%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SCT071-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n017.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 08:27:09 AM UTC 2026
% Result : Unsatisfiable 13.57s 3.60s
% Output : Refutation 14.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 435
% Syntax : Number of formulae : 871 ( 305 unt; 0 typ; 0 def)
% Number of atoms : 1759 ( 546 equ; 0 cnn)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 12754 ( 840 ~; 888 |; 0 &;11026 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 53 ( 51 usr; 5 con; 0-5 aty)
% Number of variables : 2700 ( 0 ^;2700 !; 0 ?;2700 :)
% Comments :
%------------------------------------------------------------------------------
thf(v_thesis_____decl,type,
v_thesis____: $o ).
thf(c_Set_Oinsert_decl,type,
c_Set_Oinsert: $i > $i > $i > $i ).
thf(c_Orderings_Obot__class_Obot_decl,type,
c_Orderings_Obot__class_Obot: $i > $i ).
thf(tc_fun_decl,type,
tc_fun: $i > $i > $i ).
thf(tc_bool_decl,type,
tc_bool: $i ).
thf(class_Orderings_Olinorder_decl,type,
class_Orderings_Olinorder: $i > $o ).
thf(c_HOL_Oord__class_Oless_decl,type,
c_HOL_Oord__class_Oless: $i > $i > $i > $o ).
thf(class_Orderings_Oorder_decl,type,
class_Orderings_Oorder: $i > $o ).
thf(c_lessequals_decl,type,
c_lessequals: $i > $i > $i > $o ).
thf(c_Fun_Obij_decl,type,
c_Fun_Obij: $i > $i > $i > $o ).
thf(c_Fun_Oid_decl,type,
c_Fun_Oid: $i > $i ).
thf(c_Fun_Ocomp_decl,type,
c_Fun_Ocomp: $i > $i > $i > $i > $i > $i ).
thf(hAPP_decl,type,
hAPP: $i > $i > $i ).
thf(c_HOL_Ominus__class_Ominus_decl,type,
c_HOL_Ominus__class_Ominus: $i > $i > $i > $i ).
thf(c_SetInterval_Oord__class_OlessThan_decl,type,
c_SetInterval_Oord__class_OlessThan: $i > $i > $i ).
thf(c_SetInterval_Oord__class_OatLeastLessThan_decl,type,
c_SetInterval_Oord__class_OatLeastLessThan: $i > $i > $i > $i ).
thf(tc_nat_decl,type,
tc_nat: $i ).
thf(c_Hilbert__Choice_Oinv__into_decl,type,
c_Hilbert__Choice_Oinv__into: $i > $i > $i > $i > $i ).
thf(c_Orderings_Otop__class_Otop_decl,type,
c_Orderings_Otop__class_Otop: $i > $i ).
thf(c_HOL_Ouminus__class_Ouminus_decl,type,
c_HOL_Ouminus__class_Ouminus: $i > $i ).
thf(c_Lattices_Olower__semilattice__class_Oinf_decl,type,
c_Lattices_Olower__semilattice__class_Oinf: $i > $i > $i > $i ).
thf(c_Lattices_Oupper__semilattice__class_Osup_decl,type,
c_Lattices_Oupper__semilattice__class_Osup: $i > $i > $i > $i ).
thf(class_Complete__Lattice_Ocomplete__lattice_decl,type,
class_Complete__Lattice_Ocomplete__lattice: $i > $o ).
thf(c_Complete__Lattice_OSup__class_OSup_decl,type,
c_Complete__Lattice_OSup__class_OSup: $i > $i > $i ).
thf(c_Fun_Osurj_decl,type,
c_Fun_Osurj: $i > $i > $i > $o ).
thf(c_Finite__Set_Ofinite_decl,type,
c_Finite__Set_Ofinite: $i > $i > $o ).
thf(class_Nat_Osemiring__char__0_decl,type,
class_Nat_Osemiring__char__0: $i > $o ).
thf(c_Nat_Osemiring__1__class_Oof__nat_decl,type,
c_Nat_Osemiring__1__class_Oof__nat: $i > $i > $i ).
thf(c_Fun_Oinj__on_decl,type,
c_Fun_Oinj__on: $i > $i > $i > $i > $o ).
thf(c_Set_Ovimage_decl,type,
c_Set_Ovimage: $i > $i > $i > $i > $i ).
thf(c_Set_Oimage_decl,type,
c_Set_Oimage: $i > $i > $i > $i > $i ).
thf(c_Finite__Set_Ocard_decl,type,
c_Finite__Set_Ocard: $i > $i > $i ).
thf(c_Fun_Obij__betw_decl,type,
c_Fun_Obij__betw: $i > $i > $i > $i > $i > $o ).
thf(c_Fun_Othe__inv__into_decl,type,
c_Fun_Othe__inv__into: $i > $i > $i > $i > $i ).
thf(c_Suc_decl,type,
c_Suc: $i > $i ).
thf(c_List_Omap_decl,type,
c_List_Omap: $i > $i > $i > $i > $i ).
thf(c_HOL_Ozero__class_Ozero_decl,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
thf(c_COMBB_decl,type,
c_COMBB: $i > $i > $i > $i > $i > $i ).
thf(class_Finite__Set_Ofinite_Ofinite_decl,type,
class_Finite__Set_Ofinite_Ofinite: $i > $o ).
thf(c_Typedef_Otype__definition_decl,type,
c_Typedef_Otype__definition: $i > $i > $i > $i > $i > $o ).
thf(class_Ring__and__Field_Osemiring__1_decl,type,
class_Ring__and__Field_Osemiring__1: $i > $o ).
thf(c_List_Osko__SetInterval__Xex__bij__betw__nat__finite__1__1_decl,type,
c_List_Osko__SetInterval__Xex__bij__betw__nat__finite__1__1: $i > $i > $i ).
thf(tc_Arrow__Order__Mirabelle_Oindi_decl,type,
tc_Arrow__Order__Mirabelle_Oindi: $i ).
thf(c_ATP__Linkup_Osko__Fun__XinjI__1__1_decl,type,
c_ATP__Linkup_Osko__Fun__XinjI__1__1: $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Fun__XinjI__1__2_decl,type,
c_ATP__Linkup_Osko__Fun__XinjI__1__2: $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__imp__inv__eq__1__1_decl,type,
c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__imp__inv__eq__1__1: $i > $i > $i > $i > $i ).
thf(c_List_OremoveAll_decl,type,
c_List_OremoveAll: $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Fun__Xdatatype__injI__1__1_decl,type,
c_ATP__Linkup_Osko__Fun__Xdatatype__injI__1__1: $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Fun__Xdatatype__injI__1__2_decl,type,
c_ATP__Linkup_Osko__Fun__Xdatatype__injI__1__2: $i > $i > $i > $i ).
thf(c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1_decl,type,
c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1: $i > $i > $i ).
thf(class_Ring__and__Field_Osemiring__0_decl,type,
class_Ring__and__Field_Osemiring__0: $i > $o ).
thf(94,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Un_0) ).
thf(645,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(171,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__mono_0) ).
thf(809,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(402,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 @ ( D @ ( C @ ( B @ c_List_OremoveAll ) ) @ ( A @ c_List_Omap ) ) ) )
= ( E @ ( E @ ( D @ ( C @ ( A @ c_List_Omap ) ) ) @ ( B @ ( A @ hAPP ) @ c_List_OremoveAll ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__removeAll__inj_0) ).
thf(1337,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 @ ( D @ ( C @ ( B @ c_List_OremoveAll ) ) @ ( A @ c_List_Omap ) ) ) )
= ( E @ ( E @ ( D @ ( C @ ( A @ c_List_Omap ) ) ) @ ( B @ ( A @ hAPP ) @ c_List_OremoveAll ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(264,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( B @ c_Fun_Obij ) ) )
| ~ ( D @ ( A @ ( C @ c_Fun_Obij ) ) )
| ( ( E @ ( A @ ( A @ ( E @ ( D @ ( C @ ( B @ c_Fun_Ocomp ) ) ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Hilbert__Choice_Oinv__into ) ) ) )
= ( E @ ( A @ ( D @ ( E @ ( D @ ( B @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Hilbert__Choice_Oinv__into ) ) ) @ ( D @ ( A @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Hilbert__Choice_Oinv__into ) ) ) @ c_Fun_Ocomp ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__inv__distrib_0) ).
thf(1024,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( B @ c_Fun_Obij ) ) )
| ~ ( D @ ( A @ ( C @ c_Fun_Obij ) ) )
| ( ( E @ ( A @ ( A @ ( E @ ( D @ ( C @ ( B @ c_Fun_Ocomp ) ) ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Hilbert__Choice_Oinv__into ) ) ) )
= ( E @ ( A @ ( D @ ( E @ ( D @ ( B @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Hilbert__Choice_Oinv__into ) ) ) @ ( D @ ( A @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Hilbert__Choice_Oinv__into ) ) ) @ c_Fun_Ocomp ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(341,axiom,
! [A: $i] :
( ( tc_nat @ c_HOL_Ozero__class_Ozero )
!= ( A @ c_Suc ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Zero__neq__Suc_0) ).
thf(1190,plain,
! [A: $i] :
( ( tc_nat @ c_HOL_Ozero__class_Ozero )
!= ( A @ c_Suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(147,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__disjoint_0) ).
thf(760,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(20,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_1) ).
thf(479,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(362,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( C @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_lessequals ) ) )
| ~ ( C @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( ( C @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_endo__inj__surj_0) ).
thf(1237,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( C @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_lessequals ) ) )
| ~ ( C @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( ( C @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(210,axiom,
tc_bool @ class_Complete__Lattice_Ocomplete__lattice,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Complete__Lattice_Ocomplete__lattice) ).
thf(893,plain,
tc_bool @ class_Complete__Lattice_Ocomplete__lattice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(290,axiom,
! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__upper1_0) ).
thf(1083,plain,
! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(336,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/sandbox/benchmark/theBenchmark.p',cls_vimage__UNIV_0) ).
thf(1179,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)],[336]) ).
thf(154,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( E @ ( B @ c_Fun_Osurj ) ) )
| ~ ( D @ ( C @ ( A @ c_Fun_Osurj ) ) )
| ( D @ ( E @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ocomp ) ) ) ) @ c_Fun_Osurj ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comp__surj_0) ).
thf(777,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( E @ ( B @ c_Fun_Osurj ) ) )
| ~ ( D @ ( C @ ( A @ c_Fun_Osurj ) ) )
| ( D @ ( E @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ocomp ) ) ) ) @ c_Fun_Osurj ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(21,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/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_1) ).
thf(481,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)],[21]) ).
thf(350,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_List_Omap ) ) ) )
!= ( D @ ( C @ ( E @ ( A @ c_List_Omap ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__map__eq__map_0) ).
thf(1211,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_List_Omap ) ) ) )
!= ( D @ ( C @ ( E @ ( A @ c_List_Omap ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(432,axiom,
! [A: $i] :
( ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Finite__Set_Ocard ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__empty_0) ).
thf(1406,plain,
! [A: $i] :
( ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Finite__Set_Ocard ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(202,axiom,
! [A: $i] : ( tc_bool @ ( A @ tc_fun ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__Compl__self__eq_1) ).
thf(878,plain,
! [A: $i] : ( tc_bool @ ( A @ tc_fun ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(80,axiom,
! [B: $i,A: $i] :
( ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__complement_0) ).
thf(614,plain,
! [B: $i,A: $i] :
( ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(388,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ ( F @ c_Fun_Oinj__on ) ) ) )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( D @ ( B @ ( A @ ( F @ c_Set_Oimage ) ) ) @ c_lessequals ) ) )
| ~ ( B @ ( D @ ( C @ ( E @ c_Fun_Oinj__on ) ) ) )
| ~ ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( B @ ( D @ ( C @ ( E @ c_Set_Oimage ) ) ) @ c_lessequals ) ) )
| ~ ( B @ ( A @ c_Finite__Set_Ofinite ) )
| ~ ( D @ ( C @ c_Finite__Set_Ofinite ) )
| ( ( B @ ( A @ c_Finite__Set_Ocard ) )
= ( D @ ( C @ c_Finite__Set_Ocard ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__bij__eq_0) ).
thf(1305,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ ( F @ c_Fun_Oinj__on ) ) ) )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( D @ ( B @ ( A @ ( F @ c_Set_Oimage ) ) ) @ c_lessequals ) ) )
| ~ ( B @ ( D @ ( C @ ( E @ c_Fun_Oinj__on ) ) ) )
| ~ ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( B @ ( D @ ( C @ ( E @ c_Set_Oimage ) ) ) @ c_lessequals ) ) )
| ~ ( B @ ( A @ c_Finite__Set_Ofinite ) )
| ~ ( D @ ( C @ c_Finite__Set_Ofinite ) )
| ( ( B @ ( A @ c_Finite__Set_Ocard ) )
= ( D @ ( C @ c_Finite__Set_Ocard ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(39,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
| ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__insert_1) ).
thf(523,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
| ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Finite__Set_Ofinite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(65,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Fun_Oid @ hAPP ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_id__apply_0) ).
thf(582,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Fun_Oid @ hAPP ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(148,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ c_Finite__Set_Ofinite ) )
| ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Int_0) ).
thf(762,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ c_Finite__Set_Ofinite ) )
| ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Finite__Set_Ofinite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(200,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__subset__iff_1) ).
thf(873,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(347,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( D @ ( C @ ( D @ ( F @ ( E @ ( B @ ( A @ c_Fun_Ocomp ) ) ) ) @ c_Fun_Oinj__on ) ) ) )
| ( F @ ( E @ ( E @ ( D @ ( C @ ( B @ c_Set_Oimage ) ) ) @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__imageI_0) ).
thf(1205,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( D @ ( C @ ( D @ ( F @ ( E @ ( B @ ( A @ c_Fun_Ocomp ) ) ) ) @ c_Fun_Oinj__on ) ) ) )
| ( F @ ( E @ ( E @ ( D @ ( C @ ( B @ c_Set_Oimage ) ) ) @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(6,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ c_lessequals ) ) )
| ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_1) ).
thf(449,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ c_lessequals ) ) )
| ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(288,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__subset__iff_2) ).
thf(1078,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(390,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ ( B @ c_Fun_Oinj__on ) ) ) )
| ( ( C @ ( D @ ( D @ ( C @ ( A @ ( B @ c_Set_Oimage ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Fun_Othe__inv__into ) ) ) @ c_Set_Oimage ) ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_the__inv__into__onto_0) ).
thf(1310,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ ( B @ c_Fun_Oinj__on ) ) ) )
| ( ( C @ ( D @ ( D @ ( C @ ( A @ ( B @ c_Set_Oimage ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Fun_Othe__inv__into ) ) ) @ c_Set_Oimage ) ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(50,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__is__Un_0) ).
thf(550,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(165,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
| ~ ( B @ ( C @ c_Finite__Set_Ofinite ) )
| ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__subset_0) ).
thf(797,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
| ~ ( B @ ( C @ c_Finite__Set_Ofinite ) )
| ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(125,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( E @ ( H @ ( F @ ( B @ c_Fun_Obij__betw ) ) ) ) )
| ~ ( D @ ( C @ ( G @ ( H @ ( A @ c_Fun_Obij__betw ) ) ) ) )
| ( D @ ( E @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ocomp ) ) ) ) @ c_Fun_Obij__betw ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bij__betw__trans_0) ).
thf(715,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( E @ ( H @ ( F @ ( B @ c_Fun_Obij__betw ) ) ) ) )
| ~ ( D @ ( C @ ( G @ ( H @ ( A @ c_Fun_Obij__betw ) ) ) ) )
| ( D @ ( E @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ocomp ) ) ) ) @ c_Fun_Obij__betw ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(16,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( E @ ( B @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( A @ ( D @ ( C @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( D @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastLessThan__subset__iff_0) ).
thf(472,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( E @ ( B @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( A @ ( D @ ( C @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( D @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(173,axiom,
! [A: $i] :
( A
!= ( A @ c_Suc ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_n__not__Suc__n_0) ).
thf(814,plain,
! [A: $i] :
( A
!= ( A @ c_Suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(281,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Finite__Set_Ofinite ) )
| ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Un_1) ).
thf(1063,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Finite__Set_Ofinite ) )
| ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(225,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__absorb1_0) ).
thf(930,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(370,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) )
| ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
| ( ( D @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_Finite__Set_Ocard ) )
!= ( C @ ( B @ c_Finite__Set_Ocard ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__card__imp__inj__on_0) ).
thf(1260,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) )
| ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
| ( ( D @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_Finite__Set_Ocard ) )
!= ( C @ ( B @ c_Finite__Set_Ocard ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(117,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__le__mono_1) ).
thf(698,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(404,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_Fun_Obij ) ) )
| ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bij__def_0) ).
thf(1342,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_Fun_Obij ) ) )
| ( 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)],[404]) ).
thf(219,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
| ( ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Finite__Set_Ocard ) )
= ( 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 ) ) @ c_Finite__Set_Ocard ) @ c_Suc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__insert_0) ).
thf(913,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
| ( ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Finite__Set_Ocard ) )
= ( 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 ) ) @ c_Finite__Set_Ocard ) @ c_Suc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(180,axiom,
! [A: $i] : ( tc_nat @ ( A @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__refl_0) ).
thf(829,plain,
! [A: $i] : ( tc_nat @ ( A @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(254,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_Fun_Osurj ) ) )
| ( ( C @ ( C @ ( B @ ( C @ ( B @ ( A @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Hilbert__Choice_Oinv__into ) ) ) @ ( A @ c_Fun_Ocomp ) ) ) ) )
= ( C @ c_Fun_Oid ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_surj__iff_0) ).
thf(1001,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_Fun_Osurj ) ) )
| ( ( C @ ( C @ ( B @ ( C @ ( B @ ( A @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Hilbert__Choice_Oinv__into ) ) ) @ ( A @ c_Fun_Ocomp ) ) ) ) )
= ( C @ c_Fun_Oid ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(364,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__left__absorb_0) ).
thf(1243,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(412,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_Finite__Set_Ofinite ) )
| ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_Finite__Set_Ocard ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( A @ ( B @ ( A @ c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1 ) @ c_Fun_Obij__betw ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ex__bij__betw__finite__nat_0) ).
thf(1359,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_Finite__Set_Ofinite ) )
| ( tc_nat @ ( B @ ( tc_nat @ ( B @ ( A @ c_Finite__Set_Ocard ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( A @ ( B @ ( A @ c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1 ) @ c_Fun_Obij__betw ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(1,negated_conjecture,
~ v_thesis____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(436,plain,
~ v_thesis____,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(368,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( ( D @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_Finite__Set_Ocard ) )
= ( C @ ( B @ c_Finite__Set_Ocard ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__image_0) ).
thf(1254,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( ( D @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_Finite__Set_Ocard ) )
= ( C @ ( B @ c_Finite__Set_Ocard ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(129,axiom,
tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc0_1) ).
thf(724,plain,
tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(158,axiom,
! [A: $i] : ( tc_bool @ ( A @ tc_fun ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__empty_1) ).
thf(785,plain,
! [A: $i] : ( tc_bool @ ( A @ tc_fun ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(391,axiom,
! [B: $i,A: $i] : ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__UNIV_0) ).
thf(1313,plain,
! [B: $i,A: $i] : ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(11,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/sandbox/benchmark/theBenchmark.p',cls_insert__commute_0) ).
thf(460,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)],[11]) ).
thf(67,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).
thf(587,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(397,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Fun__XinjI__1__1 ) ) )
!= ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Fun__XinjI__1__2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_injI_1) ).
thf(1323,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Fun__XinjI__1__1 ) ) )
!= ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Fun__XinjI__1__2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(82,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( A @ c_Fun_Oid @ c_Set_Ovimage ) ) ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__id_0) ).
thf(619,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( A @ c_Fun_Oid @ c_Set_Ovimage ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(185,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__le__linear_0) ).
thf(838,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(119,axiom,
! [B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty__left_0) ).
thf(702,plain,
! [B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(143,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Diff__cancel_0) ).
thf(751,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(174,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__eq__less__or__eq_0) ).
thf(817,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(191,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( 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_lessequals ) ) )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_4) ).
thf(853,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( 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_lessequals ) ) )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(199,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_lessequals ) ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__absorb2_0) ).
thf(870,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_lessequals ) ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(151,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__crazy_0) ).
thf(770,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(306,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_Suc @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__leD_0) ).
thf(1115,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_Suc @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(299,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__eq_0) ).
thf(1100,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(359,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Set_Oimage ) ) ) )
= ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( E @ ( D @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__Un_0) ).
thf(1232,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Set_Oimage ) ) ) )
= ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( E @ ( D @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(242,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = C )
| ~ ( G @ ( F @ ( E @ ( D @ ( A @ c_Typedef_Otype__definition ) ) ) ) )
| ( ( B @ ( A @ hAPP ) )
!= ( C @ ( A @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type__definition_ORep__inject_0) ).
thf(969,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = C )
| ~ ( G @ ( F @ ( E @ ( D @ ( A @ c_Typedef_Otype__definition ) ) ) ) )
| ( ( B @ ( A @ hAPP ) )
!= ( C @ ( A @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(76,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).
thf(606,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(18,axiom,
! [A: $i] :
( ( A @ ( A @ ( A @ c_Fun_Oid @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Hilbert__Choice_Oinv__into ) ) ) )
= ( A @ c_Fun_Oid ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inv__id_0) ).
thf(475,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ c_Fun_Oid @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Hilbert__Choice_Oinv__into ) ) ) )
= ( A @ c_Fun_Oid ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(69,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__linear_0) ).
thf(591,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(303,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ hAPP ) @ ( A @ hAPP ) )
= ( C @ ( F @ ( E @ ( D @ ( B @ ( A @ c_Fun_Ocomp ) ) ) ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__eq__dest__lhs_0) ).
thf(1109,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ hAPP ) @ ( A @ hAPP ) )
= ( C @ ( F @ ( E @ ( D @ ( B @ ( A @ c_Fun_Ocomp ) ) ) ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(84,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( A @ c_Fun_Oid @ c_Set_Oimage ) ) ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__id_0) ).
thf(623,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( A @ c_Fun_Oid @ c_Set_Oimage ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(401,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( F @ ( A @ c_Fun_Oinj__on ) ) ) )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( F @ ( B @ c_lessequals ) ) )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( F @ ( C @ c_lessequals ) ) )
| ( ( 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/sandbox/benchmark/theBenchmark.p',cls_inj__on__image__set__diff_0) ).
thf(1334,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( F @ ( A @ c_Fun_Oinj__on ) ) ) )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( F @ ( B @ c_lessequals ) ) )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( F @ ( C @ c_lessequals ) ) )
| ( ( 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)],[401]) ).
thf(169,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ ( C @ c_Fun_Obij ) ) )
| ~ ( D @ ( B @ ( D @ ( A @ ( C @ c_Set_Ovimage ) ) ) @ c_Finite__Set_Ofinite ) )
| ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__vimage__iff_0) ).
thf(806,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ ( C @ c_Fun_Obij ) ) )
| ~ ( D @ ( B @ ( D @ ( A @ ( C @ c_Set_Ovimage ) ) ) @ c_Finite__Set_Ofinite ) )
| ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(338,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ ( B @ c_Fun_Oinj__on ) ) ) )
| ( C @ ( D @ ( D @ ( C @ ( A @ ( B @ c_Set_Oimage ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Fun_Othe__inv__into ) ) ) @ c_Fun_Oinj__on ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__the__inv__into_0) ).
thf(1183,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ ( B @ c_Fun_Oinj__on ) ) ) )
| ( C @ ( D @ ( D @ ( C @ ( A @ ( B @ c_Set_Oimage ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Fun_Othe__inv__into ) ) ) @ c_Fun_Oinj__on ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(176,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_Fun_Osurj ) ) )
| ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( D @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_Set_Oimage ) ) ) @ ( A @ ( D @ ( C @ ( B @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_surj__Compl__image__subset_0) ).
thf(821,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_Fun_Osurj ) ) )
| ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( D @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ c_Set_Oimage ) ) ) @ ( A @ ( D @ ( C @ ( B @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(216,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/sandbox/benchmark/theBenchmark.p',cls_Diff__UNIV_0) ).
thf(905,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)],[216]) ).
thf(387,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ~ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) )
!= ( D @ ( C @ ( E @ ( A @ c_Set_Oimage ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__image__eq__iff_0) ).
thf(1302,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)],[387]) ).
thf(145,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/sandbox/benchmark/theBenchmark.p',cls_vimage__Diff_0) ).
thf(756,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)],[145]) ).
thf(422,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__left__commute_0) ).
thf(1383,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(262,axiom,
! [A: $i] :
( ( ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Complete__Lattice_OSup__class_OSup ) )
= ( A @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sup__empty_0) ).
thf(1020,plain,
! [A: $i] :
( ( ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Complete__Lattice_OSup__class_OSup ) )
= ( A @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(61,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_1) ).
thf(574,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(236,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Complete__Lattice_Ocomplete__lattice )
| ( B @ ( A @ tc_fun ) @ class_Complete__Lattice_Ocomplete__lattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Complete__Lattice_Ocomplete__lattice) ).
thf(956,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)],[236]) ).
thf(153,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( ( tc_nat @ ( B @ c_Suc @ ( A @ c_SetInterval_Oord__class_OatLeastLessThan ) ) )
= ( tc_bool @ ( tc_nat @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastLessThanSuc_1) ).
thf(774,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( ( tc_nat @ ( B @ c_Suc @ ( A @ c_SetInterval_Oord__class_OatLeastLessThan ) ) )
= ( tc_bool @ ( tc_nat @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(408,axiom,
! [A: $i] :
~ ( tc_nat @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Finite__Set_Ocard ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__gt__0__iff_0) ).
thf(1351,plain,
! [A: $i] :
~ ( tc_nat @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Finite__Set_Ocard ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(253,axiom,
! [B: $i,A: $i] :
( ~ ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_lessequals ) ) )
| ( A
= ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__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_lessequals ) ) )
| ( A
= ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(345,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ c_Fun_Osurj ) ) )
| ( A @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( A @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Hilbert__Choice_Oinv__into ) ) ) @ c_Fun_Oinj__on ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_surj__imp__inj__inv_0) ).
thf(1201,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ c_Fun_Osurj ) ) )
| ( A @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ ( A @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Hilbert__Choice_Oinv__into ) ) ) @ c_Fun_Oinj__on ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(301,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Fun_Oinj__on ) ) ) )
| ~ ( E @ ( D @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) )
| ~ ( E @ ( D @ ( C @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Set_Oimage ) ) ) @ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Set_Oimage ) ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
!= ( tc_bool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__Un_3) ).
thf(1104,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Fun_Oinj__on ) ) ) )
| ~ ( E @ ( D @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) )
| ~ ( E @ ( D @ ( C @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Set_Oimage ) ) ) @ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Set_Oimage ) ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
!= ( tc_bool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(32,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Set_Oinsert ) ) @ c_Complete__Lattice_OSup__class_OSup ) )
= ( A @ ( A @ ( C @ c_Complete__Lattice_OSup__class_OSup ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sup__insert_0) ).
thf(507,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Set_Oinsert ) ) @ c_Complete__Lattice_OSup__class_OSup ) )
= ( A @ ( A @ ( C @ c_Complete__Lattice_OSup__class_OSup ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(74,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__less_0) ).
thf(602,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(246,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__mono_0) ).
thf(981,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(331,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ~ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) )
!= ( D @ ( C @ ( E @ ( A @ c_Set_Oimage ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__Un__image__eq__iff_0) ).
thf(1169,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ~ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( 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)],[331]) ).
thf(112,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ c_Finite__Set_Ofinite ) )
| ~ ( B @ ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Finite__Set_Ofinite ) )
| ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Diff2_0) ).
thf(687,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ c_Finite__Set_Ofinite ) )
| ~ ( B @ ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Finite__Set_Ofinite ) )
| ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(286,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_termination__basic__simps_I5_J_0) ).
thf(1074,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(108,axiom,
! [B: $i,A: $i] :
( ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__empty_0) ).
thf(678,plain,
! [B: $i,A: $i] :
( ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(101,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_Suc @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eq__Suc__le_0) ).
thf(661,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_Suc @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(48,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__le_0) ).
thf(546,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(223,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( I @ ( H @ ( G @ ( B @ ( A @ c_Fun_Ocomp ) ) ) ) @ hAPP ) )
= ( F @ ( K @ ( H @ ( J @ ( E @ ( D @ c_Fun_Ocomp ) ) ) ) @ hAPP ) ) )
| ( ( C @ ( B @ hAPP ) @ ( A @ hAPP ) )
!= ( F @ ( E @ hAPP ) @ ( D @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comp__cong_0) ).
thf(925,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( I @ ( H @ ( G @ ( B @ ( A @ c_Fun_Ocomp ) ) ) ) @ hAPP ) )
= ( F @ ( K @ ( H @ ( J @ ( E @ ( D @ c_Fun_Ocomp ) ) ) ) @ hAPP ) ) )
| ( ( C @ ( B @ hAPP ) @ ( A @ hAPP ) )
!= ( F @ ( E @ hAPP ) @ ( D @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(323,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( E @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__Un_1) ).
thf(1153,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( E @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(43,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__insert__left_0) ).
thf(534,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Set_Oinsert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(283,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Set_Oimage ) ) ) @ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Set_Oimage ) ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__Un_2) ).
thf(1067,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Set_Oimage ) ) ) @ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Set_Oimage ) ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(34,axiom,
! [A: $i] : ( A @ ( A @ ( A @ c_Fun_Oid @ c_Fun_Osurj ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_surj__id_0) ).
thf(512,plain,
! [A: $i] : ( A @ ( A @ ( A @ c_Fun_Oid @ c_Fun_Osurj ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(230,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
| ~ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Finite__Set_Ofinite ) )
| ( A @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__compl_1) ).
thf(942,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
| ~ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Finite__Set_Ofinite ) )
| ( A @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_Finite__Set_Ofinite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(273,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__less__Suc__eq_0) ).
thf(1047,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(328,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__assoc_0) ).
thf(1163,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(376,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_Fun_Othe__inv__into ) ) ) @ hAPP ) )
= D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_the__inv__f__f_0) ).
thf(1274,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_Fun_Othe__inv__into ) ) ) @ hAPP ) )
= D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(218,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__SucE_0) ).
thf(910,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(140,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ c_Finite__Set_Ofinite ) )
| ~ ( tc_bool @ ( B @ tc_fun ) @ ( B @ ( E @ ( D @ ( C @ c_Set_Oimage ) ) ) @ ( A @ c_lessequals ) ) )
| ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__surj_0) ).
thf(746,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ c_Finite__Set_Ofinite ) )
| ~ ( tc_bool @ ( B @ tc_fun ) @ ( B @ ( E @ ( D @ ( C @ c_Set_Oimage ) ) ) @ ( A @ c_lessequals ) ) )
| ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(178,axiom,
! [A: $i] :
~ ( tc_nat @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__le_1) ).
thf(825,plain,
! [A: $i] :
~ ( tc_nat @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(271,axiom,
! [B: $i,A: $i] :
( ~ ( A @ class_Finite__Set_Ofinite_Ofinite )
| ~ ( B @ class_Finite__Set_Ofinite_Ofinite )
| ( B @ ( A @ tc_fun ) @ class_Finite__Set_Ofinite_Ofinite ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Finite__Set_Ofinite_Ofinite) ).
thf(1042,plain,
! [B: $i,A: $i] :
( ~ ( A @ class_Finite__Set_Ofinite_Ofinite )
| ~ ( B @ class_Finite__Set_Ofinite_Ofinite )
| ( B @ ( A @ tc_fun ) @ class_Finite__Set_Ofinite_Ofinite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(410,axiom,
! [B: $i,A: $i] : ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__refl_0) ).
thf(1355,plain,
! [B: $i,A: $i] : ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(309,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( C @ c_SetInterval_Oord__class_OlessThan ) @ ( A @ ( B @ c_SetInterval_Oord__class_OlessThan ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lessThan__subset__iff_0) ).
thf(1123,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( C @ c_SetInterval_Oord__class_OlessThan ) @ ( A @ ( B @ c_SetInterval_Oord__class_OlessThan ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(333,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/sandbox/benchmark/theBenchmark.p',cls_Diff__idemp_0) ).
thf(1174,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)],[333]) ).
thf(72,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__less_1) ).
thf(598,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(175,axiom,
! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__lower1_0) ).
thf(820,plain,
! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(55,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_0) ).
thf(561,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(132,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Diff_0) ).
thf(729,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(355,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ ( B @ c_lessequals ) ) )
| ( C @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__surj__inj_0) ).
thf(1223,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ ( B @ c_lessequals ) ) )
| ( C @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(211,axiom,
! [A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty_2) ).
thf(894,plain,
! [A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(115,axiom,
! [B: $i,A: $i] :
( ( B = A )
| ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE__nat_0) ).
thf(693,plain,
! [B: $i,A: $i] :
( ( B = A )
| ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(87,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/sandbox/benchmark/theBenchmark.p',cls_insert__Diff__single_0) ).
thf(630,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)],[87]) ).
thf(160,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ c_Fun_Obij ) ) )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( E @ ( A @ c_Set_Oimage ) ) ) @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Set_Ovimage ) ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__subset__eq_1) ).
thf(788,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ c_Fun_Obij ) ) )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( E @ ( A @ c_Set_Oimage ) ) ) @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Set_Ovimage ) ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(417,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__trans_0) ).
thf(1370,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(267,axiom,
! [A: $i] :
( ~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc0_0) ).
thf(1032,plain,
! [A: $i] :
( ~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(415,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/sandbox/benchmark/theBenchmark.p',cls_range__composition_0) ).
thf(1365,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)],[415]) ).
thf(85,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( B @ ( B @ c_Fun_Oid @ ( A @ c_Fun_Ocomp ) ) ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__id_0) ).
thf(625,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( B @ ( B @ c_Fun_Oid @ ( A @ c_Fun_Ocomp ) ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(203,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_Set_Ovimage ) ) ) @ ( A @ c_Set_Oimage ) ) ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__vimage__subset_0) ).
thf(879,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_Set_Ovimage ) ) ) @ ( A @ c_Set_Oimage ) ) ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(335,axiom,
tc_nat @ class_Ring__and__Field_Osemiring__1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__1) ).
thf(1178,plain,
tc_nat @ class_Ring__and__Field_Osemiring__1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(181,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
= ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__Int_0) ).
thf(830,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
= ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(208,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/sandbox/benchmark/theBenchmark.p',cls_bij__betw__def_0) ).
thf(889,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)],[208]) ).
thf(326,axiom,
! [A: $i] :
~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less0_0) ).
thf(1159,plain,
! [A: $i] :
~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(26,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__antisym__conv_0) ).
thf(493,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(265,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( E @ ( D @ ( A @ ( B @ c_Typedef_Otype__definition ) ) ) ) )
| ( ( C @ ( B @ hAPP ) @ ( A @ hAPP ) )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type__definition_ORep__inverse_0) ).
thf(1027,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( E @ ( D @ ( A @ ( B @ c_Typedef_Otype__definition ) ) ) ) )
| ( ( C @ ( B @ hAPP ) @ ( A @ hAPP ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(426,axiom,
! [A: $i] :
( ( A @ c_Suc )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__neq__Zero_0) ).
thf(1392,plain,
! [A: $i] :
( ( A @ c_Suc )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(187,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( A @ ( B @ c_SetInterval_Oord__class_OlessThan ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( C @ c_SetInterval_Oord__class_OlessThan ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__un_I8_J_0) ).
thf(842,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( A @ ( B @ c_SetInterval_Oord__class_OlessThan ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( C @ c_SetInterval_Oord__class_OlessThan ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(258,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Diff__Int_0) ).
thf(1012,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(220,axiom,
! [B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__disjoint2_0) ).
thf(916,plain,
! [B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(14,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( B = C )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le_2) ).
thf(467,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( B = C )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(57,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/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_3) ).
thf(566,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)],[57]) ).
thf(22,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( C @ c_lessequals ) ) )
| ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__subset__Compl__iff_1) ).
thf(484,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( C @ c_lessequals ) ) )
| ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(385,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_lessequals ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equalityI_0) ).
thf(1296,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_lessequals ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(103,axiom,
! [B: $i,A: $i] :
( ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( tc_bool @ ( B @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__disjoint_0) ).
thf(665,plain,
! [B: $i,A: $i] :
( ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( tc_bool @ ( B @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(110,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Un__distrib_0) ).
thf(682,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(343,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_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Set_Oimage ) ) ) )
= ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( E @ ( D @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__Int_0) ).
thf(1195,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_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Set_Oimage ) ) ) )
= ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( E @ ( D @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(383,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( E @ ( A @ c_Fun_Oinj__on ) ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_lessequals ) ) )
| ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__inj__on_0) ).
thf(1291,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( E @ ( A @ c_Fun_Oinj__on ) ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_lessequals ) ) )
| ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(123,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ c_Finite__Set_Ofinite ) )
| ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Diff_0) ).
thf(710,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ c_Finite__Set_Ofinite ) )
| ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Finite__Set_Ofinite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(430,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__left__commute_0) ).
thf(1402,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(360,axiom,
tc_nat @ class_Nat_Osemiring__char__0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Nat_Osemiring__char__0) ).
thf(1234,plain,
tc_nat @ class_Nat_Osemiring__char__0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(319,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__left__absorb_0) ).
thf(1143,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(96,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/sandbox/benchmark/theBenchmark.p',cls_bij__betw__inv__into_0) ).
thf(650,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)],[96]) ).
thf(419,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Finite__Set_Ofinite ) )
| ( ( B @ ( A @ c_Finite__Set_Ocard ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__eq__0__iff_2) ).
thf(1375,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Finite__Set_Ofinite ) )
| ( ( B @ ( A @ c_Finite__Set_Ocard ) )
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(130,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Finite__Set_Ofinite ) )
| ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Un_0) ).
thf(725,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Finite__Set_Ofinite ) )
| ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(297,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ c_Finite__Set_Ofinite ) )
| ( tc_nat @ ( C @ ( A @ c_Finite__Set_Ocard ) @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Finite__Set_Ocard ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__Diff1__le_0) ).
thf(1096,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ c_Finite__Set_Ofinite ) )
| ( tc_nat @ ( C @ ( A @ c_Finite__Set_Ocard ) @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Finite__Set_Ocard ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(316,axiom,
! [E: $i,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 ) ) ) )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( E @ ( A @ c_Set_Oimage ) ) ) @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Set_Ovimage ) ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__subsetI_0) ).
thf(1138,plain,
! [E: $i,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 ) ) ) )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( E @ ( A @ c_Set_Oimage ) ) ) @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Set_Ovimage ) ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(70,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/sandbox/benchmark/theBenchmark.p',cls_insert__not__empty_0) ).
thf(593,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)],[70]) ).
thf(198,axiom,
! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc__eq_2) ).
thf(869,plain,
! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(78,axiom,
! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( A @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insertI_0) ).
thf(610,plain,
! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( A @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(157,axiom,
! [A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__UNIV__eq_0) ).
thf(783,plain,
! [A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(138,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_Suc @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eq__Suc__le_1) ).
thf(742,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_Suc @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(63,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/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_0) ).
thf(578,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)],[63]) ).
thf(304,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
| ~ ( C @ ( A @ c_Finite__Set_Ofinite ) )
| ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Diff2_1) ).
thf(1111,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
| ~ ( C @ ( A @ c_Finite__Set_Ofinite ) )
| ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Finite__Set_Ofinite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(357,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/sandbox/benchmark/theBenchmark.p',cls_inj__on__diff_0) ).
thf(1227,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)],[357]) ).
thf(24,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__less_0) ).
thf(488,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(413,axiom,
! [B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__UNIV__left_0) ).
thf(1361,plain,
! [B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(226,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( E @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Set_Ovimage ) ) ) )
= ( tc_bool @ ( E @ tc_fun ) @ ( D @ ( E @ ( C @ ( A @ c_Set_Ovimage ) ) ) @ ( D @ ( E @ ( B @ ( A @ c_Set_Ovimage ) ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__Int_0) ).
thf(933,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( E @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Set_Ovimage ) ) ) )
= ( tc_bool @ ( E @ tc_fun ) @ ( D @ ( E @ ( C @ ( A @ c_Set_Ovimage ) ) ) @ ( D @ ( E @ ( B @ ( A @ c_Set_Ovimage ) ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(351,axiom,
! [E: $i,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 ) ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( E @ ( A @ c_Set_Oimage ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__image__subset__iff_1) ).
thf(1214,plain,
! [E: $i,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 ) ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( E @ ( A @ c_Set_Oimage ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(270,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Fun_Oinj__on ) ) ) )
| ( ( A @ ( A @ ( C @ ( B @ ( C @ ( A @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Hilbert__Choice_Oinv__into ) ) ) @ c_Fun_Ocomp ) ) ) ) )
!= ( A @ c_Fun_Oid ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__iff_1) ).
thf(1039,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Fun_Oinj__on ) ) ) )
| ( ( A @ ( A @ ( C @ ( B @ ( C @ ( A @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Hilbert__Choice_Oinv__into ) ) ) @ c_Fun_Ocomp ) ) ) ) )
!= ( A @ c_Fun_Oid ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(324,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/sandbox/benchmark/theBenchmark.p',cls_bij__betw__def_2) ).
thf(1155,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)],[324]) ).
thf(121,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Int__distrib2_0) ).
thf(706,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(206,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/sandbox/benchmark/theBenchmark.p',cls_image__image_0) ).
thf(884,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)],[206]) ).
thf(399,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = C )
| ~ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( ( B @ ( A @ hAPP ) )
!= ( C @ ( A @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_injD_0) ).
thf(1329,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)],[399]) ).
thf(52,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).
thf(554,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(144,axiom,
! [B: $i,A: $i] :
( ( A
= ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ~ ( B @ ( A @ c_Finite__Set_Ofinite ) )
| ( tc_nat @ ( B @ ( A @ c_Finite__Set_Ocard ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__gt__0__iff_2) ).
thf(753,plain,
! [B: $i,A: $i] :
( ( A
= ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ~ ( B @ ( A @ c_Finite__Set_Ofinite ) )
| ( tc_nat @ ( B @ ( A @ c_Finite__Set_Ocard ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(260,axiom,
! [A: $i] :
~ ( tc_nat @ ( A @ ( A @ c_Suc @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__n__not__le__n_0) ).
thf(1016,plain,
! [A: $i] :
~ ( tc_nat @ ( A @ ( A @ c_Suc @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(348,axiom,
tc_Arrow__Order__Mirabelle_Oindi @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Finite__Set_Ofinite ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__indi_0) ).
thf(1207,plain,
tc_Arrow__Order__Mirabelle_Oindi @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Finite__Set_Ofinite ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(136,axiom,
! [B: $i,A: $i] :
( ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__empty__right_0) ).
thf(738,plain,
! [B: $i,A: $i] :
( ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(372,axiom,
tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__0__eq_1) ).
thf(1266,plain,
tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(98,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( E @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__mono_0) ).
thf(654,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( E @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(248,axiom,
! [A: $i] :
( ( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Nat_Osemiring__1__class_Oof__nat ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__0_0) ).
thf(984,plain,
! [A: $i] :
( ( ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_Nat_Osemiring__1__class_Oof__nat ) )
= ( A @ c_HOL_Ozero__class_Ozero ) )
| ~ ( A @ class_Ring__and__Field_Osemiring__1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(58,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Orderings_Oorder )
| ( B @ ( A @ tc_fun ) @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Oorder) ).
thf(569,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Orderings_Oorder )
| ( B @ ( A @ tc_fun ) @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(155,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__trans__Suc_0) ).
thf(779,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(30,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( C @ ( E @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( A @ ( B @ ( D @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ c_lessequals ) ) )
| ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastLessThan__subset__iff_1) ).
thf(503,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( C @ ( E @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( A @ ( B @ ( D @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ c_lessequals ) ) )
| ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(95,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_Fun_Osurj ) ) )
| ( ( D @ ( C @ ( B @ ( A @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) @ ( A @ hAPP ) )
= D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_surj__f__inv__f_0) ).
thf(647,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_Fun_Osurj ) ) )
| ( ( D @ ( C @ ( B @ ( A @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Hilbert__Choice_Oinv__into ) ) ) @ hAPP ) @ ( A @ hAPP ) )
= D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(371,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( D @ ( E @ ( A @ c_Typedef_Otype__definition ) ) ) ) )
| ( ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Set_Oimage ) ) ) )
= D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type__definition_ORep__range_0) ).
thf(1263,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( D @ ( E @ ( A @ c_Typedef_Otype__definition ) ) ) ) )
| ( ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Set_Oimage ) ) ) )
= D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(36,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I6_J_0) ).
thf(515,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(322,axiom,
! [A: $i] :
( ( ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Complete__Lattice_OSup__class_OSup ) )
= ( A @ c_Orderings_Otop__class_Otop ) )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sup__UNIV_0) ).
thf(1150,plain,
! [A: $i] :
( ( ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Complete__Lattice_OSup__class_OSup ) )
= ( A @ c_Orderings_Otop__class_Otop ) )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(279,axiom,
! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( A @ c_Suc @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__Suc__eq_2) ).
thf(1060,plain,
! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( A @ c_Suc @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(274,axiom,
! [A: $i] :
( ( tc_nat @ ( A @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__less__Suc__eq_1) ).
thf(1050,plain,
! [A: $i] :
( ( tc_nat @ ( A @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(395,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( F @ ( A @ c_Fun_Oinj__on ) ) ) )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( F @ ( B @ c_lessequals ) ) )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( F @ ( C @ c_lessequals ) ) )
| ( ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Set_Oimage ) ) ) )
= ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( E @ ( D @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__image__Int_0) ).
thf(1318,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( F @ ( A @ c_Fun_Oinj__on ) ) ) )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( F @ ( B @ c_lessequals ) ) )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( F @ ( C @ c_lessequals ) ) )
| ( ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Set_Oimage ) ) ) )
= ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( E @ ( D @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(162,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc__eq__0__disj_3) ).
thf(792,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(46,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__antisym_0) ).
thf(541,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(276,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ocomp ) ) ) ) @ hAPP ) )
= ( F @ ( B @ hAPP ) @ ( A @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__apply_0) ).
thf(1054,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ocomp ) ) ) ) @ hAPP ) )
= ( F @ ( B @ hAPP ) @ ( A @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(330,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_Finite__Set_Ofinite ) )
| ( B @ ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_Finite__Set_Ocard ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( B @ ( A @ c_List_Osko__SetInterval__Xex__bij__betw__nat__finite__1__1 ) @ c_Fun_Obij__betw ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ex__bij__betw__nat__finite_0) ).
thf(1167,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_Finite__Set_Ofinite ) )
| ( B @ ( tc_nat @ ( A @ ( tc_nat @ ( B @ ( A @ c_Finite__Set_Ocard ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( B @ ( A @ c_List_Osko__SetInterval__Xex__bij__betw__nat__finite__1__1 ) @ c_Fun_Obij__betw ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(163,axiom,
! [B: $i,A: $i] : ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__subsetI_0) ).
thf(794,plain,
! [B: $i,A: $i] : ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(292,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
| ( tc_nat @ ( C @ ( B @ c_Finite__Set_Ocard ) @ ( D @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_Finite__Set_Ocard ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__image__le_0) ).
thf(1086,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
| ( tc_nat @ ( C @ ( B @ c_Finite__Set_Ocard ) @ ( D @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_Finite__Set_Ocard ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(228,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__subset__iff_2) ).
thf(938,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(381,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/sandbox/benchmark/theBenchmark.p',cls_image__inv__f__f_0) ).
thf(1286,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)],[381]) ).
thf(268,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
| ( D @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__imageI_0) ).
thf(1035,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
| ( D @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_Finite__Set_Ofinite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(54,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/sandbox/benchmark/theBenchmark.p',cls_empty__not__insert_0) ).
thf(558,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)],[54]) ).
thf(285,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ( ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( D @ ( C @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( D @ ( B @ c_SetInterval_Oord__class_OatLeastLessThan ) ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__un_I17_J_0) ).
thf(1071,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ( ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( D @ ( C @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( D @ ( B @ c_SetInterval_Oord__class_OatLeastLessThan ) ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(235,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( B @ c_Set_Oinsert ) ) @ c_Complete__Lattice_OSup__class_OSup ) )
= ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sup__binary_0) ).
thf(953,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( B @ c_Set_Oinsert ) ) @ c_Complete__Lattice_OSup__class_OSup ) )
= ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(339,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/sandbox/benchmark/theBenchmark.p',cls_image__set__diff_0) ).
thf(1185,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)],[339]) ).
thf(315,axiom,
! [A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop )
!= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UNIV__not__empty_0) ).
thf(1135,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)],[315]) ).
thf(367,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_lessequals ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__eq__subset_2) ).
thf(1251,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_lessequals ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(35,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/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_4) ).
thf(513,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)],[35]) ).
thf(353,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ c_Finite__Set_Ofinite ) )
| ~ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( C @ ( D @ ( C @ ( B @ ( A @ c_Set_Ovimage ) ) ) @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__vimageI_0) ).
thf(1219,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ c_Finite__Set_Ofinite ) )
| ~ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( C @ ( D @ ( C @ ( B @ ( A @ c_Set_Ovimage ) ) ) @ c_Finite__Set_Ofinite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(60,axiom,
! [B: $i,A: $i] : ( A @ ( A @ ( B @ ( A @ c_Fun_Oid @ c_Fun_Oinj__on ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__id_0) ).
thf(573,plain,
! [B: $i,A: $i] : ( A @ ( A @ ( B @ ( A @ c_Fun_Oid @ c_Fun_Oinj__on ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(113,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( E @ ( D @ ( C @ ( B @ c_List_Omap ) ) ) @ ( A @ c_List_Omap ) ) ) )
= ( F @ ( D @ ( C @ ( D @ ( F @ ( E @ ( B @ ( A @ c_Fun_Ocomp ) ) ) ) @ c_List_Omap ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__map_0) ).
thf(689,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( E @ ( D @ ( C @ ( B @ c_List_Omap ) ) ) @ ( A @ c_List_Omap ) ) ) )
= ( F @ ( D @ ( C @ ( D @ ( F @ ( E @ ( B @ ( A @ c_Fun_Ocomp ) ) ) ) @ c_List_Omap ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(4,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_0) ).
thf(444,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(134,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
= ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastLessThan ) ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastLessThan__empty__iff2_1) ).
thf(733,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
= ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastLessThan ) ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(66,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( B @ c_SetInterval_Oord__class_OlessThan ) )
!= ( A @ ( C @ c_SetInterval_Oord__class_OlessThan ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lessThan__eq__iff_0) ).
thf(584,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( B @ c_SetInterval_Oord__class_OlessThan ) )
!= ( A @ ( C @ c_SetInterval_Oord__class_OlessThan ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(244,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( D @ c_lessequals ) ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__assoc__eq_1) ).
thf(975,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( D @ c_lessequals ) ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(256,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__subset__iff_0) ).
thf(1007,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(310,axiom,
! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lessI_0) ).
thf(1125,plain,
! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(152,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__le_0) ).
thf(772,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(424,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ ( E @ c_Fun_Oinj__on ) ) ) )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( D @ ( B @ ( A @ ( E @ c_Set_Oimage ) ) ) @ c_lessequals ) ) )
| ~ ( D @ ( C @ c_Finite__Set_Ofinite ) )
| ( tc_nat @ ( D @ ( C @ c_Finite__Set_Ocard ) @ ( B @ ( A @ c_Finite__Set_Ocard ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__inj__on__le_0) ).
thf(1388,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ ( E @ c_Fun_Oinj__on ) ) ) )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( D @ ( B @ ( A @ ( E @ c_Set_Oimage ) ) ) @ c_lessequals ) ) )
| ~ ( D @ ( C @ c_Finite__Set_Ofinite ) )
| ( tc_nat @ ( D @ ( C @ c_Finite__Set_Ocard ) @ ( B @ ( A @ c_Finite__Set_Ocard ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(201,axiom,
! [A: $i] :
( ( A @ c_Suc )
!= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__n__not__n_0) ).
thf(875,plain,
! [A: $i] :
( ( A @ c_Suc )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(237,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Fun_Oinj__on ) ) ) )
| ( ( A @ ( A @ ( C @ ( B @ ( C @ ( A @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Hilbert__Choice_Oinv__into ) ) ) @ c_Fun_Ocomp ) ) ) ) )
= ( A @ c_Fun_Oid ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__iff_0) ).
thf(958,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Fun_Oinj__on ) ) ) )
| ( ( A @ ( A @ ( C @ ( B @ ( C @ ( A @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Hilbert__Choice_Oinv__into ) ) ) @ c_Fun_Ocomp ) ) ) ) )
= ( A @ c_Fun_Oid ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(92,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ c_Fun_Obij ) ) )
| ( A @ ( C @ ( C @ ( A @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Hilbert__Choice_Oinv__into ) ) ) @ c_Fun_Obij ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bij__imp__bij__inv_0) ).
thf(641,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ c_Fun_Obij ) ) )
| ( A @ ( C @ ( C @ ( A @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Hilbert__Choice_Oinv__into ) ) ) @ c_Fun_Obij ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(375,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ ( B @ c_Fun_Oinj__on ) ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( E @ c_lessequals ) ) )
| ( ( 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/sandbox/benchmark/theBenchmark.p',cls_inv__into__image__cancel_0) ).
thf(1271,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ ( B @ c_Fun_Oinj__on ) ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( E @ c_lessequals ) ) )
| ( ( 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)],[375]) ).
thf(79,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/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_2) ).
thf(611,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)],[79]) ).
thf(28,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( B = C )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__neq__trans_0) ).
thf(498,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( B = C )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(400,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__Un_0) ).
thf(1332,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(295,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( B @ c_Fun_Osurj ) ) )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( E @ ( D @ ( A @ ( B @ c_Set_Ovimage ) ) ) @ c_lessequals ) ) )
| ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( D @ ( C @ ( B @ c_Set_Oimage ) ) ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__subsetD_0) ).
thf(1092,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( B @ c_Fun_Osurj ) ) )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( E @ ( D @ ( A @ ( B @ c_Set_Ovimage ) ) ) @ c_lessequals ) ) )
| ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( D @ ( C @ ( B @ c_Set_Oimage ) ) ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(294,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( B @ c_Suc @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__SucI_0) ).
thf(1090,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( B @ c_Suc @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(120,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ c_Fun_Obij ) ) )
| ~ ( D @ ( B @ c_Finite__Set_Ofinite ) )
| ( C @ ( D @ ( C @ ( B @ ( A @ c_Set_Ovimage ) ) ) @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__vimage__iff_1) ).
thf(704,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ c_Fun_Obij ) ) )
| ~ ( D @ ( B @ c_Finite__Set_Ofinite ) )
| ( C @ ( D @ ( C @ ( B @ ( A @ c_Set_Ovimage ) ) ) @ c_Finite__Set_Ofinite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(233,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__partition_0) ).
thf(947,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(411,axiom,
! [A: $i] :
( ( tc_nat @ c_HOL_Ozero__class_Ozero )
!= ( A @ c_Suc ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Osimps_I2_J_0) ).
thf(1356,plain,
! [A: $i] :
( ( tc_nat @ c_HOL_Ozero__class_Ozero )
!= ( A @ c_Suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(278,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Int2_0) ).
thf(1058,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(302,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( E @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ocomp ) ) ) ) @ c_Set_Oimage ) ) ) )
= ( D @ ( C @ ( C @ ( E @ ( F @ ( B @ c_Set_Oimage ) ) ) @ ( A @ c_Set_Oimage ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__compose_0) ).
thf(1107,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( E @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ocomp ) ) ) ) @ c_Set_Oimage ) ) ) )
= ( D @ ( C @ ( C @ ( E @ ( F @ ( B @ c_Set_Oimage ) ) ) @ ( A @ c_Set_Oimage ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(214,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__absorb2_0) ).
thf(900,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(433,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Finite__Set_Ofinite ) )
| ~ ( B @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( B @ ( B @ ( A @ c_Fun_Osurj ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__UNIV__inj__surj_0) ).
thf(1408,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Finite__Set_Ofinite ) )
| ~ ( B @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( B @ ( B @ ( A @ c_Fun_Osurj ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(379,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
= ( A @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oimage ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__is__image_1) ).
thf(1282,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)],[379]) ).
thf(307,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
!= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty_0) ).
thf(1117,plain,
! [C: $i,B: $i,A: $i] :
( ( A
= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
!= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(135,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/sandbox/benchmark/theBenchmark.p',cls_Diff__cancel_0) ).
thf(736,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)],[135]) ).
thf(407,axiom,
! [B: $i,A: $i] :
( ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__absorb_0) ).
thf(1349,plain,
! [B: $i,A: $i] :
( ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(7,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) )
| ( 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/sandbox/benchmark/theBenchmark.p',cls_subset__singletonD_0) ).
thf(451,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) )
| ( 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)],[7]) ).
thf(204,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
| ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Int_1) ).
thf(880,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
| ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Finite__Set_Ofinite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(81,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__neq__le__trans_0) ).
thf(616,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(195,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_Suc @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__leI_0) ).
thf(863,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_Suc @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(149,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Fun_Osurj ) ) )
| ( ( C @ ( C @ ( B @ ( C @ ( B @ ( A @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Hilbert__Choice_Oinv__into ) ) ) @ ( A @ c_Fun_Ocomp ) ) ) ) )
!= ( C @ c_Fun_Oid ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_surj__iff_1) ).
thf(764,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Fun_Osurj ) ) )
| ( ( C @ ( C @ ( B @ ( C @ ( B @ ( A @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Hilbert__Choice_Oinv__into ) ) ) @ ( A @ c_Fun_Ocomp ) ) ) ) )
!= ( C @ c_Fun_Oid ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(75,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insertI2_0) ).
thf(604,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(250,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( D @ c_lessequals ) ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
!= ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__assoc__eq_0) ).
thf(990,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( D @ c_lessequals ) ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
!= ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(252,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Int_0) ).
thf(996,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(19,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I10_J_0) ).
thf(477,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(172,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( A = B )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__less__le_2) ).
thf(811,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( A = B )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(289,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_lessequals ) ) )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__diff_0) ).
thf(1080,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_lessequals ) ) )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(146,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ c_Finite__Set_Ofinite ) )
| ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
| ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Un_2) ).
thf(758,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ c_Finite__Set_Ofinite ) )
| ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
| ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Finite__Set_Ofinite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(166,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_Finite__Set_Ocard ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__gt__0__iff_1) ).
thf(799,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_Finite__Set_Ocard ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) )
| ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(83,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__leE_0) ).
thf(621,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(240,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( D @ ( B @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ ( C @ ( D @ c_SetInterval_Oord__class_OatLeastLessThan ) ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__diff_0) ).
thf(964,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( D @ ( B @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ ( C @ ( D @ c_SetInterval_Oord__class_OatLeastLessThan ) ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(405,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( A @ ( B @ c_Set_Oimage ) ) ) @ ( E @ c_lessequals ) ) )
| ( C @ ( D @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Hilbert__Choice_Oinv__into ) ) ) @ c_Fun_Oinj__on ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__inv__into_0) ).
thf(1344,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( A @ ( B @ c_Set_Oimage ) ) ) @ ( E @ c_lessequals ) ) )
| ( C @ ( D @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Hilbert__Choice_Oinv__into ) ) ) @ c_Fun_Oinj__on ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(421,axiom,
~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neq0__conv_1) ).
thf(1381,plain,
~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(193,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( E @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( E @ ( A @ c_Set_Ovimage ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Ovimage ) ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__mono_0) ).
thf(858,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( E @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( E @ ( A @ c_Set_Ovimage ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Ovimage ) ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(51,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( B @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Finite__Set_Ofinite ) )
| ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Diff__insert_0) ).
thf(552,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( B @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Finite__Set_Ofinite ) )
| ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Finite__Set_Ofinite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(189,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__greatest_0) ).
thf(848,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(118,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( E @ ( B @ c_Fun_Obij ) ) )
| ~ ( D @ ( C @ ( A @ c_Fun_Obij ) ) )
| ( D @ ( E @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ocomp ) ) ) ) @ c_Fun_Obij ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bij__comp_0) ).
thf(700,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( E @ ( B @ c_Fun_Obij ) ) )
| ~ ( D @ ( C @ ( A @ c_Fun_Obij ) ) )
| ( D @ ( E @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ocomp ) ) ) ) @ c_Fun_Obij ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(38,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( C = B )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I11_J_0) ).
thf(520,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( C = B )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(384,axiom,
! [B: $i,A: $i] :
( ( A
= ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop ) )
| ~ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Finite__Set_Ofinite ) )
| ( ( B @ ( A @ c_Finite__Set_Ocard ) )
!= ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Finite__Set_Ocard ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__eq__UNIV__imp__eq__UNIV_0) ).
thf(1293,plain,
! [B: $i,A: $i] :
( ( A
= ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop ) )
| ~ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Finite__Set_Ofinite ) )
| ( ( B @ ( A @ c_Finite__Set_Ocard ) )
!= ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Finite__Set_Ocard ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(105,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Suc )
!= ( B @ c_Suc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__inject_0) ).
thf(668,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Suc )
!= ( B @ c_Suc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(12,axiom,
! [B: $i,A: $i] :
( ( ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( B @ c_SetInterval_Oord__class_OlessThan ) @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_single__Diff__lessThan_0) ).
thf(462,plain,
! [B: $i,A: $i] :
( ( ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( B @ c_SetInterval_Oord__class_OlessThan ) @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(280,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Int__distrib_0) ).
thf(1061,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(247,axiom,
! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gr0__conv__Suc_1) ).
thf(983,plain,
! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(179,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ c_Finite__Set_Ofinite ) )
| ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
| ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__UnI_0) ).
thf(827,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ c_Finite__Set_Ofinite ) )
| ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
| ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Finite__Set_Ofinite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(9,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( G @ ( B @ hAPP ) @ ( A @ hAPP ) )
= ( G @ ( F @ hAPP ) ) )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ocomp ) ) ) ) )
!= ( E @ ( D @ ( D @ ( F @ ( D @ c_Fun_Oid @ c_Fun_Ocomp ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__eq__id__dest_0) ).
thf(455,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( G @ ( B @ hAPP ) @ ( A @ hAPP ) )
= ( G @ ( F @ hAPP ) ) )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ocomp ) ) ) ) )
!= ( E @ ( D @ ( D @ ( F @ ( D @ c_Fun_Oid @ c_Fun_Ocomp ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(305,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
= ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__Diff__eq_0) ).
thf(1113,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
= ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(300,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_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Diff__cancel2_0) ).
thf(1102,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_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(100,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_lessequals ) ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_disjoint__eq__subset__Compl_1) ).
thf(658,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_lessequals ) ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(344,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/sandbox/benchmark/theBenchmark.p',cls_inv__f__eq_0) ).
thf(1198,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)],[344]) ).
thf(428,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/sandbox/benchmark/theBenchmark.p',cls_inv__image__comp_0) ).
thf(1396,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)],[428]) ).
thf(365,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Fun__XinjI__1__1 ) ) @ ( A @ hAPP ) )
= ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Fun__XinjI__1__2 ) ) @ ( A @ hAPP ) ) )
| ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_injI_0) ).
thf(1245,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Fun__XinjI__1__1 ) ) @ ( A @ hAPP ) )
= ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Fun__XinjI__1__2 ) ) @ ( A @ hAPP ) ) )
| ( 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)],[365]) ).
thf(90,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_Fun_Obij ) ) )
| ( ( B @ ( A @ ( A @ ( B @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Hilbert__Choice_Oinv__into ) ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Hilbert__Choice_Oinv__into ) ) ) )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inv__inv__eq_0) ).
thf(636,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_Fun_Obij ) ) )
| ( ( B @ ( A @ ( A @ ( B @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Hilbert__Choice_Oinv__into ) ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Hilbert__Choice_Oinv__into ) ) ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(272,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ c_Fun_Obij ) ) )
| ( ( D @ ( C @ ( B @ ( A @ c_Set_Ovimage ) ) ) )
= ( C @ ( D @ ( B @ ( D @ ( C @ ( A @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Hilbert__Choice_Oinv__into ) ) ) @ c_Set_Oimage ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bij__vimage__eq__inv__image_0) ).
thf(1044,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ c_Fun_Obij ) ) )
| ( ( D @ ( C @ ( B @ ( A @ c_Set_Ovimage ) ) ) )
= ( C @ ( D @ ( B @ ( D @ ( C @ ( A @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Hilbert__Choice_Oinv__into ) ) ) @ c_Set_Oimage ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(334,axiom,
! [B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__UNIV__left_0) ).
thf(1176,plain,
! [B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(77,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ c_Finite__Set_Ofinite ) )
| ( tc_nat @ ( B @ ( B @ ( A @ ( C @ c_Set_Oinsert ) ) @ c_Finite__Set_Ocard ) @ ( B @ ( A @ c_Finite__Set_Ocard ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__insert__le_0) ).
thf(608,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ c_Finite__Set_Ofinite ) )
| ( tc_nat @ ( B @ ( B @ ( A @ ( C @ c_Set_Oinsert ) ) @ c_Finite__Set_Ocard ) @ ( B @ ( A @ c_Finite__Set_Ocard ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(31,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__insert__right_0) ).
thf(505,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Set_Oinsert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(2,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/sandbox/benchmark/theBenchmark.p',cls_singleton__inject_0) ).
thf(438,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)],[2]) ).
thf(128,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
| ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__subset__conv_0) ).
thf(722,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
| ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(107,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( I @ ( B @ hAPP ) @ ( A @ hAPP ) )
= ( I @ ( G @ hAPP ) @ ( F @ hAPP ) ) )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ocomp ) ) ) ) )
!= ( E @ ( D @ ( H @ ( G @ ( F @ c_Fun_Ocomp ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__eq__dest_0) ).
thf(675,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( I @ ( B @ hAPP ) @ ( A @ hAPP ) )
= ( I @ ( G @ hAPP ) @ ( F @ hAPP ) ) )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ocomp ) ) ) ) )
!= ( E @ ( D @ ( H @ ( G @ ( F @ c_Fun_Ocomp ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(377,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( tc_nat @ ( C @ ( A @ c_Finite__Set_Ocard ) @ ( C @ ( B @ c_Finite__Set_Ocard ) @ c_lessequals ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__seteq_0) ).
thf(1277,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( tc_nat @ ( C @ ( A @ c_Finite__Set_Ocard ) @ ( C @ ( B @ c_Finite__Set_Ocard ) @ c_lessequals ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(142,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Compl_0) ).
thf(749,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(403,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( E @ ( tc_bool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Set_Oimage ) ) ) @ c_Finite__Set_Ofinite ) )
| ( D @ ( D @ ( E @ ( tc_bool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( E @ ( D @ ( C @ ( B @ ( A @ c_COMBB ) ) ) ) @ c_Set_Oimage ) ) ) @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__range__imageI_0) ).
thf(1340,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( E @ ( tc_bool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( B @ c_Set_Oimage ) ) ) @ c_Finite__Set_Ofinite ) )
| ( D @ ( D @ ( E @ ( tc_bool @ ( E @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( E @ ( D @ ( C @ ( B @ ( A @ c_COMBB ) ) ) ) @ c_Set_Oimage ) ) ) @ c_Finite__Set_Ofinite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(435,axiom,
! [A: $i] :
( v_thesis____
| ~ ( tc_nat @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( ( tc_nat @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Set_Oimage ) ) ) )
!= ( tc_nat @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Finite__Set_Ocard ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_SetInterval_Oord__class_OatLeastLessThan ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_that_0) ).
thf(1413,plain,
! [A: $i] :
( v_thesis____
| ~ ( tc_nat @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( ( tc_nat @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Set_Oimage ) ) ) )
!= ( tc_nat @ ( tc_Arrow__Order__Mirabelle_Oindi @ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oindi @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Finite__Set_Ocard ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_SetInterval_Oord__class_OatLeastLessThan ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(287,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq_0) ).
thf(1076,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(346,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__assoc_0) ).
thf(1203,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(349,axiom,
! [A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gr0I_0) ).
thf(1208,plain,
! [A: $i] :
( ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) )
| ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(68,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( tc_bool @ ( C @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__subset__Compl__iff_0) ).
thf(589,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( tc_bool @ ( C @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(42,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_2) ).
thf(531,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(231,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( C @ c_SetInterval_Oord__class_OlessThan ) @ ( A @ ( B @ c_SetInterval_Oord__class_OlessThan ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lessThan__subset__iff_1) ).
thf(944,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( C @ c_SetInterval_Oord__class_OlessThan ) @ ( A @ ( B @ c_SetInterval_Oord__class_OlessThan ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(164,axiom,
! [B: $i,A: $i] :
( ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty__right_0) ).
thf(795,plain,
! [B: $i,A: $i] :
( ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(109,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_Suc @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__le__eq_0) ).
thf(680,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_Suc @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(102,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
= ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__Un_0) ).
thf(663,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
= ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(49,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( B @ ( A @ ( C @ c_Set_Oinsert ) ) @ c_Finite__Set_Ofinite ) )
| ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__insert_0) ).
thf(548,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( B @ ( A @ ( C @ c_Set_Oinsert ) ) @ c_Finite__Set_Ofinite ) )
| ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(320,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B
= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) )
!= ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__is__empty_0) ).
thf(1145,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)],[320]) ).
thf(261,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/sandbox/benchmark/theBenchmark.p',cls_empty__Diff_0) ).
thf(1018,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)],[261]) ).
thf(10,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__less_1) ).
thf(458,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(337,axiom,
( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_SetInterval_Oord__class_OlessThan ) )
= ( tc_bool @ ( tc_nat @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lessThan__0_0) ).
thf(1181,plain,
( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_SetInterval_Oord__class_OlessThan ) )
= ( tc_bool @ ( tc_nat @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(177,axiom,
! [A: $i] :
~ ( tc_nat @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__not__refl_0) ).
thf(823,plain,
! [A: $i] :
~ ( tc_nat @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(40,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv3_0) ).
thf(525,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(124,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastLessThan ) ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastLessThan__empty__iff_1) ).
thf(712,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastLessThan ) ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(192,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_lessequals ) ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__absorb1_0) ).
thf(855,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_lessequals ) ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(284,axiom,
tc_bool @ class_Finite__Set_Ofinite_Ofinite,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Finite__Set_Ofinite_Ofinite) ).
thf(1070,plain,
tc_bool @ class_Finite__Set_Ofinite_Ofinite,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(356,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
| ~ ( C @ ( B @ ( A @ c_Fun_Osurj ) ) )
| ( C @ ( B @ ( A @ c_Fun_Obij ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bijI_0) ).
thf(1225,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
| ~ ( C @ ( B @ ( A @ c_Fun_Osurj ) ) )
| ( C @ ( B @ ( A @ c_Fun_Obij ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(373,axiom,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Fun_Oinj__on ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__empty_0) ).
thf(1267,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)],[373]) ).
thf(298,axiom,
! [B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__empty__left_0) ).
thf(1098,plain,
! [B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(251,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/sandbox/benchmark/theBenchmark.p',cls_bij__betw__def_1) ).
thf(993,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)],[251]) ).
thf(106,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( D @ ( A @ ( C @ c_Set_Ovimage ) ) ) @ c_Finite__Set_Ofinite ) )
| ~ ( B @ ( D @ ( C @ c_Fun_Osurj ) ) )
| ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__vimageD_0) ).
thf(673,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( D @ ( A @ ( C @ c_Set_Ovimage ) ) ) @ c_Finite__Set_Ofinite ) )
| ~ ( B @ ( D @ ( C @ c_Fun_Osurj ) ) )
| ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(340,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
| ~ ( C @ ( B @ ( A @ c_Fun_Osurj ) ) )
| ( C @ ( B @ ( A @ c_Fun_Obij ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bij__def_2) ).
thf(1188,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
| ~ ( C @ ( B @ ( A @ c_Fun_Osurj ) ) )
| ( C @ ( B @ ( A @ c_Fun_Obij ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(3,axiom,
! [C: $i,B: $i,A: $i] :
( ( C = B )
| ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE_0) ).
thf(441,plain,
! [C: $i,B: $i,A: $i] :
( ( C = B )
| ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(126,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( A = B )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__neq__implies__less_0) ).
thf(717,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( A = B )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(186,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__mono_0) ).
thf(840,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(361,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( E @ ( A @ c_Set_Oimage ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__mono_0) ).
thf(1235,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( E @ ( A @ c_Set_Oimage ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(394,axiom,
! [B: $i,A: $i] : ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equalityE_0) ).
thf(1317,plain,
! [B: $i,A: $i] : ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(170,axiom,
! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__upper2_0) ).
thf(808,plain,
! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(313,axiom,
! [B: $i,A: $i] :
( ( B = A )
| ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat__neq__iff_0) ).
thf(1130,plain,
! [B: $i,A: $i] :
( ( B = A )
| ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(93,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_Fun_Othe__inv__into ) ) ) @ c_Fun_Obij__betw ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bij__betw__the__inv__into_0) ).
thf(643,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_Fun_Othe__inv__into ) ) ) @ c_Fun_Obij__betw ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(15,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( D @ ( A @ c_Set_Oinsert ) ) @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__mono_0) ).
thf(470,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( D @ ( A @ c_Set_Oinsert ) ) @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(62,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/sandbox/benchmark/theBenchmark.p',cls_insert__absorb2_0) ).
thf(576,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)],[62]) ).
thf(47,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_Set_Ovimage ) ) ) )
= ( B @ ( D @ ( C @ ( A @ c_Set_Ovimage ) ) ) @ ( tc_bool @ ( D @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__Compl_0) ).
thf(544,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( D @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_Set_Ovimage ) ) ) )
= ( B @ ( D @ ( C @ ( A @ c_Set_Ovimage ) ) ) @ ( tc_bool @ ( D @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(217,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= A )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
!= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__triv_0) ).
thf(907,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= A )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
!= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(431,axiom,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_SetInterval_Oord__class_OatLeastLessThan ) ) )
= ( tc_bool @ ( tc_nat @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastLessThan0_0) ).
thf(1404,plain,
! [A: $i] :
( ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_SetInterval_Oord__class_OatLeastLessThan ) ) )
= ( tc_bool @ ( tc_nat @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(139,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__least_0) ).
thf(744,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(369,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ c_Fun_Oinj__on ) ) ) )
| ( ( B @ ( E @ ( D @ ( C @ ( D @ ( E @ ( B @ ( D @ ( B @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Hilbert__Choice_Oinv__into ) ) ) @ ( A @ c_Fun_Ocomp ) ) ) ) @ c_Fun_Ocomp ) ) ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__inv__o__cancel_0) ).
thf(1257,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( C @ c_Fun_Oinj__on ) ) ) )
| ( ( B @ ( E @ ( D @ ( C @ ( D @ ( E @ ( B @ ( D @ ( B @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Hilbert__Choice_Oinv__into ) ) ) @ ( A @ c_Fun_Ocomp ) ) ) ) @ c_Fun_Ocomp ) ) ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(318,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__commute_0) ).
thf(1141,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(275,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( B @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( D @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( D @ ( B @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_Set_Oimage ) ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__image__Compl__subset_0) ).
thf(1052,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( B @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( D @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( D @ ( B @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_Set_Oimage ) ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(131,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/sandbox/benchmark/theBenchmark.p',cls_vimage__empty_0) ).
thf(727,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)],[131]) ).
thf(59,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/sandbox/benchmark/theBenchmark.p',cls_Diff__insert2_0) ).
thf(571,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)],[59]) ).
thf(418,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/sandbox/benchmark/theBenchmark.p',cls_inj__vimage__image__eq_0) ).
thf(1372,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)],[418]) ).
thf(363,axiom,
! [E: $i,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 ) ) ) )
| ( B = E )
| ( ( D @ ( C @ ( B @ ( A @ c_List_Omap ) ) ) )
!= ( D @ ( C @ ( E @ ( A @ c_List_Omap ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_map__injective_0) ).
thf(1240,plain,
! [E: $i,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 ) ) ) )
| ( B = E )
| ( ( D @ ( C @ ( B @ ( A @ c_List_Omap ) ) ) )
!= ( D @ ( C @ ( E @ ( A @ c_List_Omap ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(99,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( B @ c_Fun_Obij ) ) )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( E @ ( D @ ( A @ ( B @ c_Set_Ovimage ) ) ) @ c_lessequals ) ) )
| ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( D @ ( C @ ( B @ c_Set_Oimage ) ) ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__subset__eq_0) ).
thf(656,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( B @ c_Fun_Obij ) ) )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( E @ ( D @ ( A @ ( B @ c_Set_Ovimage ) ) ) @ c_lessequals ) ) )
| ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( D @ ( C @ ( B @ c_Set_Oimage ) ) ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(263,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( tc_bool @ ( E @ tc_fun ) @ ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( E @ ( D @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Set_Oimage ) ) ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__Int__subset_0) ).
thf(1023,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( tc_bool @ ( E @ tc_fun ) @ ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( E @ ( D @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Set_Oimage ) ) ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(354,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( D @ ( B @ ( A @ ( C @ c_Set_Oimage ) ) ) @ c_Finite__Set_Ofinite ) )
| ~ ( D @ ( B @ ( A @ ( C @ c_Fun_Oinj__on ) ) ) )
| ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__imageD_0) ).
thf(1221,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( D @ ( B @ ( A @ ( C @ c_Set_Oimage ) ) ) @ c_Finite__Set_Ofinite ) )
| ~ ( D @ ( B @ ( A @ ( C @ c_Fun_Oinj__on ) ) ) )
| ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(380,axiom,
! [B: $i,A: $i] :
( ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__absorb_0) ).
thf(1284,plain,
! [B: $i,A: $i] :
( ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(409,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( E @ ( F @ ( B @ c_Fun_Oinj__on ) ) ) )
| ~ ( D @ ( C @ ( C @ ( E @ ( F @ ( B @ c_Set_Oimage ) ) ) @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( D @ ( E @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ocomp ) ) ) ) @ c_Fun_Oinj__on ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comp__inj__on_0) ).
thf(1353,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( E @ ( F @ ( B @ c_Fun_Oinj__on ) ) ) )
| ~ ( D @ ( C @ ( C @ ( E @ ( F @ ( B @ c_Set_Oimage ) ) ) @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( D @ ( E @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ocomp ) ) ) ) @ c_Fun_Oinj__on ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(73,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__le_1) ).
thf(600,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(296,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__distrib2_0) ).
thf(1094,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(245,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( C @ ( A @ ( E @ c_Fun_Obij__betw ) ) ) ) )
| ( ( B @ ( A @ c_Finite__Set_Ocard ) )
= ( D @ ( C @ c_Finite__Set_Ocard ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bij__betw__same__card_0) ).
thf(978,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( C @ ( A @ ( E @ c_Fun_Obij__betw ) ) ) ) )
| ( ( B @ ( A @ c_Finite__Set_Ocard ) )
= ( D @ ( C @ c_Finite__Set_Ocard ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(317,axiom,
! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ c_Finite__Set_Ofinite ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__atLeastLessThan_0) ).
thf(1140,plain,
! [B: $i,A: $i] : ( tc_nat @ ( tc_nat @ ( B @ ( A @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ c_Finite__Set_Ofinite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(188,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_lessequals ) ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
!= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_disjoint__eq__subset__Compl_0) ).
thf(845,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_lessequals ) ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
!= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(13,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/sandbox/benchmark/theBenchmark.p',cls_Diff__insert_0) ).
thf(465,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)],[13]) ).
thf(86,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
!= ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__eq__Compl__iff_0) ).
thf(627,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
!= ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(53,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( C @ ( A @ ( D @ c_Set_Oinsert ) ) @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_1) ).
thf(556,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( C @ ( A @ ( D @ c_Set_Oinsert ) ) @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(45,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/sandbox/benchmark/theBenchmark.p',cls_inj__on__insert_0) ).
thf(539,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)],[45]) ).
thf(215,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__lessD_0) ).
thf(903,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(64,axiom,
tc_nat @ class_Orderings_Olinorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
thf(581,plain,
tc_nat @ class_Orderings_Olinorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(311,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_Fun_Obij ) ) )
| ( ( D @ ( B @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_Set_Oimage ) ) ) )
= ( D @ ( B @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( D @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bij__image__Compl__eq_0) ).
thf(1126,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_Fun_Obij ) ) )
| ( ( D @ ( B @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_Set_Oimage ) ) ) )
= ( D @ ( B @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( D @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(425,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 ) ) ) )
| ~ ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( C @ ( B @ ( D @ c_Set_Oimage ) ) ) @ ( E @ ( C @ ( A @ ( D @ c_Set_Oimage ) ) ) @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__image__subset__iff_0) ).
thf(1390,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 ) ) ) )
| ~ ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( C @ ( B @ ( D @ c_Set_Oimage ) ) ) @ ( E @ ( C @ ( A @ ( D @ c_Set_Oimage ) ) ) @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(382,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_Set_Ovimage ) ) ) @ ( A @ c_Set_Oimage ) ) ) )
= ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Set_Oimage ) ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__vimage__eq_0) ).
thf(1289,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_Set_Ovimage ) ) ) @ ( A @ c_Set_Oimage ) ) ) )
= ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Set_Oimage ) ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(393,axiom,
! [A: $i] : ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le0_0) ).
thf(1316,plain,
! [A: $i] : ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(291,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_Fun_Obij ) ) )
| ( C @ ( B @ ( A @ c_Fun_Osurj ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bij__def_1) ).
thf(1084,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_Fun_Obij ) ) )
| ( C @ ( B @ ( A @ c_Fun_Osurj ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(325,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oimage ) ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__empty_0) ).
thf(1157,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)],[325]) ).
thf(396,axiom,
! [B: $i,A: $i] :
( ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__UNIV__right_0) ).
thf(1321,plain,
! [B: $i,A: $i] :
( ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(352,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_Fun_Osurj ) ) )
| ( ( C @ ( B @ ( B @ ( C @ ( D @ ( C @ ( B @ ( A @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Hilbert__Choice_Oinv__into ) ) ) @ c_Set_Oimage ) ) ) @ ( A @ c_Set_Oimage ) ) ) )
= D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__surj__f__inv__f_0) ).
thf(1216,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_Fun_Osurj ) ) )
| ( ( C @ ( B @ ( B @ ( C @ ( D @ ( C @ ( B @ ( A @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Hilbert__Choice_Oinv__into ) ) ) @ c_Set_Oimage ) ) ) @ ( A @ c_Set_Oimage ) ) ) )
= D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(209,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ c_Finite__Set_Ofinite ) )
| ~ ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
| ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__finite__subset_0) ).
thf(891,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ c_Finite__Set_Ofinite ) )
| ~ ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
| ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(398,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
| ~ ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( ( D @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_Finite__Set_Ocard ) )
= ( C @ ( B @ c_Finite__Set_Ocard ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__iff__eq__card_0) ).
thf(1326,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
| ~ ( D @ ( C @ ( B @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( ( D @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_Finite__Set_Ocard ) )
= ( C @ ( B @ c_Finite__Set_Ocard ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(232,axiom,
! [A: $i] : ( tc_nat @ ( tc_nat @ ( A @ c_SetInterval_Oord__class_OlessThan ) @ c_Finite__Set_Ofinite ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__lessThan_0) ).
thf(946,plain,
! [A: $i] : ( tc_nat @ ( tc_nat @ ( A @ c_SetInterval_Oord__class_OlessThan ) @ c_Finite__Set_Ofinite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(97,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( E @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Ovimage ) ) ) )
= ( tc_bool @ ( E @ tc_fun ) @ ( 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 ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__insert_0) ).
thf(652,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( E @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Ovimage ) ) ) )
= ( tc_bool @ ( E @ tc_fun ) @ ( 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 ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(88,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_0) ).
thf(632,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(156,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_Suc @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq__eq_0) ).
thf(781,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_Suc @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(238,axiom,
! [A: $i] :
( ( tc_nat @ ( A @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( A @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__less__Suc__eq_1) ).
thf(961,plain,
! [A: $i] :
( ( tc_nat @ ( A @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( A @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(423,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Fun__Xdatatype__injI__1__1 ) ) )
!= ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Fun__Xdatatype__injI__1__2 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_datatype__injI_1) ).
thf(1385,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Fun__Xdatatype__injI__1__1 ) ) )
!= ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Fun__Xdatatype__injI__1__2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(239,axiom,
! [A: $i] : ( tc_nat @ ( A @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__imp__le_0) ).
thf(963,plain,
! [A: $i] : ( tc_nat @ ( A @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(37,axiom,
! [C: $i,B: $i,A: $i] :
( ( C = B )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I12_J_0) ).
thf(517,plain,
! [C: $i,B: $i,A: $i] :
( ( C = B )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(212,axiom,
! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__lower2_0) ).
thf(896,plain,
! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(141,axiom,
! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_zero__less__Suc_0) ).
thf(748,plain,
! [A: $i] : ( tc_nat @ ( A @ c_Suc @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(133,axiom,
! [B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__partition2_0) ).
thf(731,plain,
! [B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(159,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__subset__iff_1) ).
thf(786,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(266,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc__eq__le_1) ).
thf(1030,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(33,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le_1) ).
thf(510,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(104,axiom,
! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__subset_0) ).
thf(667,plain,
! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(389,axiom,
! [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 @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Hilbert__Choice_Oinv__into ) ) ) @ c_Fun_Osurj ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__imp__surj__inv_0) ).
thf(1308,plain,
! [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 @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Hilbert__Choice_Oinv__into ) ) ) @ c_Fun_Osurj ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(342,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Finite__Set_Ofinite ) )
| ~ ( B @ ( B @ ( A @ c_Fun_Osurj ) ) )
| ( B @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__UNIV__surj__inj_0) ).
thf(1193,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Finite__Set_Ofinite ) )
| ~ ( B @ ( B @ ( A @ c_Fun_Osurj ) ) )
| ( B @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(44,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( C = B )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__less__linear_0) ).
thf(536,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( C = B )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(327,axiom,
! [A: $i] :
~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gr__implies__not0_0) ).
thf(1161,plain,
! [A: $i] :
~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(182,axiom,
! [A: $i] : ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Finite__Set_Ofinite ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite_OemptyI_0) ).
thf(832,plain,
! [A: $i] : ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Finite__Set_Ofinite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(111,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( A
= ( B @ c_Suc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__SucE_0) ).
thf(684,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ( A
= ( B @ c_Suc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(314,axiom,
! [A: $i] :
( ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Finite__Set_Ofinite ) )
| ~ ( A @ class_Finite__Set_Ofinite_Ofinite ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__UNIV_0) ).
thf(1133,plain,
! [A: $i] :
( ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Finite__Set_Ofinite ) )
| ~ ( A @ class_Finite__Set_Ofinite_Ofinite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(5,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I8_J_0) ).
thf(447,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(378,axiom,
! [B: $i,A: $i] :
( ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__UNIV__right_0) ).
thf(1280,plain,
! [B: $i,A: $i] :
( ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(358,axiom,
! [A: $i] :
( ( A @ c_Suc )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Osimps_I3_J_0) ).
thf(1229,plain,
! [A: $i] :
( ( A @ c_Suc )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(427,axiom,
tc_nat @ class_Ring__and__Field_Osemiring__0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__0) ).
thf(1395,plain,
tc_nat @ class_Ring__and__Field_Osemiring__0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(321,axiom,
! [A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_SetInterval_Oord__class_OatLeastLessThan ) ) )
= ( tc_nat @ ( A @ c_SetInterval_Oord__class_OlessThan ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeast0LessThan_0) ).
thf(1148,plain,
! [A: $i] :
( ( tc_nat @ ( A @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_SetInterval_Oord__class_OatLeastLessThan ) ) )
= ( tc_nat @ ( A @ c_SetInterval_Oord__class_OlessThan ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(197,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__subset__iff_0) ).
thf(867,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(196,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__less__eq_0) ).
thf(865,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(183,axiom,
! [B: $i,A: $i] :
( ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
= ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_HOL_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__eq__Diff__UNIV_0) ).
thf(833,plain,
! [B: $i,A: $i] :
( ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
= ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_HOL_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(241,axiom,
! [B: $i,A: $i] :
( ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( tc_bool @ ( B @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__partition_0) ).
thf(967,plain,
! [B: $i,A: $i] :
( ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( tc_bool @ ( B @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(234,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( D @ ( C @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__int_I11_J_0) ).
thf(950,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( D @ ( C @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(184,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastLessThan ) ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastLessThan__empty_0) ).
thf(835,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastLessThan ) ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(366,axiom,
! [B: $i,A: $i] :
( ( A
= ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ~ ( B @ ( A @ c_Finite__Set_Ofinite ) )
| ( ( B @ ( A @ c_Finite__Set_Ocard ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__eq__0__iff_0) ).
thf(1248,plain,
! [B: $i,A: $i] :
( ( A
= ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ~ ( B @ ( A @ c_Finite__Set_Ofinite ) )
| ( ( B @ ( A @ c_Finite__Set_Ocard ) )
!= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(161,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( E @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Set_Ovimage ) ) ) )
= ( tc_bool @ ( E @ tc_fun ) @ ( D @ ( E @ ( C @ ( A @ c_Set_Ovimage ) ) ) @ ( D @ ( E @ ( B @ ( A @ c_Set_Ovimage ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__Un_0) ).
thf(790,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( E @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Set_Ovimage ) ) ) )
= ( tc_bool @ ( E @ tc_fun ) @ ( D @ ( E @ ( C @ ( A @ c_Set_Ovimage ) ) ) @ ( D @ ( E @ ( B @ ( A @ c_Set_Ovimage ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(56,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/sandbox/benchmark/theBenchmark.p',cls_image__insert_0) ).
thf(564,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)],[56]) ).
thf(277,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__trans_0) ).
thf(1056,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_nat @ ( C @ ( A @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ ( C @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(89,axiom,
tc_bool @ class_Orderings_Oorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Oorder) ).
thf(635,plain,
tc_bool @ class_Orderings_Oorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(282,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__le__mono_0) ).
thf(1065,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_Suc @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(116,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( E @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ocomp ) ) ) ) @ c_Set_Ovimage ) ) ) )
= ( C @ ( E @ ( D @ ( C @ ( F @ ( A @ c_Set_Ovimage ) ) ) @ ( B @ c_Set_Ovimage ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__compose_0) ).
thf(696,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( E @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ocomp ) ) ) ) @ c_Set_Ovimage ) ) ) )
= ( C @ ( E @ ( D @ ( C @ ( F @ ( A @ c_Set_Ovimage ) ) ) @ ( B @ c_Set_Ovimage ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(406,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Fun__Xdatatype__injI__1__1 ) ) @ ( A @ hAPP ) )
= ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Fun__Xdatatype__injI__1__2 ) ) @ ( A @ hAPP ) ) )
| ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_datatype__injI_0) ).
thf(1346,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Fun__Xdatatype__injI__1__1 ) ) @ ( A @ hAPP ) )
= ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Fun__Xdatatype__injI__1__2 ) ) @ ( A @ hAPP ) ) )
| ( 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)],[406]) ).
thf(221,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Suc )
!= ( B @ c_Suc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Oinject_0) ).
thf(918,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Suc )
!= ( B @ c_Suc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(167,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( G @ ( E @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Fun_Ocomp ) ) ) ) @ ( A @ c_Fun_Ocomp ) ) ) ) )
= ( F @ ( G @ ( D @ ( C @ ( D @ ( G @ ( E @ ( B @ ( A @ c_Fun_Ocomp ) ) ) ) @ c_Fun_Ocomp ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__assoc_0) ).
thf(801,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( G @ ( E @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Fun_Ocomp ) ) ) ) @ ( A @ c_Fun_Ocomp ) ) ) ) )
= ( F @ ( G @ ( D @ ( C @ ( D @ ( G @ ( E @ ( B @ ( A @ c_Fun_Ocomp ) ) ) ) @ c_Fun_Ocomp ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(414,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ c_Finite__Set_Ofinite ) )
| ~ ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( C @ c_Finite__Set_Ocard ) @ ( B @ ( A @ c_Finite__Set_Ocard ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__mono_0) ).
thf(1363,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ c_Finite__Set_Ofinite ) )
| ~ ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_nat @ ( B @ ( C @ c_Finite__Set_Ocard ) @ ( B @ ( A @ c_Finite__Set_Ocard ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(392,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__commute_0) ).
thf(1314,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(332,axiom,
! [A: $i] :
( ~ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Finite__Set_Ofinite ) )
| ( tc_nat @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Finite__Set_Ocard ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__UNIV__card__ge__0_0) ).
thf(1172,plain,
! [A: $i] :
( ~ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Finite__Set_Ofinite ) )
| ( tc_nat @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Finite__Set_Ocard ) @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(213,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ c_Fun_Osurj ) ) )
| ( ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_Set_Ovimage ) ) ) @ ( A @ c_Set_Oimage ) ) ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_surj__image__vimage__eq_0) ).
thf(897,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ c_Fun_Osurj ) ) )
| ( ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_Set_Ovimage ) ) ) @ ( A @ c_Set_Oimage ) ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(17,axiom,
tc_nat @ class_Orderings_Oorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).
thf(474,plain,
tc_nat @ class_Orderings_Oorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(434,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_Fun_Osurj ) ) )
| ( ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Set_Oimage ) ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_surj__range_0) ).
thf(1410,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_Fun_Osurj ) ) )
| ( ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Set_Oimage ) ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(150,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( A @ ( B @ c_SetInterval_Oord__class_OlessThan ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__int_I2_J_0) ).
thf(767,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( A @ ( B @ c_SetInterval_Oord__class_OlessThan ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(127,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_Suc @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq__eq_1) ).
thf(720,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_Suc @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(329,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( C @ ( B @ ( D @ c_Set_Oimage ) ) ) @ ( E @ ( C @ ( A @ ( D @ c_Set_Oimage ) ) ) @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__image__iff_2) ).
thf(1165,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( C @ ( B @ ( D @ c_Set_Oimage ) ) ) @ ( E @ ( C @ ( A @ ( D @ c_Set_Oimage ) ) ) @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(207,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
!= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty_1) ).
thf(886,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
!= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(224,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ c_Finite__Set_Ofinite ) )
| ~ ( A @ class_Finite__Set_Ofinite_Ofinite ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite_0) ).
thf(928,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ c_Finite__Set_Ofinite ) )
| ~ ( A @ class_Finite__Set_Ofinite_Ofinite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(137,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__SucI_0) ).
thf(740,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(249,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ c_Suc )
= B )
| ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__lessI_0) ).
thf(987,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ c_Suc )
= B )
| ( tc_nat @ ( B @ ( A @ c_Suc @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(312,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( E @ ( A @ c_Set_Oimage ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__diff__subset_0) ).
thf(1129,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( E @ ( A @ c_Set_Oimage ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(374,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( B @ ( A @ ( E @ c_Typedef_Otype__definition ) ) ) ) )
| ( ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) )
= ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type__definition_OAbs__image_0) ).
thf(1268,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( B @ ( A @ ( E @ c_Typedef_Otype__definition ) ) ) ) )
| ( ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) )
= ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(194,axiom,
! [B: $i,A: $i] :
( ~ ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( tc_bool @ ( B @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_lessequals ) ) )
| ( A
= ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__Compl__self__eq_0) ).
thf(860,plain,
! [B: $i,A: $i] :
( ~ ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( tc_bool @ ( B @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( A @ c_lessequals ) ) )
| ( A
= ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(41,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) )
!= ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat ) ) )
| ~ ( A @ class_Nat_Osemiring__char__0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_of__nat__eq__iff_0) ).
thf(528,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( B @ c_Nat_Osemiring__1__class_Oof__nat ) )
!= ( A @ ( C @ c_Nat_Osemiring__1__class_Oof__nat ) ) )
| ~ ( A @ class_Nat_Osemiring__char__0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(190,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__antisym_0) ).
thf(850,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(255,axiom,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( A @ c_Suc @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__antisym_0) ).
thf(1004,plain,
! [B: $i,A: $i] :
( ( tc_nat @ ( A @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( A @ c_Suc @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(386,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Hilbert__Choice_Oinv__into ) ) ) )
= B )
| ~ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__imp__inv__eq__1__1 ) ) ) @ ( B @ hAPP ) @ ( A @ hAPP ) )
!= ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__imp__inv__eq__1__1 ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__imp__inv__eq_0) ).
thf(1299,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( A @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Hilbert__Choice_Oinv__into ) ) ) )
= B )
| ~ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Otop__class_Otop @ ( A @ c_Fun_Oinj__on ) ) ) )
| ( ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__imp__inv__eq__1__1 ) ) ) @ ( B @ hAPP ) @ ( A @ hAPP ) )
!= ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__imp__inv__eq__1__1 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(114,axiom,
! [A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__empty__eq_0) ).
thf(691,plain,
! [A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(429,axiom,
! [A: $i] :
( ~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals ) ) )
| ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__0__eq_0) ).
thf(1399,plain,
! [A: $i] :
( ~ ( tc_nat @ ( tc_nat @ c_HOL_Ozero__class_Ozero @ ( A @ c_lessequals ) ) )
| ( A
= ( tc_nat @ c_HOL_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(308,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastLessThan ) ) )
!= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastLessThan__empty__iff_0) ).
thf(1120,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastLessThan ) ) )
!= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(29,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( C @ c_lessequals ) ) )
| ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__anti__mono_0) ).
thf(501,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( C @ c_lessequals ) ) )
| ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(71,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Finite__Set_Ofinite ) )
| ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Diff__insert_1) ).
thf(596,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Finite__Set_Ofinite ) )
| ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Finite__Set_Ofinite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(420,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
!= ( A @ ( D @ ( C @ ( B @ c_Set_Oimage ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__is__image_0) ).
thf(1378,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)],[420]) ).
thf(23,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( A @ ( B @ ( A @ c_Fun_Oid @ c_Fun_Ocomp ) ) ) ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_id__o_0) ).
thf(486,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( A @ ( B @ ( A @ c_Fun_Oid @ c_Fun_Ocomp ) ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(168,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
!= ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastLessThan ) ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastLessThan__empty__iff2_0) ).
thf(803,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
!= ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastLessThan ) ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(222,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
| ~ ( A @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_Finite__Set_Ofinite ) )
| ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__compl_0) ).
thf(923,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ c_Finite__Set_Ofinite ) )
| ~ ( A @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_HOL_Ouminus__class_Ouminus @ hAPP ) @ c_Finite__Set_Ofinite ) )
| ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Otop__class_Otop @ c_Finite__Set_Ofinite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(269,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ c_Suc @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__eq_1) ).
thf(1037,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ c_Suc @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_nat @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(91,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Diff_0) ).
thf(639,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(122,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__distrib_0) ).
thf(708,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(205,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Un__distrib2_0) ).
thf(882,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(416,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/sandbox/benchmark/theBenchmark.p',cls_inv__f__f_0) ).
thf(1367,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)],[416]) ).
thf(229,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__subset__conv_1) ).
thf(940,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(227,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
!= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__Un__eq_1) ).
thf(935,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
!= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(257,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ c_Complete__Lattice_OSup__class_OSup ) )
= B )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sup__singleton_0) ).
thf(1009,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ c_Complete__Lattice_OSup__class_OSup ) )
= B )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(25,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I7_J_0) ).
thf(491,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(293,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__Suc__eq__le_0) ).
thf(1088,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_nat @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(27,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( D @ ( A @ c_Set_Oinsert ) ) @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__inter__insert_0) ).
thf(496,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( D @ ( A @ c_Set_Oinsert ) ) @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Set_Oinsert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(8,axiom,
! [A: $i] : ( A @ ( A @ ( A @ c_Fun_Oid @ c_Fun_Obij ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bij__id_0) ).
thf(454,plain,
! [A: $i] : ( A @ ( A @ ( A @ c_Fun_Oid @ c_Fun_Obij ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(259,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/sandbox/benchmark/theBenchmark.p',cls_COMBB__def_0) ).
thf(1014,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)],[259]) ).
thf(243,axiom,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__less__Suc__eq_0) ).
thf(972,plain,
! [B: $i,A: $i] :
( ~ ( tc_nat @ ( A @ ( B @ c_lessequals ) ) )
| ~ ( tc_nat @ ( B @ c_Suc @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(2042,plain,
$false,
inference(e,[status(thm)],[645,809,1337,1024,1190,760,479,1237,893,1083,1179,777,481,1211,1406,878,614,1305,523,582,762,873,1205,449,1078,1310,550,797,715,472,814,1063,930,1260,698,1342,913,829,1001,1243,1359,436,1254,724,785,1313,460,587,1323,619,838,702,751,817,853,870,770,1115,1100,1232,969,606,475,591,1109,623,1334,806,1183,821,905,1302,756,1383,1020,574,956,774,1351,998,1201,1104,507,602,981,1169,687,1074,678,661,546,925,1153,534,1067,512,942,1047,1163,1274,910,746,825,1042,1355,1123,1174,598,820,561,729,1223,894,693,630,788,1370,1032,1365,625,879,1178,830,889,1159,493,1027,1392,842,1012,916,467,566,484,1296,665,682,1195,1291,710,1402,1234,1143,650,1375,725,1096,1138,593,869,610,783,742,578,1111,1227,488,1361,933,1214,1039,1155,706,884,1329,554,753,1016,1207,738,1266,654,984,569,779,503,647,1263,515,1150,1060,1050,1318,792,541,1054,1167,794,1086,938,1286,1035,558,1071,953,1185,1135,1251,513,1219,573,689,444,733,584,975,1007,1125,772,1388,875,958,641,1271,611,498,1332,1092,1090,704,947,1356,1058,1107,900,1408,1282,1117,736,1349,451,880,616,863,764,604,990,996,477,811,1080,758,799,621,964,1344,1381,858,552,848,700,520,1293,668,462,1061,983,827,455,1113,1102,658,1198,1396,1245,636,1044,1176,608,505,438,722,675,1277,749,1340,1413,1076,1203,1208,589,531,944,795,680,663,548,1145,1018,458,1181,823,525,712,855,1070,1225,1267,1098,993,673,1188,441,717,840,1235,1317,808,1130,643,470,576,544,907,1404,744,1257,1141,1052,727,571,1372,1240,656,1023,1221,1284,1353,600,1094,978,1140,845,465,627,556,539,903,581,1126,1390,1289,1316,1084,1157,1321,1216,891,1326,946,652,632,781,961,1385,963,517,896,748,731,786,1030,510,667,1308,1193,536,1161,832,684,1133,447,1280,1229,1395,1148,867,865,833,967,950,835,1248,790,564,1056,635,1065,696,1346,918,801,1363,1314,1172,897,474,1410,767,720,1165,886,928,740,987,1129,1268,860,528,850,1004,1299,691,1399,1120,501,596,1378,486,803,923,1037,639,708,882,1367,940,935,1009,491,1088,496,454,1014,972]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SCT071-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.11/0.39 % Computer : n017.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Sat Sep 26 06:20:04 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.60/0.69 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.49/0.94 % [INFO] Parsing done (250ms).
% 1.49/0.95 % [INFO] Running in sequential loop mode.
% 2.49/1.15 % [INFO] eprover registered as external prover.
% 2.49/1.15 % [INFO] Scanning for conjecture ...
% 2.70/1.28 % [INFO] Found a conjecture (or negated_conjecture) and 836 axioms. Running axiom selection ...
% 3.98/1.52 % [INFO] Axiom selection finished. Selected 434 axioms (removed 402 axioms).
% 4.87/1.74 % [INFO] Problem is propositional (TPTP CNF).
% 4.87/1.76 % [INFO] Type checking passed.
% 4.87/1.76 % [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 ...
% 12.54/3.60 % External prover 'e' found a proof!
% 13.57/3.60 % [INFO] Killing All external provers ...
% 13.57/3.60 % Time passed: 3111ms (effective reasoning time: 2643ms)
% 13.57/3.60 % Axioms used in derivation (434): cls_Int__Un__distrib_0, cls_linorder__antisym__conv2_1, cls_Int__absorb2_0, cls_surj__iff_0, cls_ivl__disj__un_I8_J_0, cls_le__0__eq_1, cls_finite__UNIV__card__ge__0_0, cls_Diff__cancel_0, cls_surj__f__inv__f_0, cls_xt1_I9_J_0, cls_atLeast0LessThan_0, cls_Compl__subset__Compl__iff_1, cls_ex__bij__betw__nat__finite_0, cls_Compl__Diff__eq_0, cls_inj__iff_1, cls_Un__Diff_0, cls_eq__imp__le_0, cls_order__eq__iff_0, cls_Suc__mono_0, cls_card__empty_0, cls_of__nat__0_0, cls_insert__inter__insert_0, cls_Un__subset__iff_0, cls_Suc__inject_0, cls_finite__atLeastLessThan_0, cls_equalityI_0, cls_bij__betw__the__inv__into_0, cls_inj__on__iff__eq__card_0, cls_inj__on__Un_2, cls_id__o_0, cls_xt1_I12_J_0, cls_subset__empty_1, cls_subset__image__iff_2, cls_finite__insert_0, cls_the__inv__f__f_0, cls_inj__on__image__Int_0, cls_empty__is__image_1, cls_inj__image__eq__iff_0, cls_image__mono_0, cls_Un__empty__left_0, cls_termination__basic__simps_I5_J_0, cls_Diff__eq_0, cls_Suc__n__not__n_0, cls_atLeastLessThan__subset__iff_1, cls_card__insert_0, cls_finite__vimageI_0, cls_linorder__neqE_0, cls_less__antisym_0, cls_vimage__Diff_0, cls_Un__upper1_0, cls_Un__commute_0, cls_image__Int_0, cls_Int__mono_0, cls_bij__betw__def_0, cls_card__gt__0__iff_1, clsarity_fun__Orderings_Oorder, cls_finite__Un_2, cls_Diff__Un_0, cls_card__eq__0__iff_2, cls_finite__vimage__iff_1, cls_Int__Un__distrib2_0, clsarity_nat__Orderings_Olinorder, cls_Suc__lessI_0, cls_finite__vimageD_0, cls_Int__subset__iff_2, cls_less__Suc__eq_2, cls_o__eq__id__dest_0, cls_the__inv__into__onto_0, cls_not__less__eq_1, cls_Diff__subset__conv_0, cls_image__vimage__subset_0, cls_inj__on__image__set__diff_0, cls_Diff__triv_0, cls_vimage__UNIV_0, cls_Int__absorb1_0, cls_inj__image__subset__iff_0, cls_Diff__insert_0, cls_inj__on__Un__image__eq__iff_0, cls_datatype__injI_0, cls_gr0I_0, cls_vimage__Compl_0, cls_inj__image__Compl__subset_0, cls_inv__inv__eq_0, cls_vimage__compose_0, cls_finite__insert_1, cls_bij__betw__inv__into_0, cls_Compl__partition_0, cls_COMBB__def_0, cls_le__0__eq_0, cls_disjoint__eq__subset__Compl_0, cls_Un__left__commute_0, clsarity_bool__Finite__Set_Ofinite_Ofinite, cls_finite__Int_1, cls_Int__empty__right_0, cls_Suc__le__mono_0, cls_Un__empty_2, cls_le__antisym_0, cls_Un__subset__iff_1, cls_finite__UNIV__inj__surj_0, clsarity_nat__Ring__and__Field_Osemiring__0, cls_Un__Int__distrib2_0, cls_gr__implies__not0_0, cls_vimage__insert_0, cls_linorder__not__less_0, cls_atLeastLessThan__empty__iff2_0, cls_ivl__disj__int_I11_J_0, cls_empty__is__image_0, cls_order__le__less_0, cls_inj__on__Un_3, cls_finite__UNIV__surj__inj_0, cls_linorder__antisym__conv1_0, cls_range__composition_0, cls_card__seteq_0, cls_Diff__UNIV_0, cls_bij__betw__def_1, cls_linorder__antisym__conv2_0, cls_inj__on__insert_0, cls_finite__range__imageI_0, cls_type__definition_ORep__inject_0, cls_Sup__UNIV_0, cls_Un__empty__right_0, cls_image__id_0, cls_inv__f__eq_0, 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% 13.57/3.60 % No. of inferences in proof: 871
% 13.57/3.60 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 3111 ms resp. 2643 ms w/o parsing
% 14.55/3.80 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 14.55/3.81 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------