE_1, cls_fun__upd__other_0, cls_ball__conj__distrib_1, cls_in__below_9, cls_inv__f__eq_0, cls_pairwise__neutrality_0, cls_Union__upper_0, cls_psubset__insert__iff_5, cls_inf__sup__aci_I8_J_0, cls_in__above_6, cls_Sup__UNIV_0, cls_notin__Lin__iff_0, cls_Un__empty__right_0, cls_insert__ident_0, cls_image__constant__conv_1, cls_vimageI_0, cls_Un__UNIV__right_0, cls_SigmaI_0, cls_Un__absorb2_0, cls_restrict__extensional_0, cls_psubset__trans_0, cls_inv__image__comp_0, clsarity_bool__Orderings_Oorder, cls_bot__least_0, cls_less__le__not__le_2, cls_2_1, cls_xt1_I10_J_0, cls_sup__eq__bot__eq2_0, cls_in__below_6, cls_UnCI_0, cls_Int__insert__right_1, cls_not__less__iff__gr__or__eq_0, cls_UN__Un_0, cls_bij__betw__restrict__eq_0, cls_inf__top__right_0, cls_Sup__singleton_0, cls_UN__constant_0, cls_Lin__irrefl_0, cls_Un__upper2_0, cls_funcset__id_0, cls_vimage__ident_0, cls_bexCI_1, cls_singleton__iff_1, cls_2_3, cls_range__ex1__eq_2, cls_complete__lattice_OInf__empty_0, cls_subset__iff_0, cls_bex__Un_6, cls_Collect__mem__eq_0, clsarity_fun__HOL_Oord, cls_Diff__idemp_0, cls_inj__on__restrict__eq_1, cls_subset__empty_0, cls_in__mkbot_3, cls_equiv__class__eq_0, cls_UnionE_1, cls_complete__lattice_OInf__UNIV_0, cls_inf__eq__top__eq1_0, cls_bexI_1, cls_UN__simps_I10_J_0, cls_inj__on__compose_0, cls_insert__code_2, cls_CHAINED_0_01, cls_rev__predicate1D_0, cls_extensional__arb_0, cls_insert__Diff__single_0, cls_inv__into__image__cancel_0, cls_image__insert_0, cls_UN__subset__iff_0, cls_unanimity__def_0, cls_vimage__Un_0, cls_diff__single__insert_0, cls_inf__absorb2_0, cls_ball__conj__distrib_0, clsarity_bool__Lattices_Oupper__semilattice, cls_UNIV__not__empty_0, cls_fold__graph_OinsertI_0, cls_bex__UN_4, cls_ord_OlessThan__iff_0, cls_doubleton__eq__iff_2, cls_bij__betw__restrict__eq_1, cls_inv__into__f__f_0, cls_SUP1__iff_2, cls_Sup__binary_0, cls_Int__Collect_0, cls_Un__insert__left_0, cls_inf__sup__ord_I2_J_0, cls_vimage__singleton__eq_1, cls_subset__insert__iff_3, cls_Inf__insert_0, cls_fun__upd__triv_0, clsarity_nat__Orderings_Obot, cls_xt1_I8_J_0, cls_SigmaD2_0, cls_vimage__const_1, cls_inf__sup__aci_I3_J_0, cls_set__eq__subset_2, cls_Un__mono_0, cls_less__infI1_0, cls_Int__insert__left_1, cls_insert__subset_1, cls_Int__empty__left_0, cls_ATP__Linkup_Ofequal__imp__equal_0, cls_Image__singleton__iff_1, cls_psubset__insert__iff_4, cls_bex__Un_5, cls_PowI_0, clsarity_nat__Lattices_Olower__semilattice, cls_Pow__top_0, cls_inj__image__subset__iff_1, cls_ex__in__conv_0, cls_sup__commute_0, cls_le__inf__iff_0, cls_Int__subset__iff_1, cls_subset__iff__psubset__eq_0, cls_inj__on__inv__into_0, cls_not__leE_0, cls_Un__subset__iff_2, cls_fold__graph_OemptyI_0, cls_in__below_10, cls_in__below_1, cls_linorder__linear_0, cls_Un__empty_0, cls_in__above_1, cls_bij__betw__def_2, cls_complete__lattice_OSup__UNIV_0, cls_bex__Un_7, clsarity_fun__Lattices_Olattice, cls_in__mktop_5, cls_Int__assoc_0, cls_extensionalityI_1, cls_order__antisym_0, cls_order__trans_0, cls_bexE_0, cls_psubset__insert__iff_9, cls_image__empty_0, cls_mktop__Lin_0, cls_subset__trans_0, cls_in__mktop_0, cls_double__diff_0, cls_inf__le2_0, cls_insert__is__Un_0, cls_ord_OatLeastAtMost__iff_1, cls_ord_OgreaterThanLessThan__iff_0, cls_DiffI_0, cls_eq__equiv__class__iff2_0, cls_Image__iff_2, cls_le__supE_0, cls_empty__not__insert_0, cls_sup__assoc_0, cls_Diff__Int__distrib2_0, cls_4_0, cls_image__constant__conv_0, cls_in__mkbot_2, cls_insertI1_0, cls_linorder__antisym__conv1_1, cls_inj__on__insert_1, cls_psubset__insert__iff_6, cls_SigmaD1_0, cls_le__sup__iff_1, clsarity_bool__Orderings_Obot, cls_mem__def_0, cls_inf__sup__aci_I7_J_0, cls_Un__Int__crazy_0, clsarity_bool__Orderings_Opreorder, cls_singleton__conv_0, cls_insert__Diff1_0, cls_Image__Int__subset_0, cls_linorder__not__le_1, cls_3_3, cls_in__mktop_4, cls_Un__absorb1_0, cls_sup__top__right_0, cls_Diff__insert2_0, cls_Sup__upper_0, cls_converse__iff_1, cls_sup__least_0, cls_rev__ImageI_0, cls_Pair__eq_0, cls_empty__subsetI_0, cls_top__greatest_0, cls_fun__upd__twist_0, cls_pairwise__neutrality_1, cls_image__ident_0, cls_ord_OatLeastLessThan__iff_1, cls_doubleton__eq__iff_0, cls_inf__sup__aci_I1_J_0, cls_sup1E_0, cls_distrib__inf__le_0, cls_in__above_5, cls_Int__commute_0, cls_Un__UNIV__left_0, cls_subset__refl_0, cls_converse__in__Lin_0, cls_vimage__subsetI_0, cls_singletonE_0, cls_image__diff__subset_0, clsarity_nat__Lattices_Olattice, cls_Int__Diff_0, cls_above__Lin_0, cls_image__iff_2, cls_insertCI_0, cls_psubset__eq_0, cls_image__Int__subset_0, cls_image__set__diff_0, cls_pred__subset__eq_1, cls_Un__Diff__cancel_0, cls_inj__on__iff_0, clsarity_nat__Orderings_Opreorder, cls_complete__lattice_OInf__insert_0, cls_image__Un_0, cls_insert__Diff_0, cls_not__less__iff__gr__or__eq_1, cls_ord_OlessThan__iff_1, cls_Inf__UNIV_0, cls_Pow__bottom_0, cls_inj__on__empty_0, cls_in__below_12, cls_UNIV__I_0, cls_DiffE_0, cls_sup1CI_1, cls_complete__lattice_OInf__binary_0, cls_order__le__neq__trans_0, cls_le__infE_0, cls_UnionE_0, cls_SUP2__iff_2, cls_fun__upd__apply_0, cls_complete__lattice_OSup__binary_0, cls_le__inf__iff_2, cls_in__above_12, cls_subset__equiv__class_0, cls_vimage__Int_0, cls_top1I_0, cls_order__eq__iff_2, cls_le__infI1_0, cls_Int__absorb_0, cls_in__above_9, cls_inf__assoc_0, cls_2_2, cls_insert__mono_0, cls_le__supI2_0, 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cls_order__le__less_1, cls_linorder__neq__iff_1, cls_psubset__subset__trans_0, cls_3_0, cls_inj__on__def_0, cls_Un__absorb_0, cls_order__antisym__conv_0, cls_psubsetD_0, cls_ord_OatLeastAtMost__iff_0, cls_SUP2__I_0, cls_Int__lower1_0, cls_InterD_0, clsarity_bool__Lattices_Olattice, cls_psubset__insert__iff_3, cls_injD_0, cls_Union__quotient_0, cls_eq__eqI_0, cls_compose__def_0, cls_vimage__eq_1, cls_bexCI_3, cls_order__less__le_2, cls_Un__Int__distrib_0, clsarity_bool__Lattices_Obounded__lattice, cls_inf__sup__ord_I1_J_0, cls_le__infI_0, cls_subset__insert__iff_4, cls_inv__into__funcset_0, cls_Int__subset__iff_0, cls_linorder__less__linear_0, cls_restrictI_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_xt1_I11_J_0, clsarity_fun__Complete__Lattice_Ocomplete__lattice, cls_quotientE_0, cls_complete__lattice_OInf__lower_0, cls_vimageE_0, cls_inf__bot__left_0, cls_inf1I_0, cls_rev__bexI_0, cls_assms_I3_J_0, cls_Union__Pow__eq_0, cls_insert__not__empty_0, cls_Int__left__commute_0, cls_le__sup__iff_2, cls_in__above_2, cls_inf__idem_0, clsarity_fun__Lattices_Obounded__lattice, cls_equiv__class__subset_0, cls_insert__absorb2_0, cls_UNION__empty__conv_I1_J_0, cls_fun__upd__idem_0, cls_IIA__def_1, cls_sup__inf__absorb_0, cls_subset__singletonD_0, cls_Int__iff_2, cls_notin__Lin__iff_1, cls_Un__Int__assoc__eq_1, cls_doubleton__eq__iff_1, cls_UN__extend__simps_I2_J_0, cls_eq__equiv__class__iff_0, cls_fun__upd__idem__iff_0, cls_4_1, cls_inf__sup__aci_I4_J_0, cls_Sup__insert_0, cls_vimage__singleton__eq_0, cls_xt1_I6_J_0, cls_subset__insert__iff_0, cls_vimage__code_1, cls_UN__I_0, cls_converse__converse_0, cls_ord_OgreaterThanLessThan__iff_1, cls_pairwise__neutrality_3, cls_quotient__disj_0, cls_equiv__class__eq__iff_1, cls_inv__into__injective_0, cls_subset__psubset__trans_0, cls_in__mkbot_1, clsarity_bool__Complete__Lattice_Ocomplete__lattice, cls_empty__Collect__eq_0, 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clsarity_fun__Orderings_Opreorder, cls_converse__in__Lin_1, cls_UN__upper_0, cls_IntE_1, cls_Un__least_0, cls_inj__on__contraD_0, cls_sup1CI_0, cls_Int__greatest_0, cls_in__above_8, cls_iso__tuple__update__accessor__cong__assist__def_0, cls_IntE_0, cls_in__mkbot_5, cls_inj__onD_0, cls_Union__disjoint_2, cls_subset__Un__eq_1, cls_sup__left__commute_0, cls_Inf__empty_0, cls_le__infE_1, cls_Int__UNIV__left_0, cls_funcsetI_1, cls_image__subset__iff_0, cls_inf__le1_0, cls_inf__left__idem_0, cls_in__below_13, cls_complete__lattice_OSup__upper_0, cls_empty__fold__graphE_0, clsarity_bool__Lattices_Odistrib__lattice, cls_mem__Sigma__iff_2, cls_image__eqI_0, cls_pred__subset__eq_0, cls_compose__Id_0, cls_in__below_4, cls_subset__UNIV_0, cls_inj__on__diff_0, cls_inj__on__insert_2, cls_inv__into__into_0, cls_restrict__in__funcset_1, cls_insertCI_1, cls_range__ex1__eq_1, cls_doubleton__eq__iff_4, cls_ord_OatMost__iff_0, cls_UnionI_0, cls_Diff__subset__conv_1, cls_rev__bexI_1, cls_insert__code_0, cls_le__eqI_1, cls_order__less__imp__le_0, cls_vimage__def_0, cls_IIA__def_0, cls_complete__lattice_OSup__empty_0, cls_Un__Diff__Int_0, cls_subset__insertI_0, cls_inj__on__id2_0, cls_vimageD_0, cls_ord_OgreaterThanLessThan__iff_2, cls_bexCI_2, cls_restrictI_1, cls_Diff__Int2_0, cls_inv__f__f_0, cls_quotient__eqI_0, cls_below__Lin_0, cls_ATP__Linkup_OCOMBI__def_0, cls_DiffE_1, cls_equiv__class__nondisjoint_0, cls_Diff__partition_0, cls_insert__image_0, cls_fun__upd__upd_0, cls_psubset__insert__iff_2, cls_image__vimage__eq_0, cls_ord_OatMost__iff_1, cls_inj__on__Un_1, cls_sup__inf__distrib1_0, cls_inf__top__left_0, cls_vimage__empty_0, cls_Un__Int__assoc__eq_0, cls_COMBI__def_0, cls_insert__commute_0, cls_quotientI_0, cls_image__image_0, cls_Diff__insert__absorb_0, cls_le__infI2_0, cls_UNION__empty__conv_I2_J_0, cls_sup__bot__left_0, cls_ord_OgreaterThan__iff_1, cls_in__below_8, cls_disjoint__iff__not__equal_0, cls_complete__Lin_1, cls_insert__iff_2, clsarity_nat__Orderings_Oorder, cls_xt1_I7_J_0, cls_image__is__empty_0, cls_3_1, cls_imageI_0, clsarity_fun__Lattices_Odistrib__lattice, cls_pairwise__neutrality_2, cls_less__eqI_1, cls_order__less__le_1, cls_less__fun__def_0, cls_equiv__class__eq__iff_2, cls_linorder__not__less_1, cls_UN__insert_0, cls_quotient__eq__iff_0, cls_Un__insert__right_0, cls_ballE_1, cls_psubset__insert__iff_7, cls_Pair__eq_1, cls_quotientE_1, cls_equalityE_0, cls_Pi__I_H_0, cls_inf__sup__distrib2_0, cls_inf__bot__right_0, cls_sup__absorb1_0, cls_dual__complete__lattice_0, cls_Union__disjoint_1, cls_ball__empty_0, cls_singleton__conv2_0, cls_UN__empty2_0, cls_psubset__eq_2, cls_funcset__compose_0, cls_lfp__lowerbound_0, cls_image__inv__f__f_0, cls_subset__insert__iff_1, cls_in__above_3, cls_compose__eq_0, clsarity_bool__Orderings_Otop, cls_in__mkbot_0, cls_inv__into__f__eq_0, cls_Int__insert__right_0, cls_eq__equiv__class__iff_1, cls_ball__conj__distrib_2, cls_Diff__subset_0, cls_predicate1D_0, cls_inf1E_0, cls_Int__Collect_2, cls_empty__Diff_0, cls_in__above_14, cls_fun__upd__idem__iff_1, cls_in__above_0
% 47.16/11.80 % No. of inferences in proof: 1505
% 47.16/11.80 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 11043 ms resp. 9621 ms w/o parsing
% 50.98/12.71 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 50.98/12.72 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------