TSTP Solution File: SWV880-1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SWV880-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n025.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 12:19:05 EDT 2023
% Result : Unsatisfiable 10.92s 3.35s
% Output : Refutation 11.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 566
% Syntax : Number of formulae : 1072 ( 195 unt; 61 typ; 0 def)
% Number of atoms : 2557 ( 502 equ; 0 cnn)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 16528 (1416 ~;1546 |; 0 &;13566 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 11 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 135 ( 135 >; 0 *; 0 +; 0 <<)
% Number of symbols : 63 ( 61 usr; 9 con; 0-6 aty)
% Number of variables : 3614 ( 0 ^;3614 !; 0 ?;3614 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_Finite__Set_Ofinite_type,type,
c_Finite__Set_Ofinite: $i > $i > $o ).
thf(v_U_type,type,
v_U: $i ).
thf(tc_Com_Opname_type,type,
tc_Com_Opname: $i ).
thf(v_G_type,type,
v_G: $i ).
thf(c_Set_Oimage_type,type,
c_Set_Oimage: $i > $i > $i > $i > $i ).
thf(v_mgt__call_type,type,
v_mgt__call: $i ).
thf(t_a_type,type,
t_a: $i ).
thf(c_in_type,type,
c_in: $i > $i > $i > $o ).
thf(v_pn_type,type,
v_pn: $i ).
thf(c_lessequals_type,type,
c_lessequals: $i > $i > $i > $o ).
thf(c_Set_Oinsert_type,type,
c_Set_Oinsert: $i > $i > $i > $i ).
thf(hAPP_type,type,
hAPP: $i > $i > $i ).
thf(c_Orderings_Obot__class_Obot_type,type,
c_Orderings_Obot__class_Obot: $i > $i ).
thf(tc_fun_type,type,
tc_fun: $i > $i > $i ).
thf(tc_bool_type,type,
tc_bool: $i ).
thf(class_Orderings_Olinorder_type,type,
class_Orderings_Olinorder: $i > $o ).
thf(c_HOL_Oord__class_Oless_type,type,
c_HOL_Oord__class_Oless: $i > $i > $i > $o ).
thf(class_Ring__and__Field_Oordered__idom_type,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
thf(class_Orderings_Oorder_type,type,
class_Orderings_Oorder: $i > $o ).
thf(class_Orderings_Opreorder_type,type,
class_Orderings_Opreorder: $i > $o ).
thf(c_Orderings_Oord__class_Omax_type,type,
c_Orderings_Oord__class_Omax: $i > $i > $i > $i ).
thf(class_OrderedGroup_Oab__group__add_type,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
thf(c_HOL_Ominus__class_Ominus_type,type,
c_HOL_Ominus__class_Ominus: $i > $i > $i > $i ).
thf(class_Lattices_Olower__semilattice_type,type,
class_Lattices_Olower__semilattice: $i > $o ).
thf(c_Lattices_Olower__semilattice__class_Oinf_type,type,
c_Lattices_Olower__semilattice__class_Oinf: $i > $i ).
thf(c_Orderings_Oord__class_Omin_type,type,
c_Orderings_Oord__class_Omin: $i > $i ).
thf(tc_nat_type,type,
tc_nat: $i ).
thf(class_Orderings_Obot_type,type,
class_Orderings_Obot: $i > $o ).
thf(c_Fun_Ofun__upd_type,type,
c_Fun_Ofun__upd: $i > $i > $i > $i > $i > $i ).
thf(c_SetInterval_Oord__class_OlessThan_type,type,
c_SetInterval_Oord__class_OlessThan: $i > $i > $i ).
thf(class_Lattices_Olattice_type,type,
class_Lattices_Olattice: $i > $o ).
thf(class_OrderedGroup_Opordered__ab__group__add_type,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
thf(class_HOL_Oord_type,type,
class_HOL_Oord: $i > $o ).
thf(class_Finite__Set_Ofinite_Ofinite_type,type,
class_Finite__Set_Ofinite_Ofinite: $i > $o ).
thf(c_Orderings_Otop__class_Otop_type,type,
c_Orderings_Otop__class_Otop: $i > $i ).
thf(hBOOL_type,type,
hBOOL: $i > $o ).
thf(c_Finite__Set_Ocard_type,type,
c_Finite__Set_Ocard: $i > $i > $i ).
thf(c_Fun_Oinj__on_type,type,
c_Fun_Oinj__on: $i > $i > $i > $i > $o ).
thf(c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__1_type,type,
c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__1: $i > $i > $i > $i > $i > $i ).
thf(c_Set_Ovimage_type,type,
c_Set_Ovimage: $i > $i > $i > $i > $i ).
thf(class_Lattices_Obounded__lattice_type,type,
class_Lattices_Obounded__lattice: $i > $o ).
thf(c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__2_type,type,
c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__2: $i > $i > $i > $i > $i > $i ).
thf(c_Finite__Set_Osetsum_type,type,
c_Finite__Set_Osetsum: $i > $i > $i > $i > $i ).
thf(c_COMBK_type,type,
c_COMBK: $i > $i > $i > $i ).
thf(c_Hilbert__Choice_Oinv__into_type,type,
c_Hilbert__Choice_Oinv__into: $i > $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1_type,type,
c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1: $i > $i > $i > $i > $i > $i ).
thf(c_Fun_Othe__inv__into_type,type,
c_Fun_Othe__inv__into: $i > $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__induct__1__2_type,type,
c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__induct__1__2: $i > $i > $i > $i ).
thf(c_Nitpick_Ofold__graph_H_type,type,
c_Nitpick_Ofold__graph_H: $i > $i > $i > $i > $i > $i > $o ).
thf(class_Orderings_Otop_type,type,
class_Orderings_Otop: $i > $o ).
thf(c_ATP__Linkup_Osko__Set__Ximage__subsetI__1__1_type,type,
c_ATP__Linkup_Osko__Set__Ximage__subsetI__1__1: $i > $i > $i > $i > $i > $i ).
thf(c_Finite__Set_Olinorder__class_OMax_type,type,
c_Finite__Set_Olinorder__class_OMax: $i > $i > $i ).
thf(c_Finite__Set_Olinorder__class_OMin_type,type,
c_Finite__Set_Olinorder__class_OMin: $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__induct__1__1_type,type,
c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__induct__1__1: $i > $i > $i > $i ).
thf(c_Inductive_Ocomplete__lattice__class_Ogfp_type,type,
c_Inductive_Ocomplete__lattice__class_Ogfp: $i > $i > $i ).
thf(class_Ring__and__Field_Oring_type,type,
class_Ring__and__Field_Oring: $i > $o ).
thf(c_Finite__Set_Ofold__graph_type,type,
c_Finite__Set_Ofold__graph: $i > $i > $i > $i > $i > $i > $o ).
thf(class_Complete__Lattice_Ocomplete__lattice_type,type,
class_Complete__Lattice_Ocomplete__lattice: $i > $o ).
thf(c_ATP__Linkup_Osko__Set__Ximage__subset__iff__1__1_type,type,
c_ATP__Linkup_Osko__Set__Ximage__subset__iff__1__1: $i > $i > $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMin__eqI__1__1_type,type,
c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMin__eqI__1__1: $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMax__eqI__1__1_type,type,
c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMax__eqI__1__1: $i > $i > $i > $i ).
thf(240,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Set_Oimage @ A @ B @ C @ D ) @ ( c_Set_Oimage @ A @ E @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ B @ E @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__mono_0) ).
thf(1036,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Set_Oimage @ A @ B @ C @ D ) @ ( c_Set_Oimage @ A @ E @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ B @ E @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(374,axiom,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ A @ B @ C ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_1) ).
thf(1337,plain,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ A @ B @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(406,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( c_Finite__Set_Ofold__graph @ A @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ B @ C @ D ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold__graph_OemptyI_0) ).
thf(1411,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( c_Finite__Set_Ofold__graph @ A @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ B @ C @ D ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(431,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oimage @ A @ ( c_Set_Ovimage @ A @ B @ C @ D ) @ C @ D )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ D @ tc_bool ) ) @ B ) @ ( c_Set_Oimage @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__vimage__eq_0) ).
thf(1469,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oimage @ A @ ( c_Set_Ovimage @ A @ B @ C @ D ) @ C @ D )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ D @ tc_bool ) ) @ B ) @ ( c_Set_Oimage @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(502,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ C )
= C )
| ~ ( c_lessequals @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__absorb2_0) ).
thf(1633,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ C )
= C )
| ~ ( c_lessequals @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).
thf(270,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Finite__Set_Ocard @ ( c_Set_Oimage @ A @ B @ C @ D ) @ D )
!= ( c_Finite__Set_Ocard @ B @ C ) )
| ~ ( c_Finite__Set_Ofinite @ B @ C )
| ( c_Fun_Oinj__on @ A @ B @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__card__imp__inj__on_0) ).
thf(1105,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Finite__Set_Ocard @ ( c_Set_Oimage @ A @ B @ C @ D ) @ D )
!= ( c_Finite__Set_Ocard @ B @ C ) )
| ~ ( c_Finite__Set_Ofinite @ B @ C )
| ( c_Fun_Oinj__on @ A @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(157,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__commute_0) ).
thf(846,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(56,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Set_Ovimage @ A @ B @ C @ D ) @ E @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ B @ ( c_Set_Oimage @ A @ E @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__subsetI_0) ).
thf(628,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Set_Ovimage @ A @ B @ C @ D ) @ E @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ B @ ( c_Set_Oimage @ A @ E @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(207,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C )
= B )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__inf_0) ).
thf(962,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C )
= B )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(199,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ ( c_Orderings_Oord__class_Omax @ B @ C @ A ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__sup__absorb_0) ).
thf(941,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ ( c_Orderings_Oord__class_Omax @ B @ C @ A ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(354,axiom,
class_Orderings_Otop @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Otop) ).
thf(1295,plain,
class_Orderings_Otop @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(466,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( c_lessequals @ B @ ( c_Inductive_Ocomplete__lattice__class_Ogfp @ C @ A ) @ A )
| ~ ( c_lessequals @ B @ ( hAPP @ C @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gfp__upperbound_0) ).
thf(1549,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( c_lessequals @ B @ ( c_Inductive_Ocomplete__lattice__class_Ogfp @ C @ A ) @ A )
| ~ ( c_lessequals @ B @ ( hAPP @ C @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).
thf(272,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Hilbert__Choice_Oinv__into @ A @ B @ C @ D ) @ E )
!= ( hAPP @ ( c_Hilbert__Choice_Oinv__into @ A @ B @ C @ D ) @ F ) )
| ( E = F )
| ~ ( c_in @ F @ ( c_Set_Oimage @ B @ A @ C @ D ) @ D )
| ~ ( c_in @ E @ ( c_Set_Oimage @ B @ A @ C @ D ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inv__into__injective_0) ).
thf(1110,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Hilbert__Choice_Oinv__into @ A @ B @ C @ D ) @ E )
!= ( hAPP @ ( c_Hilbert__Choice_Oinv__into @ A @ B @ C @ D ) @ F ) )
| ( E = F )
| ~ ( c_in @ F @ ( c_Set_Oimage @ B @ A @ C @ D ) @ D )
| ~ ( c_in @ E @ ( c_Set_Oimage @ B @ A @ C @ D ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(64,axiom,
! [B: $i,A: $i] :
( ( class_Lattices_Obounded__lattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Obounded__lattice @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Obounded__lattice) ).
thf(645,plain,
! [B: $i,A: $i] :
( ( class_Lattices_Obounded__lattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Obounded__lattice @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(177,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( c_lessequals @ B @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).
thf(892,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( c_lessequals @ B @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(298,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Oinj__on @ A @ B @ C @ D )
| ~ ( c_lessequals @ B @ E @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ A @ E @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__inj__on_0) ).
thf(1168,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Oinj__on @ A @ B @ C @ D )
| ~ ( c_lessequals @ B @ E @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ A @ E @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(116,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ~ ( c_in @ A @ ( c_HOL_Ominus__class_Ominus @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DiffE_0) ).
thf(760,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ~ ( c_in @ A @ ( c_HOL_Ominus__class_Ominus @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(364,axiom,
! [B: $i,A: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Complete__Lattice_Ocomplete__lattice @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Complete__Lattice_Ocomplete__lattice) ).
thf(1315,plain,
! [B: $i,A: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Complete__Lattice_Ocomplete__lattice @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(7,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( B = C )
| ( c_HOL_Oord__class_Oless @ C @ B @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_0) ).
thf(518,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( B = C )
| ( c_HOL_Oord__class_Oless @ C @ B @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(312,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Set_Oinsert @ B @ C @ A ) ) @ D )
= ( c_Set_Oinsert @ B @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) @ A ) )
| ~ ( c_in @ B @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__left_0) ).
thf(1200,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Set_Oinsert @ B @ C @ A ) ) @ D )
= ( c_Set_Oinsert @ B @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) @ A ) )
| ~ ( c_in @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(214,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Oord @ A )
| ~ ( c_lessequals @ B @ C @ ( tc_fun @ D @ A ) )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ ( tc_fun @ D @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__fun__def_1) ).
thf(977,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Oord @ A )
| ~ ( c_lessequals @ B @ C @ ( tc_fun @ D @ A ) )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ ( tc_fun @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(352,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ D @ B @ A ) @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__supE_1) ).
thf(1290,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ D @ B @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(254,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Finite__Set_Ocard @ ( c_Set_Oimage @ A @ B @ C @ D ) @ D )
= ( c_Finite__Set_Ocard @ B @ C ) )
| ~ ( c_Fun_Oinj__on @ A @ B @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__image_0) ).
thf(1068,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Finite__Set_Ocard @ ( c_Set_Oimage @ A @ B @ C @ D ) @ D )
= ( c_Finite__Set_Ocard @ B @ C ) )
| ~ ( c_Fun_Oinj__on @ A @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(221,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ C @ tc_bool ) ) @ A ) @ D ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1E_0) ).
thf(994,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ C @ tc_bool ) ) @ A ) @ D ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(475,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Ovimage @ A @ ( c_Set_Oimage @ A @ B @ C @ D ) @ C @ D )
= B )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__vimage__image__eq_0) ).
thf(1569,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Ovimage @ A @ ( c_Set_Oimage @ A @ B @ C @ D ) @ C @ D )
= B )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).
thf(256,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Set_Oinsert @ B @ C @ A ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) )
| ( c_in @ B @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__left_1) ).
thf(1073,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Set_Oinsert @ B @ C @ A ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) )
| ( c_in @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(463,axiom,
class_Finite__Set_Ofinite_Ofinite @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Finite__Set_Ofinite_Ofinite) ).
thf(1544,plain,
class_Finite__Set_Ofinite_Ofinite @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(314,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E ) @ B )
= C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__same_0) ).
thf(1205,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E ) @ B )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(484,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Set_Oimage @ D @ A @ C @ E ) @ ( c_Set_Oimage @ D @ B @ C @ E ) @ ( tc_fun @ E @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ D @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) @ C @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__image__subset__iff_0) ).
thf(1591,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Set_Oimage @ D @ A @ C @ E ) @ ( c_Set_Oimage @ D @ B @ C @ E ) @ ( tc_fun @ E @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ D @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) @ C @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).
thf(171,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E ) @ B )
= C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__apply_0) ).
thf(878,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E ) @ B )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(50,axiom,
! [B: $i,A: $i] : ( c_in @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UNIV__I_0) ).
thf(614,plain,
! [B: $i,A: $i] : ( c_in @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(418,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ D ) @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infI_0) ).
thf(1437,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ D ) @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(163,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) ) @ B )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__UNIV__left_0) ).
thf(861,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) ) @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(438,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E )
| ~ ( c_in @ B @ C @ D )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_bool ) ) @ D @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__image__mem__iff_1) ).
thf(1486,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E )
| ~ ( c_in @ B @ C @ D )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_bool ) ) @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).
thf(9,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__asym_0) ).
thf(523,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(294,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
= ( c_Set_Oimage @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__is__image_1) ).
thf(1158,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
= ( c_Set_Oimage @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(117,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ C ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__less__iff__disj_2) ).
thf(762,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ C ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(492,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Finite__Set_Olinorder__class_OMin @ B @ A )
= C )
| ~ ( c_in @ C @ B @ A )
| ~ ( c_lessequals @ C @ ( c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMin__eqI__1__1 @ B @ C @ A ) @ A )
| ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Min__eqI_1) ).
thf(1608,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Finite__Set_Olinorder__class_OMin @ B @ A )
= C )
| ~ ( c_in @ C @ B @ A )
| ~ ( c_lessequals @ C @ ( c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMin__eqI__1__1 @ B @ C @ A ) @ A )
| ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).
thf(285,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ ( c_Hilbert__Choice_Oinv__into @ A @ B @ C @ D ) @ ( c_Set_Oimage @ B @ E @ C @ D ) @ D @ C )
= E )
| ~ ( c_lessequals @ E @ A @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ B @ A @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inv__into__image__cancel_0) ).
thf(1137,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ ( c_Hilbert__Choice_Oinv__into @ A @ B @ C @ D ) @ ( c_Set_Oimage @ B @ E @ C @ D ) @ D @ C )
= E )
| ~ ( c_lessequals @ E @ A @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ B @ A @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(361,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ ( c_SetInterval_Oord__class_OlessThan @ B @ A ) @ ( c_SetInterval_Oord__class_OlessThan @ C @ A ) @ ( tc_fun @ A @ tc_bool ) )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lessThan__subset__iff_1) ).
thf(1310,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ ( c_SetInterval_Oord__class_OlessThan @ B @ A ) @ ( c_SetInterval_Oord__class_OlessThan @ C @ A ) @ ( tc_fun @ A @ tc_bool ) )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(21,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_Orderings_Oord__class_Omax @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oless__supI2_0) ).
thf(550,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_Orderings_Oord__class_Omax @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(133,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( c_HOL_Ominus__class_Ominus @ B @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) ) @ C )
= B )
| ~ ( c_in @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff_0) ).
thf(797,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( c_HOL_Ominus__class_Ominus @ B @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) ) @ C )
= B )
| ~ ( c_in @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(346,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oimage @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D @ E )
= ( c_Set_Oinsert @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__insert_0) ).
thf(1275,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oimage @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D @ E )
= ( c_Set_Oinsert @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(321,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( c_in @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) @ D ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rangeI_0) ).
thf(1222,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( c_in @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) @ D ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(75,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_Finite__Set_Osetsum @ B @ ( c_HOL_Ominus__class_Ominus @ C @ D @ ( tc_fun @ E @ tc_bool ) ) @ E @ A )
= ( c_HOL_Ominus__class_Ominus @ ( c_Finite__Set_Osetsum @ B @ C @ E @ A ) @ ( c_Finite__Set_Osetsum @ B @ D @ E @ A ) @ A ) )
| ~ ( c_lessequals @ D @ C @ ( tc_fun @ E @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ C @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__diff_0) ).
thf(670,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_Finite__Set_Osetsum @ B @ ( c_HOL_Ominus__class_Ominus @ C @ D @ ( tc_fun @ E @ tc_bool ) ) @ E @ A )
= ( c_HOL_Ominus__class_Ominus @ ( c_Finite__Set_Osetsum @ B @ C @ E @ A ) @ ( c_Finite__Set_Osetsum @ B @ D @ E @ A ) @ A ) )
| ~ ( c_lessequals @ D @ C @ ( tc_fun @ E @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ C @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(339,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
!= ( hAPP @ A @ C ) )
| ~ ( c_in @ C @ D @ E )
| ~ ( c_in @ B @ D @ E )
| ~ ( c_Fun_Oinj__on @ A @ D @ E @ F )
| ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__def_0) ).
thf(1260,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
!= ( hAPP @ A @ C ) )
| ~ ( c_in @ C @ D @ E )
| ~ ( c_in @ B @ D @ E )
| ~ ( c_Fun_Oinj__on @ A @ D @ E @ F )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(87,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ A @ B ) @ C @ D )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__triv_0) ).
thf(698,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ A @ B ) @ C @ D )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(377,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_lessequals @ C @ B @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__le__not__le_2) ).
thf(1342,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_lessequals @ C @ B @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(110,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Set_Oinsert @ B @ C @ A ) ) @ ( c_Set_Oinsert @ B @ D @ A ) )
= ( c_Set_Oinsert @ B @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__inter__insert_0) ).
thf(747,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Set_Oinsert @ B @ C @ A ) ) @ ( c_Set_Oinsert @ B @ D @ A ) )
= ( c_Set_Oinsert @ B @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(15,axiom,
class_Orderings_Opreorder @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).
thf(538,plain,
class_Orderings_Opreorder @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(382,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ C ) @ D ) @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__inf__iff_2) ).
thf(1354,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ C ) @ D ) @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(225,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) @ A )
| ~ ( c_Finite__Set_Ofinite @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Int_1) ).
thf(1001,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) @ A )
| ~ ( c_Finite__Set_Ofinite @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(478,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ D ) @ C ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infE_1) ).
thf(1576,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ D ) @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).
thf(154,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ~ ( c_in @ A @ D @ C )
| ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__mp_0) ).
thf(841,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ~ ( c_in @ A @ D @ C )
| ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(384,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ B @ C @ A ) @ D @ A )
| ~ ( c_lessequals @ C @ D @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Osup__least_0) ).
thf(1359,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ B @ C @ A ) @ D @ A )
| ~ ( c_lessequals @ C @ D @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(28,axiom,
class_Lattices_Olattice @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Olattice) ).
thf(565,plain,
class_Lattices_Olattice @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(457,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ B @ C )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
| ( c_in @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Ononempty__iff_2) ).
thf(1529,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ B @ C )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
| ( c_in @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(331,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__left__idem_0) ).
thf(1243,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(281,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D )
| ( c_in @ A @ C @ D )
| ~ ( c_in @ A @ B @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__iff_2) ).
thf(1127,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D )
| ( c_in @ A @ C @ D )
| ~ ( c_in @ A @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(212,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( hAPP @ A @ B ) @ ( c_Inductive_Ocomplete__lattice__class_Ogfp @ C @ ( tc_fun @ D @ tc_bool ) ) @ D )
| ~ ( c_lessequals @ ( c_Set_Oimage @ A @ E @ F @ D ) @ ( hAPP @ C @ ( c_Set_Oimage @ A @ E @ F @ D ) ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_in @ B @ E @ F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_weak__coinduct__image_0) ).
thf(973,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( hAPP @ A @ B ) @ ( c_Inductive_Ocomplete__lattice__class_Ogfp @ C @ ( tc_fun @ D @ tc_bool ) ) @ D )
| ~ ( c_lessequals @ ( c_Set_Oimage @ A @ E @ F @ D ) @ ( hAPP @ C @ ( c_Set_Oimage @ A @ E @ F @ D ) ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_in @ B @ E @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(174,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ ( c_Orderings_Oord__class_Omax @ C @ B @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__maxI2_0) ).
thf(885,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ ( c_Orderings_Oord__class_Omax @ C @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(489,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ C )
| ~ ( c_Finite__Set_Ofinite @ A @ C )
| ~ ( c_Finite__Set_Ofinite @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Diff2_1) ).
thf(1601,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ C )
| ~ ( c_Finite__Set_Ofinite @ A @ C )
| ~ ( c_Finite__Set_Ofinite @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).
thf(395,axiom,
! [B: $i,A: $i] :
~ ( c_in @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__iff_0) ).
thf(1386,plain,
! [B: $i,A: $i] :
~ ( c_in @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(324,axiom,
! [C: $i,B: $i,A: $i] : ( c_in @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertI1_0) ).
thf(1228,plain,
! [C: $i,B: $i,A: $i] : ( c_in @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(436,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__Diff_0) ).
thf(1482,plain,
! [B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(336,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Oord @ A )
| ( c_lessequals @ ( hAPP @ B @ C ) @ ( hAPP @ D @ C ) @ A )
| ~ ( c_lessequals @ B @ D @ ( tc_fun @ E @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__funD_0) ).
thf(1254,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Oord @ A )
| ( c_lessequals @ ( hAPP @ B @ C ) @ ( hAPP @ D @ C ) @ A )
| ~ ( c_lessequals @ B @ D @ ( tc_fun @ E @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(100,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__insert_0) ).
thf(724,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(351,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
!= ( c_Set_Oinsert @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__not__insert_0) ).
thf(1287,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
!= ( c_Set_Oinsert @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(414,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D ) @ B @ E )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ E @ tc_bool ) ) @ ( c_Set_Oimage @ A @ C @ B @ E ) ) @ ( c_Set_Oimage @ A @ D @ B @ E ) ) )
| ~ ( c_lessequals @ D @ F @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_lessequals @ C @ F @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ A @ F @ B @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__image__Int_0) ).
thf(1430,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D ) @ B @ E )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ E @ tc_bool ) ) @ ( c_Set_Oimage @ A @ C @ B @ E ) ) @ ( c_Set_Oimage @ A @ D @ B @ E ) ) )
| ~ ( c_lessequals @ D @ F @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_lessequals @ C @ F @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ A @ F @ B @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(356,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Orderings_Oord__class_Omax @ B @ C @ A )
= C )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__iff__sup_0) ).
thf(1298,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Orderings_Oord__class_Omax @ B @ C @ A )
= C )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(128,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_in @ A @ D @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__rev__mp_0) ).
thf(785,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_in @ A @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(341,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ B @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_in @ A @ D @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_2) ).
thf(1264,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ B @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_in @ A @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(368,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D ) @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__greatest_0) ).
thf(1323,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D ) @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(135,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Set_Ovimage @ B @ C @ D @ E ) @ D )
| ~ ( c_in @ ( hAPP @ B @ A ) @ C @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__eq_1) ).
thf(802,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Set_Ovimage @ B @ C @ D @ E ) @ D )
| ~ ( c_in @ ( hAPP @ B @ A ) @ C @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(425,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__less_1) ).
thf(1455,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(308,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_lessequals @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__le_0) ).
thf(1191,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_lessequals @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(18,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( B = C )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv3_0) ).
thf(542,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( B = C )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(449,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Oinj__on @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E ) @ F @ D @ E )
| ( c_in @ C @ ( c_Set_Oimage @ A @ F @ D @ E ) @ E )
| ~ ( c_Fun_Oinj__on @ A @ F @ D @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__fun__updI_0) ).
thf(1511,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Oinj__on @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E ) @ F @ D @ E )
| ( c_in @ C @ ( c_Set_Oimage @ A @ F @ D @ E ) @ E )
| ~ ( c_Fun_Oinj__on @ A @ F @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).
thf(188,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Finite__Set_Olinorder__class_OMax @ ( c_Set_Oinsert @ B @ C @ A ) @ A )
= ( c_Orderings_Oord__class_Omax @ B @ ( c_Finite__Set_Olinorder__class_OMax @ C @ A ) @ A ) )
| ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Max__insert_0) ).
thf(917,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Finite__Set_Olinorder__class_OMax @ ( c_Set_Oinsert @ B @ C @ A ) @ A )
= ( c_Orderings_Oord__class_Omax @ B @ ( c_Finite__Set_Olinorder__class_OMax @ C @ A ) @ A ) )
| ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(89,axiom,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ A @ ( tc_fun @ C @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__subset_0) ).
thf(702,plain,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ A @ ( tc_fun @ C @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(112,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ A @ C @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_9) ).
thf(751,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ A @ C @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(363,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ( c_in @ D @ A @ C )
| ( c_in @ D @ B @ C )
| ~ ( c_HOL_Oord__class_Oless @ A @ ( c_Set_Oinsert @ D @ B @ C ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_2) ).
thf(1313,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ( c_in @ D @ A @ C )
| ( c_in @ D @ B @ C )
| ~ ( c_HOL_Oord__class_Oless @ A @ ( c_Set_Oinsert @ D @ B @ C ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(348,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Set_Oimage @ A @ B @ C @ D ) @ E @ ( tc_fun @ D @ tc_bool ) )
| ( c_in @ ( c_ATP__Linkup_Osko__Set__Ximage__subset__iff__1__1 @ B @ E @ A @ C @ D ) @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__subset__iff_1) ).
thf(1279,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Set_Oimage @ A @ B @ C @ D ) @ E @ ( tc_fun @ D @ tc_bool ) )
| ( c_in @ ( c_ATP__Linkup_Osko__Set__Ximage__subset__iff__1__1 @ B @ E @ A @ C @ D ) @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(428,axiom,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__idem_0) ).
thf(1462,plain,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(250,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ~ ( c_in @ ( hAPP @ D @ A ) @ ( c_Set_Oimage @ D @ B @ C @ E ) @ E )
| ~ ( c_Fun_Oinj__on @ D @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) @ C @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__image__mem__iff_0) ).
thf(1059,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ~ ( c_in @ ( hAPP @ D @ A ) @ ( c_Set_Oimage @ D @ B @ C @ E ) @ E )
| ~ ( c_Fun_Oinj__on @ D @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) @ C @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(283,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( B = C )
| ~ ( c_lessequals @ C @ B @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_2) ).
thf(1132,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( B = C )
| ~ ( c_lessequals @ C @ B @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(464,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_lessequals @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__leE_0) ).
thf(1545,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_lessequals @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(25,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_1) ).
thf(559,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(392,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E ) @ F @ D @ E )
= ( c_Set_Oinsert @ C @ ( c_Set_Oimage @ A @ ( c_HOL_Ominus__class_Ominus @ F @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ D @ E ) @ E ) )
| ~ ( c_in @ B @ F @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__image_0) ).
thf(1379,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E ) @ F @ D @ E )
= ( c_Set_Oinsert @ C @ ( c_Set_Oimage @ A @ ( c_HOL_Ominus__class_Ominus @ F @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ D @ E ) @ E ) )
| ~ ( c_in @ B @ F @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(289,axiom,
! [B: $i,A: $i] :
( ( class_Lattices_Olattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Olattice @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olattice) ).
thf(1147,plain,
! [B: $i,A: $i] :
( ( class_Lattices_Olattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Olattice @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(366,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_in @ B @ C @ D )
| ~ ( c_HOL_Oord__class_Oless @ A @ C @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_6) ).
thf(1319,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_in @ B @ C @ D )
| ~ ( c_HOL_Oord__class_Oless @ A @ C @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(435,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Finite__Set_Olinorder__class_OMax @ B @ A )
= C )
| ~ ( c_in @ C @ B @ A )
| ~ ( c_lessequals @ ( c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMax__eqI__1__1 @ B @ C @ A ) @ C @ A )
| ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Max__eqI_1) ).
thf(1479,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Finite__Set_Olinorder__class_OMax @ B @ A )
= C )
| ~ ( c_in @ C @ B @ A )
| ~ ( c_lessequals @ ( c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMax__eqI__1__1 @ B @ C @ A ) @ C @ A )
| ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(400,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ B )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__empty__left_0) ).
thf(1398,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ B )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(274,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Set_Ovimage @ B @ C @ D @ E ) @ D )
| ~ ( c_in @ ( hAPP @ B @ A ) @ C @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimageI_0) ).
thf(1115,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Set_Ovimage @ B @ C @ D @ E ) @ D )
| ~ ( c_in @ ( hAPP @ B @ A ) @ C @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(268,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ D ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ ( c_Orderings_Oord__class_Omax @ C @ D @ A ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Odistrib__inf__le_0) ).
thf(1100,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ D ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ ( c_Orderings_Oord__class_Omax @ C @ D @ A ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(326,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ~ ( c_in @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ C @ tc_bool ) ) @ B ) @ D ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntE_0) ).
thf(1232,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ~ ( c_in @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ C @ tc_bool ) ) @ B ) @ D ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(61,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ C ) @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__le2_0) ).
thf(638,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ C ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(160,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__left__commute_0) ).
thf(853,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(46,axiom,
class_Lattices_Olower__semilattice @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Olower__semilattice) ).
thf(606,plain,
class_Lattices_Olower__semilattice @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(476,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( c_in @ ( c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__induct__1__1 @ C @ A @ D ) @ ( c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__induct__1__2 @ C @ A @ D ) @ D )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) ) )
| ~ ( c_lessequals @ B @ C @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ B @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__subset__induct_2) ).
thf(1572,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( c_in @ ( c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__induct__1__1 @ C @ A @ D ) @ ( c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__induct__1__2 @ C @ A @ D ) @ D )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) ) )
| ~ ( c_lessequals @ B @ C @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).
thf(429,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__le_1) ).
thf(1465,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(130,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__commute_0) ).
thf(789,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(423,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Finite__Set_Olinorder__class_OMin @ B @ A )
= C )
| ~ ( c_in @ C @ B @ A )
| ( c_in @ ( c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMin__eqI__1__1 @ B @ C @ A ) @ B @ A )
| ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Min__eqI_0) ).
thf(1450,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Finite__Set_Olinorder__class_OMin @ B @ A )
= C )
| ~ ( c_in @ C @ B @ A )
| ( c_in @ ( c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMin__eqI__1__1 @ B @ C @ A ) @ B @ A )
| ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(40,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omax @ B @ C @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_max__less__iff__conj_2) ).
thf(591,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omax @ B @ C @ A ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(390,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
!= ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
| ( A = E )
| ( A = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_0) ).
thf(1373,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
!= ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
| ( A = E )
| ( A = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(242,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ( C = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I12_J_0) ).
thf(1040,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ( C = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(54,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Oinj__on @ A @ ( c_Set_Oimage @ B @ C @ D @ D ) @ D @ E )
| ~ ( c_Fun_Oinj__on @ A @ C @ D @ E )
| ~ ( c_Fun_Oinj__on @ B @ C @ D @ D )
| ( c_in @ ( c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__1 @ C @ B @ A @ D @ E ) @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__image__iff_1) ).
thf(623,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Oinj__on @ A @ ( c_Set_Oimage @ B @ C @ D @ D ) @ D @ E )
| ~ ( c_Fun_Oinj__on @ A @ C @ D @ E )
| ~ ( c_Fun_Oinj__on @ B @ C @ D @ D )
| ( c_in @ ( c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__1 @ C @ B @ A @ D @ E ) @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(291,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Set_Oimage @ A @ ( c_Set_Ovimage @ A @ B @ C @ D ) @ C @ D ) @ B @ ( tc_fun @ D @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__vimage__subset_0) ).
thf(1151,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Set_Oimage @ A @ ( c_Set_Ovimage @ A @ B @ C @ D ) @ C @ D ) @ B @ ( tc_fun @ D @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(137,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__le1_0) ).
thf(806,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(247,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ A @ B @ C @ C )
= B )
| ~ ( c_Fun_Oinj__on @ A @ B @ C @ C )
| ~ ( c_lessequals @ ( c_Set_Oimage @ A @ B @ C @ C ) @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_endo__inj__surj_0) ).
thf(1051,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ A @ B @ C @ C )
= B )
| ~ ( c_Fun_Oinj__on @ A @ B @ C @ C )
| ~ ( c_lessequals @ ( c_Set_Oimage @ A @ B @ C @ C ) @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(234,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Oinj__on @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E )
| ~ ( c_Fun_Oinj__on @ A @ B @ D @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__diff_0) ).
thf(1020,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Oinj__on @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E )
| ~ ( c_Fun_Oinj__on @ A @ B @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(32,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__asym_H_0) ).
thf(574,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(119,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Oinj__on @ ( c_Fun_Othe__inv__into @ A @ B @ C @ D ) @ ( c_Set_Oimage @ B @ A @ C @ D ) @ D @ C )
| ~ ( c_Fun_Oinj__on @ B @ A @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__the__inv__into_0) ).
thf(766,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Oinj__on @ ( c_Fun_Othe__inv__into @ A @ B @ C @ D ) @ ( c_Set_Oimage @ B @ A @ C @ D ) @ D @ C )
| ~ ( c_Fun_Oinj__on @ B @ A @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(59,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( c_in @ ( hAPP @ D @ A ) @ ( c_Set_Oimage @ D @ B @ C @ E ) @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__iff_2) ).
thf(634,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( c_in @ ( hAPP @ D @ A ) @ ( c_Set_Oimage @ D @ B @ C @ E ) @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(104,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ A @ C @ ( tc_fun @ B @ tc_bool ) ) @ B )
| ~ ( c_Finite__Set_Ofinite @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Diff2_0) ).
thf(734,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ A @ C @ ( tc_fun @ B @ tc_bool ) ) @ B )
| ~ ( c_Finite__Set_Ofinite @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(422,axiom,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ ( c_Orderings_Otop__class_Otop @ A ) ) @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__top__left_0) ).
thf(1447,plain,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ ( c_Orderings_Otop__class_Otop @ A ) ) @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(456,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__neq__le__trans_0) ).
thf(1526,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).
thf(381,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C )
!= ( c_Orderings_Otop__class_Otop @ A ) )
| ( B
= ( c_Orderings_Otop__class_Otop @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__eq__top__eq1_0) ).
thf(1351,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C )
!= ( c_Orderings_Otop__class_Otop @ A ) )
| ( B
= ( c_Orderings_Otop__class_Otop @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(71,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
!= ( hAPP @ A @ C ) )
| ~ ( c_in @ C @ D @ E )
| ~ ( c_in @ B @ D @ E )
| ( B = C )
| ~ ( c_Fun_Oinj__on @ A @ D @ E @ F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__contraD_0) ).
thf(660,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
!= ( hAPP @ A @ C ) )
| ~ ( c_in @ C @ D @ E )
| ~ ( c_in @ B @ D @ E )
| ( B = C )
| ~ ( c_Fun_Oinj__on @ A @ D @ E @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(223,axiom,
class_Orderings_Opreorder @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Opreorder) ).
thf(998,plain,
class_Orderings_Opreorder @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(415,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ C ) @ ( tc_fun @ A @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) @ D @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Int2_0) ).
thf(1433,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ C ) @ ( tc_fun @ A @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) @ D @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(2,negated_conjecture,
( v_G
= ( c_Set_Oimage @ v_mgt__call @ v_U @ tc_Com_Opname @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(507,plain,
( v_G
= ( c_Set_Oimage @ v_mgt__call @ v_U @ tc_Com_Opname @ t_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(276,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring @ A )
| ( ( c_Finite__Set_Osetsum @ B @ ( c_HOL_Ominus__class_Ominus @ C @ ( c_Set_Oinsert @ D @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_bool ) ) @ E ) @ ( tc_fun @ E @ tc_bool ) ) @ E @ A )
= ( c_HOL_Ominus__class_Ominus @ ( c_Finite__Set_Osetsum @ B @ C @ E @ A ) @ ( hAPP @ B @ D ) @ A ) )
| ~ ( c_in @ D @ C @ E )
| ~ ( c_Finite__Set_Ofinite @ C @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__diff1__ring_0) ).
thf(1119,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oring @ A )
| ( ( c_Finite__Set_Osetsum @ B @ ( c_HOL_Ominus__class_Ominus @ C @ ( c_Set_Oinsert @ D @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_bool ) ) @ E ) @ ( tc_fun @ E @ tc_bool ) ) @ E @ A )
= ( c_HOL_Ominus__class_Ominus @ ( c_Finite__Set_Osetsum @ B @ C @ E @ A ) @ ( hAPP @ B @ D ) @ A ) )
| ~ ( c_in @ D @ C @ E )
| ~ ( c_Finite__Set_Ofinite @ C @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(497,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ ( c_Set_Oinsert @ D @ B @ C ) @ ( tc_fun @ C @ tc_bool ) )
| ( c_in @ D @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert_0) ).
thf(1622,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ ( c_Set_Oinsert @ D @ B @ C ) @ ( tc_fun @ C @ tc_bool ) )
| ( c_in @ D @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).
thf(189,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) @ D @ ( tc_fun @ A @ tc_bool ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_HOL_Ominus__class_Ominus @ C @ D @ ( tc_fun @ A @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Diff_0) ).
thf(920,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) @ D @ ( tc_fun @ A @ tc_bool ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_HOL_Ominus__class_Ominus @ C @ D @ ( tc_fun @ A @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(5,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_HOL_Oord__class_Oless @ C @ B @ A )
| ( C = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE_0) ).
thf(512,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_HOL_Oord__class_Oless @ C @ B @ A )
| ( C = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(78,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_lessequals @ D @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le__trans_0) ).
thf(678,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_lessequals @ D @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(191,axiom,
! [B: $i,A: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot1E_0) ).
thf(925,plain,
! [B: $i,A: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(359,axiom,
! [B: $i,A: $i] :
( ( class_Orderings_Oorder @ ( tc_fun @ A @ B ) )
| ~ ( class_Orderings_Oorder @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Oorder) ).
thf(1306,plain,
! [B: $i,A: $i] :
( ( class_Orderings_Oorder @ ( tc_fun @ A @ B ) )
| ~ ( class_Orderings_Oorder @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(139,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ B @ C )
| ( ( hAPP @ ( c_Hilbert__Choice_Oinv__into @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ A @ B @ C ) @ ( hAPP @ A @ D ) )
= D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inv__f__eq_0) ).
thf(810,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ B @ C )
| ( ( hAPP @ ( c_Hilbert__Choice_Oinv__into @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ A @ B @ C ) @ ( hAPP @ A @ D ) )
= D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(375,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Set_Ovimage @ A @ B @ C @ D ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ B @ ( hAPP @ A @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__code_1) ).
thf(1338,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Set_Ovimage @ A @ B @ C @ D ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ B @ ( hAPP @ A @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(95,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ C @ D ) )
| ~ ( hBOOL @ ( hAPP @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1I_0) ).
thf(714,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ C @ D ) )
| ~ ( hBOOL @ ( hAPP @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(503,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oimage @ A @ B @ C @ D ) @ ( c_Set_Oimage @ A @ E @ C @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ ( c_Set_Oimage @ A @ ( c_HOL_Ominus__class_Ominus @ B @ E @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) @ ( tc_fun @ D @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__diff__subset_0) ).
thf(1636,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oimage @ A @ B @ C @ D ) @ ( c_Set_Oimage @ A @ E @ C @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ ( c_Set_Oimage @ A @ ( c_HOL_Ominus__class_Ominus @ B @ E @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) @ ( tc_fun @ D @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).
thf(245,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ D ) @ C ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__infE_1) ).
thf(1047,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ D ) @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(296,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofold__graph @ A @ B @ C @ ( hAPP @ ( hAPP @ A @ D ) @ E ) @ F @ G )
| ~ ( c_in @ D @ C @ F )
| ~ ( c_Finite__Set_Ofold__graph @ A @ B @ ( c_HOL_Ominus__class_Ominus @ C @ ( c_Set_Oinsert @ D @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ F @ tc_bool ) ) @ F ) @ ( tc_fun @ F @ tc_bool ) ) @ E @ F @ G ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff1__fold__graph_0) ).
thf(1163,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofold__graph @ A @ B @ C @ ( hAPP @ ( hAPP @ A @ D ) @ E ) @ F @ G )
| ~ ( c_in @ D @ C @ F )
| ~ ( c_Finite__Set_Ofold__graph @ A @ B @ ( c_HOL_Ominus__class_Ominus @ C @ ( c_Set_Oinsert @ D @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ F @ tc_bool ) ) @ F ) @ ( tc_fun @ F @ tc_bool ) ) @ E @ F @ G ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(264,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__assoc_0) ).
thf(1091,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(125,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__infI2_0) ).
thf(778,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(480,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ ( c_HOL_Ominus__class_Ominus @ C @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ D @ E ) @ E )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__insert_1) ).
thf(1580,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ ( c_HOL_Ominus__class_Ominus @ C @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ D @ E ) @ E )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).
thf(278,axiom,
class_Lattices_Olower__semilattice @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olower__semilattice) ).
thf(1123,plain,
class_Lattices_Olower__semilattice @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(319,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_in @ B @ A @ D )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__single__insert_0) ).
thf(1217,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_in @ B @ A @ D )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(143,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__commute_0) ).
thf(820,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(26,axiom,
class_Orderings_Olinorder @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
thf(561,plain,
class_Orderings_Olinorder @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(389,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( c_Finite__Set_Ofold__graph @ C @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ A @ D @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__fold__graphE_0) ).
thf(1370,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( c_Finite__Set_Ofold__graph @ C @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ A @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(102,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( c_in @ ( hAPP @ D @ A ) @ ( c_Set_Oimage @ D @ B @ C @ E ) @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__image__eqI_0) ).
thf(729,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( c_in @ ( hAPP @ D @ A ) @ ( c_Set_Oimage @ D @ B @ C @ E ) @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(329,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ ( c_Orderings_Oord__class_Omax @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__max__iff__disj_2) ).
thf(1238,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ ( c_Orderings_Oord__class_Omax @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(471,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E )
| ~ ( c_in @ B @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__eqI_0) ).
thf(1560,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E )
| ~ ( c_in @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
thf(205,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C )
= C )
| ~ ( c_lessequals @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__absorb2_0) ).
thf(957,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C )
= C )
| ~ ( c_lessequals @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(322,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ~ ( c_Fun_Oinj__on @ D @ B @ C @ E )
| ( ( hAPP @ ( c_Hilbert__Choice_Oinv__into @ B @ D @ C @ E ) @ ( hAPP @ D @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inv__into__f__eq_0) ).
thf(1223,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ~ ( c_Fun_Oinj__on @ D @ B @ C @ E )
| ( ( hAPP @ ( c_Hilbert__Choice_Oinv__into @ B @ D @ C @ E ) @ ( hAPP @ D @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(178,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ( c_in @ D @ A @ C )
| ~ ( c_lessequals @ A @ ( c_Set_Oinsert @ D @ B @ C ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_1) ).
thf(894,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ( c_in @ D @ A @ C )
| ~ ( c_lessequals @ A @ ( c_Set_Oinsert @ D @ B @ C ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(85,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__idem_0) ).
thf(693,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(57,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__imp__le_0) ).
thf(630,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(411,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Set_Oimage @ A @ B @ C @ D ) @ E @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_in @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Set__Ximage__subsetI__1__1 @ B @ E @ A @ C @ D ) ) @ E @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__subsetI_1) ).
thf(1423,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Set_Oimage @ A @ B @ C @ D ) @ E @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_in @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Set__Ximage__subsetI__1__1 @ B @ E @ A @ C @ D ) ) @ E @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(29,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
!= ( c_HOL_Ominus__class_Ominus @ D @ E @ A ) )
| ( c_HOL_Oord__class_Oless @ D @ E @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eqI_0) ).
thf(566,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
!= ( c_HOL_Ominus__class_Ominus @ D @ E @ A ) )
| ( c_HOL_Oord__class_Oless @ D @ E @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(387,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Finite__Set_Ocard @ ( c_Set_Oimage @ A @ B @ C @ D ) @ D )
= ( c_Finite__Set_Ocard @ B @ C ) )
| ~ ( c_Fun_Oinj__on @ A @ B @ C @ D )
| ~ ( c_Finite__Set_Ofinite @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__iff__eq__card_0) ).
thf(1365,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Finite__Set_Ocard @ ( c_Set_Oimage @ A @ B @ C @ D ) @ D )
= ( c_Finite__Set_Ocard @ B @ C ) )
| ~ ( c_Fun_Oinj__on @ A @ B @ C @ D )
| ~ ( c_Finite__Set_Ofinite @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(55,axiom,
! [A: $i] :
( ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UNIV__not__empty_0) ).
thf(625,plain,
! [A: $i] :
( ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(469,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( B = C )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_0) ).
thf(1555,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( B = C )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).
thf(302,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( c_lessequals @ B @ A @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equalityI_0) ).
thf(1178,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( c_lessequals @ B @ A @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(426,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ ( hAPP @ B @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Set_Ovimage @ B @ A @ D @ E ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__code_0) ).
thf(1457,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ ( hAPP @ B @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Set_Ovimage @ B @ A @ D @ E ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(498,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofold__graph @ A @ B @ ( c_Set_Oinsert @ C @ D @ E ) @ ( hAPP @ ( hAPP @ A @ C ) @ F ) @ E @ G )
| ~ ( c_Finite__Set_Ofold__graph @ A @ B @ D @ F @ E @ G )
| ( c_in @ C @ D @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold__graph_OinsertI_0) ).
thf(1624,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofold__graph @ A @ B @ ( c_Set_Oinsert @ C @ D @ E ) @ ( hAPP @ ( hAPP @ A @ C ) @ F ) @ E @ G )
| ~ ( c_Finite__Set_Ofold__graph @ A @ B @ D @ F @ E @ G )
| ( c_in @ C @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).
thf(316,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Set_Oinsert @ D @ A @ C ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_1) ).
thf(1210,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Set_Oinsert @ D @ A @ C ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(115,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ C ) @ D @ A )
= ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ ( c_HOL_Ominus__class_Ominus @ B @ D @ A ) ) @ ( c_HOL_Ominus__class_Ominus @ C @ D @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__diff__distrib__left_0) ).
thf(757,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ C ) @ D @ A )
= ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ ( c_HOL_Ominus__class_Ominus @ B @ D @ A ) ) @ ( c_HOL_Ominus__class_Ominus @ C @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(349,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E ) @ F )
= ( hAPP @ A @ F ) )
| ( F = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__other_0) ).
thf(1281,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E ) @ F )
= ( hAPP @ A @ F ) )
| ( F = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(93,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ~ ( c_in @ A @ ( c_HOL_Ominus__class_Ominus @ D @ B @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DiffE_1) ).
thf(710,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ~ ( c_in @ A @ ( c_HOL_Ominus__class_Ominus @ D @ B @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(231,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E ) @ F @ D @ E )
= ( c_Set_Oimage @ A @ F @ D @ E ) )
| ( c_in @ B @ F @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__image_1) ).
thf(1012,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E ) @ F @ D @ E )
= ( c_Set_Oimage @ A @ F @ D @ E ) )
| ( c_in @ B @ F @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(355,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ A @ B ) @ C @ D )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__idem_0) ).
thf(1296,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ A @ B ) @ C @ D )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(73,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ A @ B @ C @ D )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) )
| ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__is__empty_0) ).
thf(665,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ A @ B @ C @ D )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) )
| ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(37,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Orderings_Oord__class_Omax @ ( c_Orderings_Oord__class_Omax @ B @ C @ A ) @ D @ A )
= ( c_Orderings_Oord__class_Omax @ B @ ( c_Orderings_Oord__class_Omax @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Osup__assoc_0) ).
thf(583,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Orderings_Oord__class_Omax @ ( c_Orderings_Oord__class_Omax @ B @ C @ A ) @ D @ A )
= ( c_Orderings_Oord__class_Omax @ B @ ( c_Orderings_Oord__class_Omax @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(148,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) @ D @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infI1_0) ).
thf(830,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) @ D @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(258,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( c_in @ A @ ( c_Set_Ovimage @ B @ ( c_Set_Oinsert @ ( hAPP @ B @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ D @ C ) @ D ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__singleton__eq_1) ).
thf(1079,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( c_in @ A @ ( c_Set_Ovimage @ B @ ( c_Set_Oinsert @ ( hAPP @ B @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ D @ C ) @ D ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(237,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E )
!= A )
| ( ( hAPP @ A @ B )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__idem__iff_0) ).
thf(1027,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E )
!= A )
| ( ( hAPP @ A @ B )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(80,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Obot @ A )
| ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ A ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot__least_0) ).
thf(682,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Obot @ A )
| ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(310,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Orderings_Oord__class_Omax @ B @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ C ) @ D ) @ A )
= ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ ( c_Orderings_Oord__class_Omax @ B @ C @ A ) ) @ ( c_Orderings_Oord__class_Omax @ B @ D @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Osup__inf__distrib1_0) ).
thf(1195,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Orderings_Oord__class_Omax @ B @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ C ) @ D ) @ A )
= ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ ( c_Orderings_Oord__class_Omax @ B @ C @ A ) ) @ ( c_Orderings_Oord__class_Omax @ B @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(404,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
!= ( c_HOL_Ominus__class_Ominus @ D @ E @ A ) )
| ( c_lessequals @ C @ B @ A )
| ~ ( c_lessequals @ E @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__eqI_1) ).
thf(1407,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
!= ( c_HOL_Ominus__class_Ominus @ D @ E @ A ) )
| ( c_lessequals @ C @ B @ A )
| ~ ( c_lessequals @ E @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(402,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ ( c_Finite__Set_Olinorder__class_OMax @ C @ A ) @ A )
| ~ ( c_in @ B @ C @ A )
| ~ ( c_Finite__Set_Ofinite @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Max__ge_0) ).
thf(1402,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ ( c_Finite__Set_Olinorder__class_OMax @ C @ A ) @ A )
| ~ ( c_in @ B @ C @ A )
| ~ ( c_Finite__Set_Ofinite @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(108,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_in @ D @ B @ C )
| ~ ( c_HOL_Oord__class_Oless @ A @ ( c_Set_Oinsert @ D @ B @ C ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_0) ).
thf(742,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_in @ D @ B @ C )
| ~ ( c_HOL_Oord__class_Oless @ A @ ( c_Set_Oinsert @ D @ B @ C ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(344,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Ovimage @ ( c_COMBK @ A @ B @ C ) @ D @ C @ B )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) )
| ~ ( c_in @ A @ D @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__const_0) ).
thf(1270,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Ovimage @ ( c_COMBK @ A @ B @ C ) @ D @ C @ B )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) )
| ~ ( c_in @ A @ D @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(202,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__left__commute_0) ).
thf(948,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(51,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ A @ B @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_2) ).
thf(615,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ A @ B @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(370,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ C )
= B )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__iff__inf_0) ).
thf(1328,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ C )
= B )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(252,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ E ) @ ( tc_fun @ A @ tc_bool ) )
| ~ ( c_lessequals @ C @ E @ ( tc_fun @ A @ tc_bool ) )
| ~ ( c_lessequals @ B @ D @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__mono_0) ).
thf(1064,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ D ) @ E ) @ ( tc_fun @ A @ tc_bool ) )
| ~ ( c_lessequals @ C @ E @ ( tc_fun @ A @ tc_bool ) )
| ~ ( c_lessequals @ B @ D @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(443,axiom,
! [B: $i,A: $i] :
( ( class_Finite__Set_Ofinite_Ofinite @ ( tc_fun @ A @ B ) )
| ~ ( class_Finite__Set_Ofinite_Ofinite @ B )
| ~ ( class_Finite__Set_Ofinite_Ofinite @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Finite__Set_Ofinite_Ofinite) ).
thf(1498,plain,
! [B: $i,A: $i] :
( ( class_Finite__Set_Ofinite_Ofinite @ ( tc_fun @ A @ B ) )
| ~ ( class_Finite__Set_Ofinite_Ofinite @ B )
| ~ ( class_Finite__Set_Ofinite_Ofinite @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(412,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ ( c_Orderings_Oord__class_Omax @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__supI2_0) ).
thf(1425,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ ( c_Orderings_Oord__class_Omax @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(266,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ B @ D @ A ) @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__sup__iff_0) ).
thf(1096,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ B @ D @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(227,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
= ( c_Set_Oinsert @ B @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_4) ).
thf(1006,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
= ( c_Set_Oinsert @ B @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(41,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_Orderings_Oord__class_Omax @ B @ C @ A ) @ D @ A )
= ( c_Orderings_Oord__class_Omax @ ( c_HOL_Ominus__class_Ominus @ B @ D @ A ) @ ( c_HOL_Ominus__class_Ominus @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_max__diff__distrib__left_0) ).
thf(593,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_Orderings_Oord__class_Omax @ B @ C @ A ) @ D @ A )
= ( c_Orderings_Oord__class_Omax @ ( c_HOL_Ominus__class_Ominus @ B @ D @ A ) @ ( c_HOL_Ominus__class_Ominus @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(167,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Set_Oimage @ A @ B @ C @ D ) @ E @ ( tc_fun @ D @ tc_bool ) )
| ( c_in @ ( c_ATP__Linkup_Osko__Set__Ximage__subsetI__1__1 @ B @ E @ A @ C @ D ) @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__subsetI_0) ).
thf(869,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Set_Oimage @ A @ B @ C @ D ) @ E @ ( tc_fun @ D @ tc_bool ) )
| ( c_in @ ( c_ATP__Linkup_Osko__Set__Ximage__subsetI__1__1 @ B @ E @ A @ C @ D ) @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(127,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Ovimage @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ C @ B )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__empty_0) ).
thf(783,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Ovimage @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ C @ B )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(263,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Oinj__on @ A @ B @ C @ D )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Set_Oimage @ E @ B @ C @ C ) @ C @ D )
| ~ ( c_Fun_Oinj__on @ E @ B @ C @ C )
| ( c_in @ ( c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__1 @ B @ E @ A @ C @ D ) @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__image__iff_0) ).
thf(1089,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Oinj__on @ A @ B @ C @ D )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Set_Oimage @ E @ B @ C @ C ) @ C @ D )
| ~ ( c_Fun_Oinj__on @ E @ B @ C @ C )
| ( c_in @ ( c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__1 @ B @ E @ A @ C @ D ) @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(327,axiom,
! [B: $i,A: $i] :
( ~ ( class_Finite__Set_Ofinite_Ofinite @ A )
| ( c_Finite__Set_Ofinite @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite_0) ).
thf(1234,plain,
! [B: $i,A: $i] :
( ~ ( class_Finite__Set_Ofinite_Ofinite @ A )
| ( c_Finite__Set_Ofinite @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(462,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Hilbert__Choice_Oinv__into @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ B @ A @ C ) @ ( hAPP @ B @ D ) )
= D )
| ~ ( c_Fun_Oinj__on @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inv__f__f_0) ).
thf(1541,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Hilbert__Choice_Oinv__into @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ B @ A @ C ) @ ( hAPP @ B @ D ) )
= D )
| ~ ( c_Fun_Oinj__on @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).
thf(169,axiom,
class_Orderings_Obot @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Obot) ).
thf(874,plain,
class_Orderings_Obot @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(287,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( hAPP @ A @ B ) @ C @ D )
| ~ ( c_in @ B @ ( c_Set_Ovimage @ A @ C @ E @ D ) @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimageD_0) ).
thf(1143,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( hAPP @ A @ B ) @ C @ D )
| ~ ( c_in @ B @ ( c_Set_Ovimage @ A @ C @ E @ D ) @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(459,axiom,
! [B: $i,A: $i] :
~ ( c_HOL_Oord__class_Oless @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__psubset__empty_0) ).
thf(1534,plain,
! [B: $i,A: $i] :
~ ( c_HOL_Oord__class_Oless @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(233,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__left__idem_0) ).
thf(1017,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(474,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ~ ( c_lessequals @ ( c_Set_Oinsert @ A @ D @ C ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_0) ).
thf(1567,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ~ ( c_lessequals @ ( c_Set_Oinsert @ A @ D @ C ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(295,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ C )
!= B )
| ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__iff__inf_1) ).
thf(1160,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ C )
!= B )
| ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(260,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__left__commute_0) ).
thf(1082,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(385,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Inductive_Ocomplete__lattice__class_Ogfp @ B @ ( tc_fun @ C @ tc_bool ) ) @ C )
| ~ ( c_lessequals @ D @ ( hAPP @ B @ D ) @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_in @ A @ D @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_weak__coinduct_0) ).
thf(1361,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Inductive_Ocomplete__lattice__class_Ogfp @ B @ ( tc_fun @ C @ tc_bool ) ) @ C )
| ~ ( c_lessequals @ D @ ( hAPP @ B @ D ) @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_in @ A @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(353,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( B = C )
| ~ ( c_lessequals @ B @ C @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_0) ).
thf(1292,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( B = C )
| ~ ( c_lessequals @ B @ C @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(304,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ C )
| ~ ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ D @ B @ C ) @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Diff__insert_0) ).
thf(1182,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ C )
| ~ ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ D @ B @ C ) @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(63,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C )
= C )
| ~ ( c_lessequals @ C @ B @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__absorb1_0) ).
thf(642,plain,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C )
= C )
| ~ ( c_lessequals @ C @ B @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(408,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ B @ C )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__not__empty_0) ).
thf(1414,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ B @ C )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(318,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Finite__Set_Ocard @ A @ B )
= ( c_Finite__Set_Ocard @ C @ D ) )
| ~ ( c_Finite__Set_Ofinite @ C @ D )
| ~ ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_lessequals @ ( c_Set_Oimage @ E @ C @ D @ B ) @ A @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ E @ C @ D @ B )
| ~ ( c_lessequals @ ( c_Set_Oimage @ F @ A @ B @ D ) @ C @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ F @ A @ B @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__bij__eq_0) ).
thf(1214,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Finite__Set_Ocard @ A @ B )
= ( c_Finite__Set_Ocard @ C @ D ) )
| ~ ( c_Finite__Set_Ofinite @ C @ D )
| ~ ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_lessequals @ ( c_Set_Oimage @ E @ C @ D @ B ) @ A @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ E @ C @ D @ B )
| ~ ( c_lessequals @ ( c_Set_Oimage @ F @ A @ B @ D ) @ C @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ F @ A @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(315,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ ( c_COMBK @ A @ B @ C ) @ D @ C @ B )
= ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) )
| ( D
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__constant__conv_1) ).
thf(1207,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ ( c_COMBK @ A @ B @ C ) @ D @ C @ B )
= ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) )
| ( D
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(210,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ C ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__less__iff__disj_1) ).
thf(970,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ C ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(293,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( B = C )
| ~ ( c_lessequals @ C @ B @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__antisym_0) ).
thf(1155,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( B = C )
| ~ ( c_lessequals @ C @ B @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(23,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Ofun__upd @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E ) @ B @ F @ D @ E )
= ( c_Fun_Ofun__upd @ A @ B @ F @ D @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__upd_0) ).
thf(554,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Ofun__upd @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E ) @ B @ F @ D @ E )
= ( c_Fun_Ofun__upd @ A @ B @ F @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(113,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E )
| ~ ( c_in @ B @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_imageI_0) ).
thf(753,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E )
| ~ ( c_in @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(181,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_in @ ( c_Finite__Set_Olinorder__class_OMax @ B @ A ) @ B @ A )
| ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Max__in_0) ).
thf(901,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_in @ ( c_Finite__Set_Olinorder__class_OMax @ B @ A ) @ B @ A )
| ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(82,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D )
| ( c_in @ A @ C @ D )
| ~ ( c_in @ A @ B @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DiffI_0) ).
thf(686,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D )
| ( c_in @ A @ C @ D )
| ~ ( c_in @ A @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(152,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ B ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__subset__iff_1) ).
thf(837,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ B ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(483,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C )
= B )
| ~ ( c_lessequals @ B @ C @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__absorb2_0) ).
thf(1588,plain,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C )
= B )
| ~ ( c_lessequals @ B @ C @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).
thf(6,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_HOL_Oord__class_Oless @ C @ B @ A )
| ( C = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE__ordered__idom_0) ).
thf(515,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Ring__and__Field_Oordered__idom @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_HOL_Oord__class_Oless @ C @ B @ A )
| ( C = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(106,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1 @ A @ B @ C @ D @ E ) @ D )
| ~ ( c_lessequals @ B @ ( c_Set_Oimage @ C @ A @ D @ E ) @ ( tc_fun @ E @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ B @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__subset__image_1) ).
thf(738,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1 @ A @ B @ C @ D @ E ) @ D )
| ~ ( c_lessequals @ B @ ( c_Set_Oimage @ C @ A @ D @ E ) @ ( tc_fun @ E @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ B @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(393,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( hAPP @ A @ B ) @ C @ D )
| ~ ( c_in @ B @ ( c_Set_Ovimage @ A @ C @ E @ D ) @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimageE_0) ).
thf(1382,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( hAPP @ A @ B ) @ C @ D )
| ~ ( c_in @ B @ ( c_Set_Ovimage @ A @ C @ E @ D ) @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(342,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ C ) @ D ) @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__greatest_0) ).
thf(1266,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ C ) @ D ) @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(68,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ B )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__absorb_0) ).
thf(654,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(30,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Orderings_Oord__class_Omax @ B @ ( c_Orderings_Oord__class_Omax @ C @ D @ A ) @ A )
= ( c_Orderings_Oord__class_Omax @ C @ ( c_Orderings_Oord__class_Omax @ B @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Osup__left__commute_0) ).
thf(569,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Orderings_Oord__class_Omax @ B @ ( c_Orderings_Oord__class_Omax @ C @ D @ A ) @ A )
= ( c_Orderings_Oord__class_Omax @ C @ ( c_Orderings_Oord__class_Omax @ B @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(398,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__le__not__le_1) ).
thf(1393,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ~ ( c_lessequals @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(455,axiom,
! [B: $i,A: $i] : ( c_lessequals @ A @ A @ ( tc_fun @ B @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__refl_0) ).
thf(1525,plain,
! [B: $i,A: $i] : ( c_lessequals @ A @ A @ ( tc_fun @ B @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(65,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Oord @ A )
| ( c_in @ B @ ( c_SetInterval_Oord__class_OlessThan @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lessThan__iff_1) ).
thf(647,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Oord @ A )
| ( c_in @ B @ ( c_SetInterval_Oord__class_OlessThan @ C @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(340,axiom,
! [B: $i,A: $i] : ( c_lessequals @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__UNIV_0) ).
thf(1263,plain,
! [B: $i,A: $i] : ( c_lessequals @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(217,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ ( c_Orderings_Oord__class_Omax @ B @ C @ A ) ) @ D )
= ( c_Orderings_Oord__class_Omax @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ C ) @ D ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__sup__distrib2_0) ).
thf(984,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ ( c_Orderings_Oord__class_Omax @ B @ C @ A ) ) @ D )
= ( c_Orderings_Oord__class_Omax @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ C ) @ D ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(185,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Orderings_Oord__class_Omax @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ C ) @ D @ A )
= ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ ( c_Orderings_Oord__class_Omax @ B @ D @ A ) ) @ ( c_Orderings_Oord__class_Omax @ C @ D @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Osup__inf__distrib2_0) ).
thf(911,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Orderings_Oord__class_Omax @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ C ) @ D @ A )
= ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ ( c_Orderings_Oord__class_Omax @ B @ D @ A ) ) @ ( c_Orderings_Oord__class_Omax @ C @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(488,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__eq_0) ).
thf(1599,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).
thf(332,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ ( c_Orderings_Oord__class_Omax @ B @ C @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__maxI1_0) ).
thf(1246,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ ( c_Orderings_Oord__class_Omax @ B @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(372,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ ( c_Finite__Set_Olinorder__class_OMin @ B @ A ) @ C @ A )
| ~ ( c_in @ C @ B @ A )
| ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Min__le_0) ).
thf(1333,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ ( c_Finite__Set_Olinorder__class_OMin @ B @ A ) @ C @ A )
| ~ ( c_in @ C @ B @ A )
| ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(131,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ~ ( hBOOL @ ( hAPP @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_1) ).
thf(792,plain,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ~ ( hBOOL @ ( hAPP @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(3,negated_conjecture,
c_in @ v_pn @ v_U @ tc_Com_Opname,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(508,plain,
c_in @ v_pn @ v_U @ tc_Com_Opname,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(17,axiom,
class_Orderings_Obot @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Obot) ).
thf(541,plain,
class_Orderings_Obot @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(248,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Set_Oinsert @ A @ B @ C ) @ C )
| ~ ( c_Finite__Set_Ofinite @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__insert_1) ).
thf(1054,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Set_Oinsert @ A @ B @ C ) @ C )
| ~ ( c_Finite__Set_Ofinite @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(299,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__finite__subset_0) ).
thf(1170,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(255,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ A @ tc_bool ) ) ) @ D )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Int__distrib2_0) ).
thf(1071,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ A @ tc_bool ) ) ) @ D )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(451,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( c_in @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bex__empty_0) ).
thf(1515,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( c_in @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).
thf(12,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_Orderings_Oord__class_Omax @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__max__iff__disj_2) ).
thf(530,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_Orderings_Oord__class_Omax @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(97,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_in @ B @ A @ C )
| ( c_in @ B @ D @ C )
| ~ ( c_HOL_Oord__class_Oless @ A @ ( c_Set_Oinsert @ B @ D @ C ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_1) ).
thf(718,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_in @ B @ A @ C )
| ( c_in @ B @ D @ C )
| ~ ( c_HOL_Oord__class_Oless @ A @ ( c_Set_Oinsert @ B @ D @ C ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(262,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( c_lessequals @ B @ A @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__eq__subset_2) ).
thf(1086,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( c_lessequals @ B @ A @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(197,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_Finite__Set_Ofinite @ C @ B )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__subset_0) ).
thf(938,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_Finite__Set_Ofinite @ C @ B )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(123,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ A @ B ) @ C @ D )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__idem__iff_1) ).
thf(773,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Ofun__upd @ A @ B @ ( hAPP @ A @ B ) @ C @ D )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(132,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E )
= ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oimage @ A @ B @ D @ E ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ ( tc_fun @ E @ tc_bool ) ) )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_bool ) ) @ D @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__set__diff_0) ).
thf(794,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E )
= ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oimage @ A @ B @ D @ E ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ ( tc_fun @ E @ tc_bool ) ) )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_bool ) ) @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(38,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__trans_0) ).
thf(586,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(183,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I1_J_0) ).
thf(906,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(284,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Oord @ A )
| ( c_lessequals @ B @ C @ ( tc_fun @ D @ A ) )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ ( tc_fun @ D @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__fun__def_0) ).
thf(1135,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Oord @ A )
| ( c_lessequals @ B @ C @ ( tc_fun @ D @ A ) )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ ( tc_fun @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(208,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Finite__Set_Osetsum @ A @ ( c_HOL_Ominus__class_Ominus @ B @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ D @ tc_nat )
= ( c_Finite__Set_Osetsum @ A @ B @ D @ tc_nat ) )
| ( c_in @ C @ B @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__diff1__nat_1) ).
thf(965,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Finite__Set_Osetsum @ A @ ( c_HOL_Ominus__class_Ominus @ B @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ D @ tc_nat )
= ( c_Finite__Set_Osetsum @ A @ B @ D @ tc_nat ) )
| ( c_in @ C @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(345,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__left__absorb_0) ).
thf(1273,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(161,axiom,
! [B: $i,A: $i] :
( ( class_HOL_Oord @ ( tc_fun @ A @ B ) )
| ~ ( class_HOL_Oord @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__HOL_Oord) ).
thf(856,plain,
! [B: $i,A: $i] :
( ( class_HOL_Oord @ ( tc_fun @ A @ B ) )
| ~ ( class_HOL_Oord @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(357,axiom,
! [B: $i,A: $i] :
( ( class_Lattices_Olower__semilattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Olattice @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olower__semilattice) ).
thf(1301,plain,
! [B: $i,A: $i] :
( ( class_Lattices_Olower__semilattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Olattice @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(501,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_SetInterval_Oord__class_OlessThan @ B @ A ) @ ( c_SetInterval_Oord__class_OlessThan @ C @ A ) @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lessThan__subset__iff_0) ).
thf(1631,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_SetInterval_Oord__class_OlessThan @ B @ A ) @ ( c_SetInterval_Oord__class_OlessThan @ C @ A ) @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).
thf(44,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
!= ( c_HOL_Ominus__class_Ominus @ D @ E @ A ) )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ E @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eqI_1) ).
thf(601,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
!= ( c_HOL_Ominus__class_Ominus @ D @ E @ A ) )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ E @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(320,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( C = B )
| ~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ C @ A @ D ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_0) ).
thf(1219,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( C = B )
| ~ ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ C @ A @ D ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(145,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__UNIV__right_0) ).
thf(824,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(155,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( hAPP @ A @ B ) @ C @ D )
| ~ ( c_in @ B @ E @ F )
| ~ ( c_lessequals @ ( c_Set_Oimage @ A @ E @ F @ D ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__subset__iff_0) ).
thf(843,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( hAPP @ A @ B ) @ C @ D )
| ~ ( c_in @ B @ E @ F )
| ~ ( c_lessequals @ ( c_Set_Oimage @ A @ E @ F @ D ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(496,axiom,
! [B: $i,A: $i] :
~ ( c_in @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_emptyE_0) ).
thf(1620,plain,
! [B: $i,A: $i] :
~ ( c_in @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).
thf(396,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1E_1) ).
thf(1388,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(34,axiom,
class_HOL_Oord @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__HOL_Oord) ).
thf(579,plain,
class_HOL_Oord @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(453,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__assoc_0) ).
thf(1520,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(279,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ D ) @ C ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__less__iff__conj_1) ).
thf(1124,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ D ) @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(27,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_SetInterval_Oord__class_OlessThan @ B @ A )
!= ( c_SetInterval_Oord__class_OlessThan @ C @ A ) )
| ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lessThan__eq__iff_0) ).
thf(562,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_SetInterval_Oord__class_OlessThan @ B @ A )
!= ( c_SetInterval_Oord__class_OlessThan @ C @ A ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(182,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I7_J_0) ).
thf(904,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(213,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) )
| ( c_in @ B @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_5) ).
thf(975,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) )
| ( c_in @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(170,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Fun_Oinj__on @ A @ B @ C @ D )
| ( ( hAPP @ ( c_Fun_Othe__inv__into @ B @ A @ C @ D ) @ ( hAPP @ A @ E ) )
= E )
| ~ ( c_in @ E @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_the__inv__into__f__eq_0) ).
thf(875,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Fun_Oinj__on @ A @ B @ C @ D )
| ( ( hAPP @ ( c_Fun_Othe__inv__into @ B @ A @ C @ D ) @ ( hAPP @ A @ E ) )
= E )
| ~ ( c_in @ E @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(146,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_lessequals @ A @ ( c_Set_Oimage @ C @ D @ E @ B ) @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ D @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__surj_0) ).
thf(826,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_lessequals @ A @ ( c_Set_Oimage @ C @ D @ E @ B ) @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(337,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ D ) @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__inf__iff_2) ).
thf(1256,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ D ) @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(323,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ C @ B ) )
| ~ ( c_lessequals @ C @ A @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_predicate1D_0) ).
thf(1226,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ C @ B ) )
| ~ ( c_lessequals @ C @ A @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(19,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ B @ A )
!= ( c_HOL_Ominus__class_Ominus @ C @ D @ A ) )
| ( C = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__eqI_0) ).
thf(545,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ B @ A )
!= ( c_HOL_Ominus__class_Ominus @ C @ D @ A ) )
| ( C = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(439,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Set_Oimage @ A @ B @ C @ D ) @ D )
| ~ ( c_Finite__Set_Ofinite @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__imageI_0) ).
thf(1488,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Set_Oimage @ A @ B @ C @ D ) @ D )
| ~ ( c_Finite__Set_Ofinite @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(445,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Oinj__on @ ( c_Hilbert__Choice_Oinv__into @ A @ B @ C @ D ) @ E @ D @ C )
| ~ ( c_lessequals @ E @ ( c_Set_Oimage @ B @ A @ C @ D ) @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__inv__into_0) ).
thf(1503,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Oinj__on @ ( c_Hilbert__Choice_Oinv__into @ A @ B @ C @ D ) @ E @ D @ C )
| ~ ( c_lessequals @ E @ ( c_Set_Oimage @ B @ A @ C @ D ) @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(196,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_Set_Oinsert @ ( c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__induct__1__1 @ C @ A @ D ) @ ( c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__induct__1__2 @ C @ A @ D ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) ) )
| ~ ( c_lessequals @ B @ C @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ B @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__subset__induct_4) ).
thf(936,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_Set_Oinsert @ ( c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__induct__1__1 @ C @ A @ D ) @ ( c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__induct__1__2 @ C @ A @ D ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) ) )
| ~ ( c_lessequals @ B @ C @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(31,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).
thf(572,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(362,axiom,
! [B: $i,A: $i] : ( c_lessequals @ A @ A @ ( tc_fun @ B @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equalityE_0) ).
thf(1312,plain,
! [B: $i,A: $i] : ( c_lessequals @ A @ A @ ( tc_fun @ B @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(129,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( c_Finite__Set_Ofinite @ ( c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__induct__1__2 @ C @ A @ D ) @ D )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) ) )
| ~ ( c_lessequals @ B @ C @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ B @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__subset__induct_0) ).
thf(787,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( c_Finite__Set_Ofinite @ ( c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__induct__1__2 @ C @ A @ D ) @ D )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) ) )
| ~ ( c_lessequals @ B @ C @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(136,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ B @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_1) ).
thf(804,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_lessequals @ B @ B @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(338,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ C ) @ D ) @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__infI_0) ).
thf(1258,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ C ) @ D ) @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(383,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ( A = D )
| ~ ( c_in @ A @ ( c_Set_Oinsert @ D @ B @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertE_0) ).
thf(1356,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ( A = D )
| ~ ( c_in @ A @ ( c_Set_Oinsert @ D @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(275,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ D @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__trans_0) ).
thf(1117,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ D @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(105,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__idemp_0) ).
thf(736,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(380,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ C ) @ D ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__inf__iff_0) ).
thf(1349,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ C ) @ D ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(277,axiom,
! [B: $i,A: $i] : ( c_in @ A @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__iff_1) ).
thf(1122,plain,
! [B: $i,A: $i] : ( c_in @ A @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(118,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ C )
| ~ ( c_Finite__Set_Ofinite @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Diff_0) ).
thf(764,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ C )
| ~ ( c_Finite__Set_Ofinite @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(215,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Orderings_Oord__class_Omax @ B @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ C ) @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Osup__inf__absorb_0) ).
thf(979,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Orderings_Oord__class_Omax @ B @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ C ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(45,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_Orderings_Oord__class_Omax @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oless__supI1_0) ).
thf(604,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_Orderings_Oord__class_Omax @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(477,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D ) @ B )
| ~ ( c_in @ A @ D @ B )
| ~ ( c_in @ A @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntI_0) ).
thf(1574,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D ) @ B )
| ~ ( c_in @ A @ D @ B )
| ~ ( c_in @ A @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).
thf(230,axiom,
! [A: $i] : ( c_Finite__Set_Ofinite @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite_OemptyI_0) ).
thf(1011,plain,
! [A: $i] : ( c_Finite__Set_Ofinite @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(219,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__le2_0) ).
thf(990,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(222,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ D ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__inf__iff_0) ).
thf(996,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ D ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(441,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Oinj__on @ A @ B @ C @ D )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Set_Oimage @ E @ B @ C @ C ) @ C @ D )
| ~ ( c_Fun_Oinj__on @ E @ B @ C @ C )
| ( ( hAPP @ A @ ( c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__1 @ B @ E @ A @ C @ D ) )
= ( hAPP @ A @ ( c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__2 @ B @ E @ A @ C @ D ) ) )
| ( ( hAPP @ A @ ( hAPP @ E @ ( c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__1 @ B @ E @ A @ C @ D ) ) )
= ( hAPP @ A @ ( hAPP @ E @ ( c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__2 @ B @ E @ A @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__image__iff_4) ).
thf(1492,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Oinj__on @ A @ B @ C @ D )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Set_Oimage @ E @ B @ C @ C ) @ C @ D )
| ~ ( c_Fun_Oinj__on @ E @ B @ C @ C )
| ( ( hAPP @ A @ ( c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__1 @ B @ E @ A @ C @ D ) )
= ( hAPP @ A @ ( c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__2 @ B @ E @ A @ C @ D ) ) )
| ( ( hAPP @ A @ ( hAPP @ E @ ( c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__1 @ B @ E @ A @ C @ D ) ) )
= ( hAPP @ A @ ( hAPP @ E @ ( c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__2 @ B @ E @ A @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).
thf(490,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ ( c_Hilbert__Choice_Oinv__into @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ B @ A @ C ) @ ( c_Set_Oimage @ B @ D @ A @ C ) @ C @ A )
= D )
| ~ ( c_Fun_Oinj__on @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inv__image__comp_0) ).
thf(1603,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ ( c_Hilbert__Choice_Oinv__into @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ B @ A @ C ) @ ( c_Set_Oimage @ B @ D @ A @ C ) @ C @ A )
= D )
| ~ ( c_Fun_Oinj__on @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).
thf(4,negated_conjecture,
~ ( c_lessequals @ ( c_Set_Oinsert @ ( hAPP @ v_mgt__call @ v_pn ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_bool ) ) @ t_a ) @ ( c_Set_Oimage @ v_mgt__call @ v_U @ tc_Com_Opname @ t_a ) @ ( tc_fun @ t_a @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
thf(509,plain,
~ ( c_lessequals @ ( c_Set_Oinsert @ ( hAPP @ v_mgt__call @ v_pn ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_bool ) ) @ t_a ) @ ( c_Set_Oimage @ v_mgt__call @ v_U @ tc_Com_Opname @ t_a ) @ ( tc_fun @ t_a @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(172,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ C ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oless__infI2_0) ).
thf(880,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ C ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(66,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__1 @ B @ C @ A @ D @ E ) )
!= ( hAPP @ A @ ( c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__2 @ B @ C @ A @ D @ E ) ) )
| ( ( hAPP @ A @ ( hAPP @ C @ ( c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__1 @ B @ C @ A @ D @ E ) ) )
!= ( hAPP @ A @ ( hAPP @ C @ ( c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__2 @ B @ C @ A @ D @ E ) ) ) )
| ( c_Fun_Oinj__on @ A @ ( c_Set_Oimage @ C @ B @ D @ D ) @ D @ E )
| ~ ( c_Fun_Oinj__on @ A @ B @ D @ E )
| ~ ( c_Fun_Oinj__on @ C @ B @ D @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__image__iff_7) ).
thf(649,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__1 @ B @ C @ A @ D @ E ) )
!= ( hAPP @ A @ ( c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__2 @ B @ C @ A @ D @ E ) ) )
| ( ( hAPP @ A @ ( hAPP @ C @ ( c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__1 @ B @ C @ A @ D @ E ) ) )
!= ( hAPP @ A @ ( hAPP @ C @ ( c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__2 @ B @ C @ A @ D @ E ) ) ) )
| ( c_Fun_Oinj__on @ A @ ( c_Set_Oimage @ C @ B @ D @ D ) @ D @ E )
| ~ ( c_Fun_Oinj__on @ A @ B @ D @ E )
| ~ ( c_Fun_Oinj__on @ C @ B @ D @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(243,axiom,
! [B: $i,A: $i] :
~ ( c_HOL_Oord__class_Oless @ A @ A @ ( tc_fun @ B @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__eq_1) ).
thf(1043,plain,
! [B: $i,A: $i] :
~ ( c_HOL_Oord__class_Oless @ A @ A @ ( tc_fun @ B @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(43,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_Orderings_Oord__class_Omax @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__max__iff__disj_1) ).
thf(599,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( c_Orderings_Oord__class_Omax @ C @ D @ A ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(391,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
!= ( hAPP @ A @ C ) )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_bool ) ) @ D @ E )
| ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_injD_0) ).
thf(1376,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
!= ( hAPP @ A @ C ) )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_bool ) ) @ D @ E )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(419,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ ( c_Orderings_Oord__class_Omax @ C @ D @ A ) )
= ( c_Orderings_Oord__class_Omax @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ D ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__sup__distrib1_0) ).
thf(1439,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ ( c_Orderings_Oord__class_Omax @ C @ D @ A ) )
= ( c_Orderings_Oord__class_Omax @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ D ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(164,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_in @ B @ A @ D )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_3) ).
thf(863,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_in @ B @ A @ D )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(301,axiom,
! [B: $i,A: $i] :
( ( ( c_Finite__Set_Ocard @ A @ B )
!= ( c_Finite__Set_Ocard @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ B ) )
| ~ ( c_Finite__Set_Ofinite @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ B )
| ( A
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__eq__UNIV__imp__eq__UNIV_0) ).
thf(1175,plain,
! [B: $i,A: $i] :
( ( ( c_Finite__Set_Ocard @ A @ B )
!= ( c_Finite__Set_Ocard @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ B ) )
| ~ ( c_Finite__Set_Ofinite @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ B )
| ( A
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(176,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ B @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ C ) @ D ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ ( c_Orderings_Oord__class_Omax @ B @ C @ A ) ) @ ( c_Orderings_Oord__class_Omax @ B @ D @ A ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Odistrib__sup__le_0) ).
thf(890,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ B @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ C ) @ D ) @ A ) @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ ( c_Orderings_Oord__class_Omax @ B @ C @ A ) ) @ ( c_Orderings_Oord__class_Omax @ B @ D @ A ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(432,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Finite__Set_Olinorder__class_OMin @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Min__singleton_0) ).
thf(1471,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Finite__Set_Olinorder__class_OMin @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(259,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1 @ A @ B @ C @ D @ E ) @ A @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ B @ ( c_Set_Oimage @ C @ A @ D @ E ) @ ( tc_fun @ E @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ B @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__subset__image_0) ).
thf(1080,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1 @ A @ B @ C @ D @ E ) @ A @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ B @ ( c_Set_Oimage @ C @ A @ D @ E ) @ ( tc_fun @ E @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ B @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(14,axiom,
! [A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ A )
= ( c_Orderings_Oord__class_Omin @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__min_0) ).
thf(535,plain,
! [A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ A )
= ( c_Orderings_Oord__class_Omin @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(141,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
| ( c_in @ B @ A @ D )
| ( c_in @ B @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_3) ).
thf(816,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
| ( c_in @ B @ A @ D )
| ( c_in @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(48,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B )
!= ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) )
| ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__inject_0) ).
thf(609,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B )
!= ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(101,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( B = C )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le_2) ).
thf(726,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( B = C )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(369,axiom,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ ( c_Orderings_Obot__class_Obot @ A ) ) @ B )
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__bot__left_0) ).
thf(1325,plain,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ ( c_Orderings_Obot__class_Obot @ A ) ) @ B )
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(290,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Oinj__on @ A @ B @ C @ D )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Set_Oinsert @ E @ B @ C ) @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__insert_0) ).
thf(1149,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Oinj__on @ A @ B @ C @ D )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Set_Oinsert @ E @ B @ C ) @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(187,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__subset__trans_0) ).
thf(915,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(378,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ ( c_Orderings_Oord__class_Omax @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__max__iff__disj_1) ).
thf(1344,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ ( c_Orderings_Oord__class_Omax @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(121,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) @ A )
| ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Int_0) ).
thf(769,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) @ A )
| ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(235,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I1_J_0) ).
thf(1022,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(74,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ B @ A )
| ( c_lessequals @ B @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_1) ).
thf(668,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ B @ A )
| ( c_lessequals @ B @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(162,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( B = C )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__less_0) ).
thf(858,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( B = C )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(22,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omax @ B @ D @ A ) @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_max__less__iff__conj_0) ).
thf(552,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omax @ B @ D @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(158,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
!= ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
| ( B = D )
| ( A = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_1) ).
thf(848,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
!= ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
| ( B = D )
| ( A = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(88,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ( c_lessequals @ ( c_Set_Oimage @ D @ A @ C @ E ) @ ( c_Set_Oimage @ D @ B @ C @ E ) @ ( tc_fun @ E @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__image__iff_2) ).
thf(700,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ( c_lessequals @ ( c_Set_Oimage @ D @ A @ C @ E ) @ ( c_Set_Oimage @ D @ B @ C @ E ) @ ( tc_fun @ E @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(194,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I3_J_0) ).
thf(932,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ D ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(251,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Set_Oinsert @ C @ D @ A ) )
= ( c_Set_Oinsert @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) @ A ) )
| ~ ( c_in @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__right_0) ).
thf(1061,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Set_Oinsert @ C @ D @ A ) )
= ( c_Set_Oinsert @ C @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) @ A ) )
| ~ ( c_in @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(8,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I10_J_0) ).
thf(521,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(311,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_HOL_Ominus__class_Ominus @ C @ D @ ( tc_fun @ A @ tc_bool ) ) )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Int__distrib_0) ).
thf(1198,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_HOL_Ominus__class_Ominus @ C @ D @ ( tc_fun @ A @ tc_bool ) ) )
= ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(433,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E ) @ F )
= ( hAPP @ A @ F ) )
| ( F = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__apply_1) ).
thf(1474,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E ) @ F )
= ( hAPP @ A @ F ) )
| ( F = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(486,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( c_in @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singletonE_0) ).
thf(1594,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( c_in @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).
thf(120,axiom,
class_Lattices_Obounded__lattice @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Obounded__lattice) ).
thf(768,plain,
class_Lattices_Obounded__lattice @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(60,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( c_lessequals @ C @ A @ ( tc_fun @ D @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__predicate1D_0) ).
thf(636,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( c_lessequals @ C @ A @ ( tc_fun @ D @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(126,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__1 @ B @ C @ A @ D @ E ) )
!= ( hAPP @ A @ ( c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__2 @ B @ C @ A @ D @ E ) ) )
| ( ( hAPP @ A @ ( hAPP @ C @ ( c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__1 @ B @ C @ A @ D @ E ) ) )
!= ( hAPP @ A @ ( hAPP @ C @ ( c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__2 @ B @ C @ A @ D @ E ) ) ) )
| ( c_Fun_Oinj__on @ A @ B @ D @ E )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Set_Oimage @ C @ B @ D @ D ) @ D @ E )
| ~ ( c_Fun_Oinj__on @ C @ B @ D @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__image__iff_6) ).
thf(780,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__1 @ B @ C @ A @ D @ E ) )
!= ( hAPP @ A @ ( c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__2 @ B @ C @ A @ D @ E ) ) )
| ( ( hAPP @ A @ ( hAPP @ C @ ( c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__1 @ B @ C @ A @ D @ E ) ) )
!= ( hAPP @ A @ ( hAPP @ C @ ( c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__2 @ B @ C @ A @ D @ E ) ) ) )
| ( c_Fun_Oinj__on @ A @ B @ D @ E )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Set_Oimage @ C @ B @ D @ D ) @ D @ E )
| ~ ( c_Fun_Oinj__on @ C @ B @ D @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(232,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ~ ( c_in @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntE_1) ).
thf(1015,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ~ ( c_in @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(273,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
| ( c_in @ B @ A @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert_1) ).
thf(1113,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
| ( c_in @ B @ A @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(416,axiom,
class_HOL_Oord @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__HOL_Oord) ).
thf(1435,plain,
class_HOL_Oord @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(434,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Set_Oimage @ A @ B @ C @ D ) @ E @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_in @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Set__Ximage__subset__iff__1__1 @ B @ E @ A @ C @ D ) ) @ E @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__subset__iff_2) ).
thf(1477,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Set_Oimage @ A @ B @ C @ D ) @ E @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_in @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Set__Ximage__subset__iff__1__1 @ B @ E @ A @ C @ D ) ) @ E @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(334,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ~ ( c_in @ A @ D @ C )
| ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subsetD_0) ).
thf(1250,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ~ ( c_in @ A @ D @ C )
| ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(190,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Finite__Set_Olinorder__class_OMin @ ( c_Set_Oinsert @ B @ C @ A ) @ A )
= ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ ( c_Finite__Set_Olinorder__class_OMin @ C @ A ) ) )
| ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Min__insert_0) ).
thf(922,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Finite__Set_Olinorder__class_OMin @ ( c_Set_Oinsert @ B @ C @ A ) @ A )
= ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ ( c_Finite__Set_Olinorder__class_OMin @ C @ A ) ) )
| ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(70,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A )
| ~ ( c_lessequals @ D @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I8_J_0) ).
thf(658,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A )
| ~ ( c_lessequals @ D @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(472,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
= C )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ C @ A @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__diff_0) ).
thf(1562,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
= C )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ C @ A @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).
thf(253,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_4) ).
thf(1066,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(421,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__induct__1__2 @ C @ A @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) ) )
| ~ ( c_lessequals @ B @ C @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ B @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__subset__induct_3) ).
thf(1445,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__induct__1__2 @ C @ A @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) ) )
| ~ ( c_lessequals @ B @ C @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(159,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__assoc_0) ).
thf(851,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(269,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ~ ( c_in @ A @ D @ C )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ B )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_disjoint__iff__not__equal_0) ).
thf(1102,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ~ ( c_in @ A @ D @ C )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ B )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(257,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_in @ ( c_Finite__Set_Olinorder__class_OMin @ B @ A ) @ B @ A )
| ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Min__in_0) ).
thf(1076,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_in @ ( c_Finite__Set_Olinorder__class_OMin @ B @ A ) @ B @ A )
| ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(499,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_Finite__Set_Osetsum @ B @ ( c_HOL_Ominus__class_Ominus @ C @ ( c_Set_Oinsert @ D @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_bool ) ) @ E ) @ ( tc_fun @ E @ tc_bool ) ) @ E @ A )
= ( c_Finite__Set_Osetsum @ B @ C @ E @ A ) )
| ( c_in @ D @ C @ E )
| ~ ( c_Finite__Set_Ofinite @ C @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__diff1_1) ).
thf(1626,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_Finite__Set_Osetsum @ B @ ( c_HOL_Ominus__class_Ominus @ C @ ( c_Set_Oinsert @ D @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_bool ) ) @ E ) @ ( tc_fun @ E @ tc_bool ) ) @ E @ A )
= ( c_Finite__Set_Osetsum @ B @ C @ E @ A ) )
| ( c_in @ D @ C @ E )
| ~ ( c_Finite__Set_Ofinite @ C @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).
thf(99,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D )
= ( c_Set_Oinsert @ B @ ( c_Set_Oinsert @ A @ C @ D ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__commute_0) ).
thf(722,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D )
= ( c_Set_Oinsert @ B @ ( c_Set_Oinsert @ A @ C @ D ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(77,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
= ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) )
| ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
| ~ ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__singletonD_0) ).
thf(675,plain,
! [C: $i,B: $i,A: $i] :
( ( A
= ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) )
| ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
| ~ ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(313,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ C ) @ D @ A )
| ~ ( c_lessequals @ C @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__infI2_0) ).
thf(1203,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ C ) @ D @ A )
| ~ ( c_lessequals @ C @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(200,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ C @ A )
| ( c_lessequals @ B @ D @ A )
| ~ ( c_lessequals @ B @ ( c_Orderings_Oord__class_Omax @ D @ C @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__max__iff__disj_0) ).
thf(944,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ C @ A )
| ( c_lessequals @ B @ D @ A )
| ~ ( c_lessequals @ B @ ( c_Orderings_Oord__class_Omax @ D @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(430,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ C @ A )
| ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__less_0) ).
thf(1467,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ C @ A )
| ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(79,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__empty_0) ).
thf(680,plain,
! [B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(410,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Ovimage @ ( c_COMBK @ A @ B @ C ) @ D @ C @ B )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
| ( c_in @ A @ D @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__const_1) ).
thf(1420,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Ovimage @ ( c_COMBK @ A @ B @ C ) @ D @ C @ B )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
| ( c_in @ A @ D @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(192,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Set_Oimage @ A @ B @ C @ D ) @ ( c_Set_Oimage @ A @ E @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ B @ E @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__image__subset__iff_1) ).
thf(927,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Set_Oimage @ A @ B @ C @ D ) @ ( c_Set_Oimage @ A @ E @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ B @ E @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(347,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Oinj__on @ A @ ( c_Set_Oimage @ B @ C @ D @ D ) @ D @ E )
| ~ ( c_Fun_Oinj__on @ A @ C @ D @ E )
| ~ ( c_Fun_Oinj__on @ B @ C @ D @ D )
| ( c_in @ ( c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__2 @ C @ B @ A @ D @ E ) @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__image__iff_3) ).
thf(1277,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Oinj__on @ A @ ( c_Set_Oimage @ B @ C @ D @ D ) @ D @ E )
| ~ ( c_Fun_Oinj__on @ A @ C @ D @ E )
| ~ ( c_Fun_Oinj__on @ B @ C @ D @ D )
| ( c_in @ ( c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__2 @ C @ B @ A @ D @ E ) @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(111,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Set_Oinsert @ A @ B @ C ) @ ( c_Set_Oinsert @ A @ D @ C ) @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ B @ D @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__mono_0) ).
thf(749,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Set_Oinsert @ A @ B @ C ) @ ( c_Set_Oinsert @ A @ D @ C ) @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ B @ D @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(52,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Finite__Set_Ocard @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) ) @ C )
= ( c_Finite__Set_Ocard @ A @ C ) )
| ( c_in @ B @ A @ C )
| ~ ( c_Finite__Set_Ofinite @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__Diff__singleton__if_1) ).
thf(617,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Finite__Set_Ocard @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) ) @ C )
= ( c_Finite__Set_Ocard @ A @ C ) )
| ( c_in @ B @ A @ C )
| ~ ( c_Finite__Set_Ofinite @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(376,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ D @ C @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__trans_0) ).
thf(1340,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ D @ C @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(288,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Oord @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_in @ B @ ( c_SetInterval_Oord__class_OlessThan @ C @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lessThan__iff_0) ).
thf(1145,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Oord @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_in @ B @ ( c_SetInterval_Oord__class_OlessThan @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(467,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D ) @ B )
| ~ ( c_in @ A @ D @ B )
| ~ ( c_in @ A @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__iff_2) ).
thf(1551,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D ) @ B )
| ~ ( c_in @ A @ D @ B )
| ~ ( c_in @ A @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).
thf(246,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( c_in @ ( c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__induct__1__1 @ C @ A @ D ) @ C @ D )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) ) )
| ~ ( c_lessequals @ B @ C @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ B @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__subset__induct_1) ).
thf(1049,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( c_in @ ( c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__induct__1__1 @ C @ A @ D ) @ C @ D )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) ) )
| ~ ( c_lessequals @ B @ C @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(72,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ C ) @ D @ A )
| ~ ( c_lessequals @ C @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__le__iff__disj_2) ).
thf(663,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ C ) @ D @ A )
| ~ ( c_lessequals @ C @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(20,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).
thf(548,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(209,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_Fun_Oinj__on @ C @ A @ B @ D )
| ~ ( c_Finite__Set_Ofinite @ ( c_Set_Oimage @ C @ A @ B @ D ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__imageD_0) ).
thf(968,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_Fun_Oinj__on @ C @ A @ B @ D )
| ~ ( c_Finite__Set_Ofinite @ ( c_Set_Oimage @ C @ A @ B @ D ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(303,axiom,
class_Complete__Lattice_Ocomplete__lattice @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Complete__Lattice_Ocomplete__lattice) ).
thf(1181,plain,
class_Complete__Lattice_Ocomplete__lattice @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(144,axiom,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) @ B @ ( tc_fun @ A @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__lower1_0) ).
thf(823,plain,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) @ B @ ( tc_fun @ A @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(465,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_in @ B @ A @ C )
| ~ ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ D @ C ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_0) ).
thf(1547,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_in @ B @ A @ C )
| ~ ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ D @ C ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(10,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Orderings_Oord__class_Omax @ B @ B @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Osup__idem_0) ).
thf(525,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Orderings_Oord__class_Omax @ B @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(35,axiom,
class_Orderings_Oorder @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).
thf(580,plain,
class_Orderings_Oorder @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(62,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( c_in @ B @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_0) ).
thf(640,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( c_in @ B @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(236,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_HOL_Oord__class_Oless @ D @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ D ) @ B ) @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__less__iff__disj_0) ).
thf(1025,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_HOL_Oord__class_Oless @ D @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ D ) @ B ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(401,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ C ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oless__infI1_0) ).
thf(1400,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ C ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(175,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Set_Oinsert @ A @ ( c_HOL_Ominus__class_Ominus @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ C ) )
| ( c_in @ A @ D @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff__if_1) ).
thf(887,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Set_Oinsert @ A @ ( c_HOL_Ominus__class_Ominus @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ C ) )
| ( c_in @ A @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(388,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C )
= ( c_Set_Oinsert @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__absorb2_0) ).
thf(1368,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C )
= ( c_Set_Oinsert @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(437,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insertI2_0) ).
thf(1484,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(267,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Set_Ovimage @ A @ B @ C @ D ) @ ( c_Set_Ovimage @ A @ E @ C @ D ) @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ B @ E @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__mono_0) ).
thf(1098,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Set_Ovimage @ A @ B @ C @ D ) @ ( c_Set_Ovimage @ A @ E @ C @ D ) @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ B @ E @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(94,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( hAPP @ ( c_Hilbert__Choice_Oinv__into @ A @ B @ C @ D ) @ E ) @ A @ C )
| ~ ( c_in @ E @ ( c_Set_Oimage @ B @ A @ C @ D ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inv__into__into_0) ).
thf(712,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( hAPP @ ( c_Hilbert__Choice_Oinv__into @ A @ B @ C @ D ) @ E ) @ A @ C )
| ~ ( c_in @ E @ ( c_Set_Oimage @ B @ A @ C @ D ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(226,axiom,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ A ) )
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__bot__right_0) ).
thf(1003,plain,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ ( c_Orderings_Obot__class_Obot @ A ) )
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(91,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ ( c_SetInterval_Oord__class_OlessThan @ B @ A ) @ ( tc_fun @ A @ tc_bool ) )
= ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_single__Diff__lessThan_0) ).
thf(705,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ ( c_SetInterval_Oord__class_OlessThan @ B @ A ) @ ( tc_fun @ A @ tc_bool ) )
= ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(493,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
!= ( hAPP @ A @ C ) )
| ~ ( c_Fun_Oinj__on @ A @ D @ E @ F )
| ( B = C )
| ~ ( c_in @ C @ D @ E )
| ~ ( c_in @ B @ D @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__onD_0) ).
thf(1611,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
!= ( hAPP @ A @ C ) )
| ~ ( c_Fun_Oinj__on @ A @ D @ E @ F )
| ( B = C )
| ~ ( c_in @ C @ D @ E )
| ~ ( c_in @ B @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).
thf(204,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ A @ B @ C ) @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) )
= B )
| ( c_in @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__insert__absorb_0) ).
thf(954,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ A @ B @ C ) @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) )
= B )
| ( c_in @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(335,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D )
| ~ ( c_in @ A @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertCI_0) ).
thf(1252,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D )
| ~ ( c_in @ A @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(76,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oimage @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B @ C )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__empty_0) ).
thf(673,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oimage @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B @ C )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(504,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Oord @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ ( tc_fun @ D @ A ) )
| ( c_lessequals @ C @ B @ ( tc_fun @ D @ A ) )
| ~ ( c_lessequals @ B @ C @ ( tc_fun @ D @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__fun__def_2) ).
thf(1637,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Oord @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ ( tc_fun @ D @ A ) )
| ( c_lessequals @ C @ B @ ( tc_fun @ D @ A ) )
| ~ ( c_lessequals @ B @ C @ ( tc_fun @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).
thf(241,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ B @ D @ A ) @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__supE_0) ).
thf(1038,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ B @ D @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(365,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ ( c_HOL_Ominus__class_Ominus @ B @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) ) @ C )
= ( c_Set_Oinsert @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff__single_0) ).
thf(1317,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ ( c_HOL_Ominus__class_Ominus @ B @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) ) @ C )
= ( c_Set_Oinsert @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(33,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Orderings_Oord__class_Omax @ B @ C @ A )
= ( c_Orderings_Oord__class_Omax @ C @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Osup__commute_0) ).
thf(576,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Orderings_Oord__class_Omax @ B @ C @ A )
= ( c_Orderings_Oord__class_Omax @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(307,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ A @ B @ C @ D )
!= ( c_Set_Oimage @ A @ E @ C @ D ) )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) @ C @ D )
| ( B = E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__image__eq__iff_0) ).
thf(1188,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ A @ B @ C @ D )
!= ( c_Set_Oimage @ A @ E @ C @ D ) )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) @ C @ D )
| ( B = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(306,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ C @ A )
| ( c_lessequals @ D @ C @ A )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ D ) @ B ) @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__le__iff__disj_0) ).
thf(1186,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ C @ A )
| ( c_lessequals @ D @ C @ A )
| ~ ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ D ) @ B ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(461,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Hilbert__Choice_Oinv__into @ A @ B @ C @ D ) @ ( hAPP @ B @ E ) )
= E )
| ~ ( c_in @ E @ A @ C )
| ~ ( c_Fun_Oinj__on @ B @ A @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inv__into__f__f_0) ).
thf(1538,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Hilbert__Choice_Oinv__into @ A @ B @ C @ D ) @ ( hAPP @ B @ E ) )
= E )
| ~ ( c_in @ E @ A @ C )
| ~ ( c_Fun_Oinj__on @ B @ A @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(203,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( B = C )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__neq__trans_0) ).
thf(951,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( B = C )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(138,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ C ) @ D ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__less__iff__conj_2) ).
thf(808,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ C ) @ D ) @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(403,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Orderings_Oord__class_Omax @ B @ C @ A )
= B )
| ~ ( c_lessequals @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Osup__absorb1_0) ).
thf(1404,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Orderings_Oord__class_Omax @ B @ C @ A )
= B )
| ~ ( c_lessequals @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(109,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Orderings_Oord__class_Omax @ B @ C @ A )
!= C )
| ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__iff__sup_1) ).
thf(744,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Orderings_Oord__class_Omax @ B @ C @ A )
!= C )
| ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(90,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__infI1_0) ).
thf(703,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_HOL_Oord__class_Oless @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(460,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__trans_0) ).
thf(1536,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).
thf(69,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ D @ E @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ E @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__mono_0) ).
thf(656,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ D @ E @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ E @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(350,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D ) @ B @ E )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ E @ tc_bool ) ) @ ( c_Set_Oimage @ A @ C @ B @ E ) ) @ ( c_Set_Oimage @ A @ D @ B @ E ) ) )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ B @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__Int_0) ).
thf(1284,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D ) @ B @ E )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ E @ tc_bool ) ) @ ( c_Set_Oimage @ A @ C @ B @ E ) ) @ ( c_Set_Oimage @ A @ D @ B @ E ) ) )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ B @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(447,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ B @ C @ A ) @ D @ A )
| ~ ( c_lessequals @ C @ D @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__sup__iff_2) ).
thf(1506,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ B @ C @ A ) @ D @ A )
| ~ ( c_lessequals @ C @ D @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(413,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E )
= ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oimage @ A @ B @ D @ E ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ ( tc_fun @ E @ tc_bool ) ) )
| ~ ( c_lessequals @ C @ F @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ B @ F @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ A @ F @ D @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__image__set__diff_0) ).
thf(1427,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E )
= ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oimage @ A @ B @ D @ E ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ ( tc_fun @ E @ tc_bool ) ) )
| ~ ( c_lessequals @ C @ F @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ B @ F @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ A @ F @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(228,axiom,
! [C: $i,B: $i,A: $i] : ( c_in @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__iff_1) ).
thf(1008,plain,
! [C: $i,B: $i,A: $i] : ( c_in @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(49,axiom,
! [A: $i] :
( ~ ( class_Finite__Set_Ofinite_Ofinite @ A )
| ( c_Finite__Set_Ofinite @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__UNIV_0) ).
thf(612,plain,
! [A: $i] :
( ~ ( class_Finite__Set_Ofinite_Ofinite @ A )
| ( c_Finite__Set_Ofinite @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(482,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Finite__Set_Olinorder__class_OMax @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Max__singleton_0) ).
thf(1585,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Finite__Set_Olinorder__class_OMax @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).
thf(265,axiom,
! [B: $i,A: $i] :
( ( class_Orderings_Otop @ ( tc_fun @ A @ B ) )
| ~ ( class_Orderings_Otop @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Otop) ).
thf(1094,plain,
! [B: $i,A: $i] :
( ( class_Orderings_Otop @ ( tc_fun @ A @ B ) )
| ~ ( class_Orderings_Otop @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(286,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Fun_Othe__inv__into @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ B @ A @ C ) @ ( hAPP @ B @ D ) )
= D )
| ~ ( c_Fun_Oinj__on @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_the__inv__f__f_0) ).
thf(1140,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Fun_Othe__inv__into @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ B @ A @ C ) @ ( hAPP @ B @ D ) )
= D )
| ~ ( c_Fun_Oinj__on @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(330,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ ( c_Fun_Othe__inv__into @ A @ B @ C @ D ) @ ( c_Set_Oimage @ B @ A @ C @ D ) @ D @ C )
= A )
| ~ ( c_Fun_Oinj__on @ B @ A @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_the__inv__into__onto_0) ).
thf(1240,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ ( c_Fun_Othe__inv__into @ A @ B @ C @ D ) @ ( c_Set_Oimage @ B @ A @ C @ D ) @ D @ C )
= A )
| ~ ( c_Fun_Oinj__on @ B @ A @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(495,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Finite__Set_Olinorder__class_OMax @ B @ A )
= C )
| ~ ( c_in @ C @ B @ A )
| ( c_in @ ( c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMax__eqI__1__1 @ B @ C @ A ) @ B @ A )
| ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Max__eqI_0) ).
thf(1617,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Finite__Set_Olinorder__class_OMax @ B @ A )
= C )
| ~ ( c_in @ C @ B @ A )
| ( c_in @ ( c_ATP__Linkup_Osko__Finite__Set__Xlinorder__class__XMax__eqI__1__1 @ B @ C @ A ) @ B @ A )
| ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).
thf(156,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Set_Oimage @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D ) @ B @ E ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ E @ tc_bool ) ) @ ( c_Set_Oimage @ A @ C @ B @ E ) ) @ ( c_Set_Oimage @ A @ D @ B @ E ) ) @ ( tc_fun @ E @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__Int__subset_0) ).
thf(845,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Set_Oimage @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D ) @ B @ E ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ E @ tc_bool ) ) @ ( c_Set_Oimage @ A @ C @ B @ E ) ) @ ( c_Set_Oimage @ A @ D @ B @ E ) ) @ ( tc_fun @ E @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(261,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ D ) @ C ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__inf__iff_1) ).
thf(1084,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ D ) @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(427,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
!= ( hAPP @ A @ C ) )
| ~ ( c_in @ C @ D @ E )
| ~ ( c_in @ B @ D @ E )
| ~ ( c_Fun_Oinj__on @ A @ D @ E @ F )
| ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__iff_0) ).
thf(1459,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
!= ( hAPP @ A @ C ) )
| ~ ( c_in @ C @ D @ E )
| ~ ( c_in @ B @ D @ E )
| ~ ( c_Fun_Oinj__on @ A @ D @ E @ F )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(24,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Orderings_Oord__class_Omax @ B @ ( c_Orderings_Oord__class_Omax @ B @ C @ A ) @ A )
= ( c_Orderings_Oord__class_Omax @ B @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Osup__left__idem_0) ).
thf(556,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Orderings_Oord__class_Omax @ B @ ( c_Orderings_Oord__class_Omax @ B @ C @ A ) @ A )
= ( c_Orderings_Oord__class_Omax @ B @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(16,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omax @ D @ B @ A ) @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_max__less__iff__conj_1) ).
thf(539,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Orderings_Oord__class_Omax @ D @ B @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(468,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ B @ C @ A ) @ D @ A )
| ~ ( c_lessequals @ C @ D @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__supI_0) ).
thf(1553,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ B @ C @ A ) @ D @ A )
| ~ ( c_lessequals @ C @ D @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
thf(367,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_HOL_Ominus__class_Ominus @ C @ B @ ( tc_fun @ A @ tc_bool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__disjoint_0) ).
thf(1321,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_HOL_Ominus__class_Ominus @ C @ B @ ( tc_fun @ A @ tc_bool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(83,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
!= ( c_HOL_Ominus__class_Ominus @ D @ E @ A ) )
| ( c_lessequals @ E @ D @ A )
| ~ ( c_lessequals @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__eqI_0) ).
thf(688,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
!= ( c_HOL_Ominus__class_Ominus @ D @ E @ A ) )
| ( c_lessequals @ E @ D @ A )
| ~ ( c_lessequals @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(36,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le_1) ).
thf(581,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(407,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ C @ A )
| ( c_lessequals @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__linear_0) ).
thf(1412,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ C @ A )
| ( c_lessequals @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(452,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
!= ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
| ( A = E )
| ( B = E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_2) ).
thf(1517,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
!= ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
| ( A = E )
| ( B = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(280,axiom,
! [C: $i,B: $i,A: $i] : ( c_Fun_Oinj__on @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B @ C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__empty_0) ).
thf(1126,plain,
! [C: $i,B: $i,A: $i] : ( c_Fun_Oinj__on @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B @ C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(397,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Finite__Set_Ocard @ ( c_Set_Oinsert @ A @ B @ C ) @ C )
= ( c_Finite__Set_Ocard @ B @ C ) )
| ~ ( c_in @ A @ B @ C )
| ~ ( c_Finite__Set_Ofinite @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_card__insert__if_0) ).
thf(1390,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Finite__Set_Ocard @ ( c_Set_Oinsert @ A @ B @ C ) @ C )
= ( c_Finite__Set_Ocard @ B @ C ) )
| ~ ( c_in @ A @ B @ C )
| ~ ( c_Finite__Set_Ofinite @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(424,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ D )
| ~ ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Diff__insert_1) ).
thf(1453,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ D )
| ~ ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(122,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D ) @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__subset__iff_2) ).
thf(771,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D ) @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(271,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ C ) @ D @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__le__iff__disj_1) ).
thf(1108,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ C ) @ D @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(39,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( C = B )
| ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__less__linear_0) ).
thf(588,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( C = B )
| ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(140,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( c_Set_Oimage @ B @ ( c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1 @ C @ A @ B @ D @ E ) @ D @ E ) )
| ~ ( c_lessequals @ A @ ( c_Set_Oimage @ B @ C @ D @ E ) @ ( tc_fun @ E @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ A @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__subset__image_2) ).
thf(813,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( c_Set_Oimage @ B @ ( c_ATP__Linkup_Osko__Finite__Set__Xfinite__subset__image__1__1 @ C @ A @ B @ D @ E ) @ D @ E ) )
| ~ ( c_lessequals @ A @ ( c_Set_Oimage @ B @ C @ D @ E ) @ ( tc_fun @ E @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ A @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(179,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( B = C )
| ~ ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__antisym__conv_0) ).
thf(896,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( B = C )
| ~ ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(505,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ A @ tc_bool ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__triv_0) ).
thf(1639,plain,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ A @ tc_bool ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).
thf(448,axiom,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ ( c_Orderings_Otop__class_Otop @ A ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__top__right_0) ).
thf(1508,plain,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ ( c_Orderings_Otop__class_Otop @ A ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).
thf(201,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ D ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infE_0) ).
thf(946,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ D ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(67,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_in @ B @ A @ D )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ A @ C @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_8) ).
thf(652,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_in @ B @ A @ D )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ A @ C @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(500,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ C @ tc_bool ) ) @ B ) @ D ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__subset__iff_0) ).
thf(1629,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ C @ tc_bool ) ) @ B ) @ D ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).
thf(58,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
| ( c_in @ B @ A @ D )
| ~ ( c_HOL_Oord__class_Oless @ A @ C @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_7) ).
thf(632,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
| ( c_in @ B @ A @ D )
| ~ ( c_HOL_Oord__class_Oless @ A @ C @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(454,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ D ) @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__greatest_0) ).
thf(1523,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ D ) @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).
thf(103,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( hAPP @ ( c_Hilbert__Choice_Oinv__into @ B @ A @ C @ D ) @ E ) )
= E )
| ~ ( c_in @ E @ ( c_Set_Oimage @ A @ B @ C @ D ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_f__inv__into__f_0) ).
thf(731,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( hAPP @ ( c_Hilbert__Choice_Oinv__into @ B @ A @ C @ D ) @ E ) )
= E )
| ~ ( c_in @ E @ ( c_Set_Oimage @ A @ B @ C @ D ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(470,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( hAPP @ ( c_Fun_Othe__inv__into @ A @ B @ C @ D ) @ E ) @ F @ C )
| ~ ( c_lessequals @ A @ F @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_in @ E @ ( c_Set_Oimage @ B @ A @ C @ D ) @ D )
| ~ ( c_Fun_Oinj__on @ B @ A @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_the__inv__into__into_0) ).
thf(1558,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( hAPP @ ( c_Fun_Othe__inv__into @ A @ B @ C @ D ) @ E ) @ F @ C )
| ~ ( c_lessequals @ A @ F @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_in @ E @ ( c_Set_Oimage @ B @ A @ C @ D ) @ D )
| ~ ( c_Fun_Oinj__on @ B @ A @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(238,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I2_J_0) ).
thf(1030,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) ) @ D )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(186,axiom,
! [A: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ A @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__empty_1) ).
thf(914,plain,
! [A: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ A @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(193,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ B @ C )
= B )
| ~ ( c_in @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__absorb_0) ).
thf(929,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ B @ C )
= B )
| ~ ( c_in @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(360,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) @ D @ A )
| ~ ( c_lessequals @ C @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infI2_0) ).
thf(1308,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) @ D @ A )
| ~ ( c_lessequals @ C @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(309,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_Finite__Set_Ofinite @ ( c_Set_Oinsert @ C @ A @ B ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__insert_0) ).
thf(1193,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_Finite__Set_Ofinite @ ( c_Set_Oinsert @ C @ A @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(317,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ D ) @ C ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__inf__iff_1) ).
thf(1212,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ D ) @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(450,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I2_J_0) ).
thf(1513,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(180,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ C @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__less__trans_0) ).
thf(899,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ C @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(420,axiom,
! [B: $i,A: $i] :
( ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
| ~ ( c_lessequals @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__empty_0) ).
thf(1442,plain,
! [B: $i,A: $i] :
( ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
| ~ ( c_lessequals @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(244,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Ovimage @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D ) @ E @ B )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ E @ tc_bool ) ) @ ( c_Set_Ovimage @ A @ C @ E @ B ) ) @ ( c_Set_Ovimage @ A @ D @ E @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__Int_0) ).
thf(1045,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Ovimage @ A @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D ) @ E @ B )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ E @ tc_bool ) ) @ ( c_Set_Ovimage @ A @ C @ E @ B ) ) @ ( c_Set_Ovimage @ A @ D @ E @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(149,axiom,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) @ C @ ( tc_fun @ A @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__lower2_0) ).
thf(832,plain,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C ) @ C @ ( tc_fun @ A @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(81,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( c_in @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ball__empty_0) ).
thf(684,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( c_in @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(96,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ C ) @ D @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__infI1_0) ).
thf(716,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ C ) @ D @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(494,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( hAPP @ ( c_Fun_Othe__inv__into @ B @ A @ C @ D ) @ E ) )
= E )
| ~ ( c_in @ E @ ( c_Set_Oimage @ A @ B @ C @ D ) @ D )
| ~ ( c_Fun_Oinj__on @ A @ B @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_f__the__inv__into__f_0) ).
thf(1614,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( hAPP @ ( c_Fun_Othe__inv__into @ B @ A @ C @ D ) @ E ) )
= E )
| ~ ( c_in @ E @ ( c_Set_Oimage @ A @ B @ C @ D ) @ D )
| ~ ( c_Fun_Oinj__on @ A @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).
thf(134,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ C ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Oinf__le1_0) ).
thf(800,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ B ) @ C ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(479,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Oinj__on @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D @ E )
| ( c_in @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ ( c_HOL_Ominus__class_Ominus @ C @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ D @ E ) @ E )
| ~ ( c_Fun_Oinj__on @ A @ C @ D @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__insert_2) ).
thf(1578,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Oinj__on @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D @ E )
| ( c_in @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ ( c_HOL_Ominus__class_Ominus @ C @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ D @ E ) @ E )
| ~ ( c_Fun_Oinj__on @ A @ C @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).
thf(150,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Ovimage @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ E @ D )
= ( c_HOL_Ominus__class_Ominus @ ( c_Set_Ovimage @ A @ B @ E @ D ) @ ( c_Set_Ovimage @ A @ C @ E @ D ) @ ( tc_fun @ E @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__Diff_0) ).
thf(833,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Ovimage @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ E @ D )
= ( c_HOL_Ominus__class_Ominus @ ( c_Set_Ovimage @ A @ B @ E @ D ) @ ( c_Set_Ovimage @ A @ C @ E @ D ) @ ( tc_fun @ E @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(151,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ~ ( c_in @ A @ D @ C )
| ~ ( c_HOL_Oord__class_Oless @ D @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubsetD_0) ).
thf(835,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ~ ( c_in @ A @ D @ C )
| ~ ( c_HOL_Oord__class_Oless @ D @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(325,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ ( c_COMBK @ A @ B @ C ) @ D @ C @ B )
= ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) )
| ~ ( c_in @ E @ D @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__constant_0) ).
thf(1229,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ ( c_COMBK @ A @ B @ C ) @ D @ C @ B )
= ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) )
| ~ ( c_in @ E @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(399,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ ( c_Finite__Set_Olinorder__class_OMax @ B @ A ) @ ( c_Finite__Set_Olinorder__class_OMax @ C @ A ) @ A )
| ~ ( c_Finite__Set_Ofinite @ C @ A )
| ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( c_lessequals @ B @ C @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Max__mono_0) ).
thf(1395,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ ( c_Finite__Set_Olinorder__class_OMax @ B @ A ) @ ( c_Finite__Set_Olinorder__class_OMax @ C @ A ) @ A )
| ~ ( c_Finite__Set_Ofinite @ C @ A )
| ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( c_lessequals @ B @ C @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(142,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Nitpick_Ofold__graph_H @ A @ B @ C @ ( hAPP @ ( hAPP @ A @ D ) @ E ) @ F @ G )
| ~ ( c_Nitpick_Ofold__graph_H @ A @ B @ ( c_HOL_Ominus__class_Ominus @ C @ ( c_Set_Oinsert @ D @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ F @ tc_bool ) ) @ F ) @ ( tc_fun @ F @ tc_bool ) ) @ E @ F @ G )
| ~ ( c_in @ D @ C @ F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold__graph_H_Ointros_I2_J_0) ).
thf(818,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Nitpick_Ofold__graph_H @ A @ B @ C @ ( hAPP @ ( hAPP @ A @ D ) @ E ) @ F @ G )
| ~ ( c_Nitpick_Ofold__graph_H @ A @ B @ ( c_HOL_Ominus__class_Ominus @ C @ ( c_Set_Oinsert @ D @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ F @ tc_bool ) ) @ F ) @ ( tc_fun @ F @ tc_bool ) ) @ E @ F @ G )
| ~ ( c_in @ D @ C @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(485,axiom,
class_Orderings_Oorder @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Oorder) ).
thf(1593,plain,
class_Orderings_Oorder @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).
thf(358,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
!= ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
| ( B = D )
| ( B = E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_3) ).
thf(1303,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
!= ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
| ( B = D )
| ( B = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(333,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__UNIV_0) ).
thf(1248,plain,
! [B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(166,axiom,
! [B: $i,A: $i] :
( ( class_Orderings_Obot @ ( tc_fun @ A @ B ) )
| ~ ( class_Orderings_Obot @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Obot) ).
thf(867,plain,
! [B: $i,A: $i] :
( ( class_Orderings_Obot @ ( tc_fun @ A @ B ) )
| ~ ( class_Orderings_Obot @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(165,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Oinj__on @ A @ B @ C @ D )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Set_Oimage @ E @ B @ C @ C ) @ C @ D )
| ~ ( c_Fun_Oinj__on @ E @ B @ C @ C )
| ( c_in @ ( c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__2 @ B @ E @ A @ C @ D ) @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__image__iff_2) ).
thf(865,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Oinj__on @ A @ B @ C @ D )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Set_Oimage @ E @ B @ C @ C ) @ C @ D )
| ~ ( c_Fun_Oinj__on @ E @ B @ C @ C )
| ( c_in @ ( c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__2 @ B @ E @ A @ C @ D ) @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(224,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_COMBK @ A @ B @ C ) @ D )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBK__def_0) ).
thf(999,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_COMBK @ A @ B @ C ) @ D )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(53,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E )
= ( c_Set_Oimage @ A @ C @ D @ E ) )
| ~ ( c_in @ B @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__image_0) ).
thf(620,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E )
= ( c_Set_Oimage @ A @ C @ D @ E ) )
| ~ ( c_in @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(417,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( c_Nitpick_Ofold__graph_H @ A @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ B @ C @ D ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold__graph_H_Ointros_I1_J_0) ).
thf(1436,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( c_Nitpick_Ofold__graph_H @ A @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ B @ C @ D ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(386,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ C ) @ D ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__infE_0) ).
thf(1363,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ B @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ C ) @ D ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(442,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ ( c_Finite__Set_Olinorder__class_OMin @ B @ A ) @ ( c_Finite__Set_Olinorder__class_OMin @ C @ A ) @ A )
| ~ ( c_Finite__Set_Ofinite @ B @ A )
| ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( c_lessequals @ C @ B @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Min__antimono_0) ).
thf(1495,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ ( c_Finite__Set_Olinorder__class_OMin @ B @ A ) @ ( c_Finite__Set_Olinorder__class_OMin @ C @ A ) @ A )
| ~ ( c_Finite__Set_Ofinite @ B @ A )
| ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( c_lessequals @ C @ B @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).
thf(1,negated_conjecture,
c_Finite__Set_Ofinite @ v_U @ tc_Com_Opname,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(506,plain,
c_Finite__Set_Ofinite @ v_U @ tc_Com_Opname,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(373,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__insert2_0) ).
thf(1335,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(249,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I4_J_0) ).
thf(1056,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(239,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( C = B )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I11_J_0) ).
thf(1033,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( C = B )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(147,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ A @ A @ ( tc_fun @ B @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__cancel_0) ).
thf(828,plain,
! [B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ A @ A @ ( tc_fun @ B @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(206,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Set_Ovimage @ A @ B @ C @ D ) @ C )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) @ C @ D )
| ~ ( c_Finite__Set_Ofinite @ B @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__vimageI_0) ).
thf(960,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Set_Ovimage @ A @ B @ C @ D ) @ C )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) @ C @ D )
| ~ ( c_Finite__Set_Ofinite @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(13,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
!= ( c_HOL_Ominus__class_Ominus @ D @ D @ A ) )
| ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__eqI_1) ).
thf(532,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_HOL_Ominus__class_Ominus @ B @ C @ A )
!= ( c_HOL_Ominus__class_Ominus @ D @ D @ A ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(86,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ D @ B @ A ) @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__sup__iff_1) ).
thf(696,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_Orderings_Oord__class_Omax @ D @ B @ A ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(379,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ B @ C )
!= ( c_Set_Oinsert @ A @ D @ C ) )
| ( c_in @ A @ D @ C )
| ( c_in @ A @ B @ C )
| ( B = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__ident_0) ).
thf(1346,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ B @ C )
!= ( c_Set_Oinsert @ A @ D @ C ) )
| ( c_in @ A @ D @ C )
| ( c_in @ A @ B @ C )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(300,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_Finite__Set_Osetsum @ B @ ( c_HOL_Ominus__class_Ominus @ C @ ( c_Set_Oinsert @ D @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_bool ) ) @ E ) @ ( tc_fun @ E @ tc_bool ) ) @ E @ A )
= ( c_HOL_Ominus__class_Ominus @ ( c_Finite__Set_Osetsum @ B @ C @ E @ A ) @ ( hAPP @ B @ D ) @ A ) )
| ~ ( c_in @ D @ C @ E )
| ~ ( c_Finite__Set_Ofinite @ C @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_setsum__diff1_0) ).
thf(1172,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( c_Finite__Set_Osetsum @ B @ ( c_HOL_Ominus__class_Ominus @ C @ ( c_Set_Oinsert @ D @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_bool ) ) @ E ) @ ( tc_fun @ E @ tc_bool ) ) @ E @ A )
= ( c_HOL_Ominus__class_Ominus @ ( c_Finite__Set_Osetsum @ B @ C @ E @ A ) @ ( hAPP @ B @ D ) @ A ) )
| ~ ( c_in @ D @ C @ E )
| ~ ( c_Finite__Set_Ofinite @ C @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(405,axiom,
! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_top1I_0) ).
thf(1410,plain,
! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(98,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_lessequals @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__less_1) ).
thf(720,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_lessequals @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(297,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ ( c_Hilbert__Choice_Oinv__into @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ B @ A @ C ) @ ( c_Set_Oimage @ B @ D @ A @ C ) @ C @ A )
= D )
| ~ ( c_Fun_Oinj__on @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__inv__f__f_0) ).
thf(1165,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ ( c_Hilbert__Choice_Oinv__into @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ B @ A @ C ) @ ( c_Set_Oimage @ B @ D @ A @ C ) @ C @ A )
= D )
| ~ ( c_Fun_Oinj__on @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(153,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Otop @ A )
| ( c_lessequals @ B @ ( c_Orderings_Otop__class_Otop @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_top__greatest_0) ).
thf(839,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Otop @ A )
| ( c_lessequals @ B @ ( c_Orderings_Otop__class_Otop @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(107,axiom,
! [B: $i,A: $i] :
~ ( c_in @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ex__in__conv_0) ).
thf(740,plain,
! [B: $i,A: $i] :
~ ( c_in @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(282,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ B @ D @ ( tc_fun @ C @ tc_bool ) ) )
| ~ ( c_in @ A @ D @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff1_0) ).
thf(1129,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ B @ D @ ( tc_fun @ C @ tc_bool ) ) )
| ~ ( c_in @ A @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(343,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ ( c_Orderings_Oord__class_Omax @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__max_Ole__supI1_0) ).
thf(1268,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ ( c_Orderings_Oord__class_Omax @ C @ D @ A ) @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(292,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Oinj__on @ A @ ( c_Set_Oimage @ B @ C @ D @ D ) @ D @ E )
| ~ ( c_Fun_Oinj__on @ A @ C @ D @ E )
| ~ ( c_Fun_Oinj__on @ B @ C @ D @ D )
| ( ( hAPP @ A @ ( c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__1 @ C @ B @ A @ D @ E ) )
= ( hAPP @ A @ ( c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__2 @ C @ B @ A @ D @ E ) ) )
| ( ( hAPP @ A @ ( hAPP @ B @ ( c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__1 @ C @ B @ A @ D @ E ) ) )
= ( hAPP @ A @ ( hAPP @ B @ ( c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__2 @ C @ B @ A @ D @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inj__on__image__iff_5) ).
thf(1152,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Oinj__on @ A @ ( c_Set_Oimage @ B @ C @ D @ D ) @ D @ E )
| ~ ( c_Fun_Oinj__on @ A @ C @ D @ E )
| ~ ( c_Fun_Oinj__on @ B @ C @ D @ D )
| ( ( hAPP @ A @ ( c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__1 @ C @ B @ A @ D @ E ) )
= ( hAPP @ A @ ( c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__2 @ C @ B @ A @ D @ E ) ) )
| ( ( hAPP @ A @ ( hAPP @ B @ ( c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__1 @ C @ B @ A @ D @ E ) ) )
= ( hAPP @ A @ ( hAPP @ B @ ( c_ATP__Linkup_Osko__Fun__Xinj__on__image__iff__1__2 @ C @ B @ A @ D @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(458,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D )
| ~ ( c_in @ A @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__iff_2) ).
thf(1532,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D )
| ~ ( c_in @ A @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).
thf(394,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_lessequals @ B @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).
thf(1384,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_lessequals @ B @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(42,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Fun_Ofun__upd @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E ) @ F @ G @ D @ E )
= ( c_Fun_Ofun__upd @ ( c_Fun_Ofun__upd @ A @ F @ G @ D @ E ) @ B @ C @ D @ E ) )
| ( B = F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__upd__twist_0) ).
thf(596,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Fun_Ofun__upd @ ( c_Fun_Ofun__upd @ A @ B @ C @ D @ E ) @ F @ G @ D @ E )
= ( c_Fun_Ofun__upd @ ( c_Fun_Ofun__upd @ A @ F @ G @ D @ E ) @ B @ C @ D @ E ) )
| ( B = F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(481,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
!= ( c_Set_Oimage @ B @ C @ D @ A ) )
| ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__is__image_0) ).
thf(1582,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
!= ( c_Set_Oimage @ B @ C @ D @ A ) )
| ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).
thf(11,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_HOL_Oord__class_Oless @ B @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_Orderings_Oord__class_Omax @ D @ C @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__max__iff__disj_0) ).
thf(528,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_HOL_Oord__class_Oless @ B @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_Orderings_Oord__class_Omax @ D @ C @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(444,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Set_Oinsert @ C @ D @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) )
| ( c_in @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__right_1) ).
thf(1500,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Set_Oinsert @ C @ D @ A ) )
= ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ D ) )
| ( c_in @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(84,axiom,
! [B: $i,A: $i] :
( ( class_Orderings_Opreorder @ ( tc_fun @ A @ B ) )
| ~ ( class_Orderings_Opreorder @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Opreorder) ).
thf(691,plain,
! [B: $i,A: $i] :
( ( class_Orderings_Opreorder @ ( tc_fun @ A @ B ) )
| ~ ( class_Orderings_Opreorder @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(168,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ( c_HOL_Oord__class_Oless @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__iff__psubset__eq_0) ).
thf(871,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ( c_HOL_Oord__class_Oless @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(446,axiom,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ A @ C ) @ ( tc_fun @ C @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insertI_0) ).
thf(1505,plain,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ A @ C ) @ ( tc_fun @ C @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(47,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__irrefl_0) ).
thf(607,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(328,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Set_Ovimage @ B @ C @ D @ E ) @ D )
| ~ ( c_in @ ( hAPP @ B @ A ) @ C @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimageI2_0) ).
thf(1236,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Set_Ovimage @ B @ C @ D @ E ) @ D )
| ~ ( c_in @ ( hAPP @ B @ A ) @ C @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(218,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
= C )
| ~ ( c_in @ B @ ( c_Set_Ovimage @ A @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ E @ D ) @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__singleton__eq_0) ).
thf(987,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
= C )
| ~ ( c_in @ B @ ( c_Set_Ovimage @ A @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ E @ D ) @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(184,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Fun_Othe__inv__into @ A @ B @ C @ D ) @ ( hAPP @ B @ E ) )
= E )
| ~ ( c_in @ E @ A @ C )
| ~ ( c_Fun_Oinj__on @ B @ A @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_the__inv__into__f__f_0) ).
thf(908,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Fun_Othe__inv__into @ A @ B @ C @ D ) @ ( hAPP @ B @ E ) )
= E )
| ~ ( c_in @ E @ A @ C )
| ~ ( c_Fun_Oinj__on @ B @ A @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(220,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Fun_Oinj__on @ A @ B @ C @ C )
| ~ ( c_lessequals @ B @ ( c_Set_Oimage @ A @ B @ C @ C ) @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__surj__inj_0) ).
thf(992,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Fun_Oinj__on @ A @ B @ C @ C )
| ~ ( c_lessequals @ B @ ( c_Set_Oimage @ A @ B @ C @ C ) @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(487,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_Finite__Set_Ofold__graph @ C @ D @ A @ E @ B @ F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fold__graph__imp__finite_0) ).
thf(1597,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_Finite__Set_Ofold__graph @ C @ D @ A @ E @ B @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).
thf(216,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ C ) @ D ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_min__less__iff__conj_0) ).
thf(982,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Omin @ A ) @ C ) @ D ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(198,axiom,
class_Lattices_Olattice @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olattice) ).
thf(940,plain,
class_Lattices_Olattice @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(305,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__empty__right_0) ).
thf(1184,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(473,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ D @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__psubset__trans_0) ).
thf(1565,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_HOL_Oord__class_Oless @ D @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).
thf(114,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Ovimage @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ C @ B )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__UNIV_0) ).
thf(755,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Ovimage @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ C @ B )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(92,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oimage @ ( c_COMBK @ A @ B @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C @ B )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__constant__conv_0) ).
thf(708,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oimage @ ( c_COMBK @ A @ B @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C @ B )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(173,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C )
!= B )
| ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__inf_1) ).
thf(882,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C )
!= B )
| ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(371,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
| ( c_in @ B @ A @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_2) ).
thf(1331,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
| ( c_in @ B @ A @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(491,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_in @ B @ A @ D )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) )
| ( c_in @ B @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_4) ).
thf(1606,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_in @ B @ A @ D )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) )
| ( c_in @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).
thf(195,axiom,
! [B: $i,A: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__subsetI_0) ).
thf(935,plain,
! [B: $i,A: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(229,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( c_lessequals @ D @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I6_J_0) ).
thf(1009,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( c_lessequals @ D @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(440,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ~ ( c_in @ A @ D @ C )
| ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__iff_0) ).
thf(1490,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ~ ( c_in @ A @ D @ C )
| ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).
thf(124,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C )
!= ( c_Orderings_Otop__class_Otop @ A ) )
| ( C
= ( c_Orderings_Otop__class_Otop @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__eq__top__eq2_0) ).
thf(775,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A ) @ B ) @ C )
!= ( c_Orderings_Otop__class_Otop @ A ) )
| ( C
= ( c_Orderings_Otop__class_Otop @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(409,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ( A = B )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__eq_2) ).
thf(1417,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ( A = B )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(211,axiom,
! [C: $i,B: $i,A: $i] : ( c_in @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertCI_1) ).
thf(972,plain,
! [C: $i,B: $i,A: $i] : ( c_in @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(1882,plain,
$false,
inference(cvc4,[status(thm)],[1036,1337,1411,1469,1633,1105,846,628,962,941,1295,1549,1110,645,892,1168,760,1315,518,1200,977,1290,1068,994,1569,1073,1544,1205,1591,878,614,1437,861,1486,523,1158,762,1608,1137,1310,550,797,1275,1222,670,1260,698,1342,747,538,1354,1001,1576,841,1359,565,1529,1243,1127,973,885,1601,1386,1228,1482,1254,724,1287,1430,1298,785,1264,1323,802,1455,1191,542,1511,917,702,751,1313,1279,1462,1059,1132,1545,559,1379,1147,1319,1479,1398,1115,1100,1232,638,853,606,1572,1465,789,1450,591,1373,1040,623,1151,806,1051,1020,574,766,634,734,1447,1526,1351,660,998,1433,507,1119,1622,920,512,678,925,1306,810,1338,714,1636,1047,1163,1091,778,1580,1123,1217,820,561,1370,729,1238,1560,957,1223,894,693,630,1423,566,1365,625,1555,1178,1457,1624,1210,757,1281,710,1012,1296,665,583,830,1079,1027,682,1195,1407,1402,742,1270,948,615,1328,1064,1498,1425,1096,1006,593,869,783,1089,1234,1541,874,1143,1534,1017,1567,1160,1082,1361,1292,1182,642,1414,1214,1207,970,1155,554,753,901,686,837,1588,515,738,1382,1266,654,569,1393,1525,647,1263,984,911,1599,1246,1333,792,508,541,1054,1170,1071,1515,530,718,1086,938,773,794,586,906,1135,965,1273,856,1301,1631,601,1219,824,843,1620,1388,579,1520,1124,562,904,975,875,826,1256,1226,545,1488,1503,936,572,1312,787,804,1258,1356,1117,736,1349,1122,764,979,604,1574,1011,990,996,1492,1603,509,880,649,1043,599,1376,1439,863,1175,890,1471,1080,535,816,609,726,1325,1149,915,1344,769,1022,668,858,552,848,700,932,1061,521,1198,1474,1594,768,636,780,1015,1113,1435,1477,1250,922,658,1562,1066,1445,851,1102,1076,1626,722,675,1203,944,1467,680,1420,927,1277,749,617,1340,1145,1551,1049,663,548,968,1181,823,1547,525,580,640,1025,1400,887,1368,1484,1098,712,1003,705,1611,954,1252,673,1637,1038,1317,576,1188,1186,1538,951,808,1404,744,703,1536,656,1284,1506,1427,1008,612,1585,1094,1140,1240,1617,845,1084,1459,556,539,1553,1321,688,581,1412,1517,1126,1390,1453,771,1108,588,813,896,1639,1508,946,652,1629,632,1523,731,1558,1030,914,929,1308,1193,1212,1513,899,1442,1045,832,684,716,1614,800,1578,833,835,1229,1395,818,1593,1303,1248,867,865,999,620,1436,1363,1495,506,1335,1056,1033,828,960,532,696,1346,1172,1410,720,1165,839,740,1129,1268,1152,1532,1384,596,1582,528,1500,691,871,1505,607,1236,987,908,992,1597,982,940,1184,1565,755,708,882,1331,1606,935,1009,1490,775,1417,972]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWV880-1 : TPTP v8.1.2. Released v4.1.0.
% 0.11/0.15 % Command : run_Leo-III %s %d
% 0.15/0.35 % Computer : n025.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Fri May 19 03:03:34 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.99/0.90 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.78/1.13 % [INFO] Parsing done (230ms).
% 1.78/1.14 % [INFO] Running in sequential loop mode.
% 2.27/1.34 % [INFO] eprover registered as external prover.
% 2.27/1.34 % [INFO] cvc4 registered as external prover.
% 2.27/1.35 % [INFO] Scanning for conjecture ...
% 2.66/1.46 % [INFO] Found a conjecture and 503 axioms. Running axiom selection ...
% 2.99/1.56 % [INFO] Axiom selection finished. Selected 501 axioms (removed 2 axioms).
% 3.80/1.71 % [INFO] Problem is propositional (TPTP CNF).
% 3.95/1.72 % [INFO] Type checking passed.
% 3.95/1.72 % [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 ...
% 10.92/3.34 % External prover 'cvc4' found a proof!
% 10.92/3.34 % [INFO] Killing All external provers ...
% 10.92/3.35 % Time passed: 2833ms (effective reasoning time: 2203ms)
% 10.92/3.35 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 10.92/3.35 % Axioms used in derivation (501): cls_inj__image__mem__iff_1, clsarity_fun__Lattices_Olower__semilattice, cls_inf__sup__aci_I2_J_0, cls_xt1_I9_J_0, cls_linorder__antisym__conv2_1, cls_Int__absorb2_0, cls_subset__insert_1, cls_Diff__iff_2, cls_Min__insert_0, clsarity_nat__HOL_Oord, cls_vimage__code_0, cls_Diff__cancel_0, cls_min__max_Oinf__commute_0, cls_Diff1__fold__graph_0, cls_min__max_Ole__infE_0, cls_order__le__less__trans_0, cls_min__max_Oless__infI1_0, cls_image__constant_0, cls_insertE_0, cls_less__fun__def_1, cls_order__less__le__trans_0, cls_order__eq__iff_0, cls_equalityI_0, cls_insert__inter__insert_0, cls_min__max_Osup__inf__distrib1_0, cls_inj__on__iff__eq__card_0, cls_setsum__diff_0, cls_inj__on__image__iff_4, cls_subset__empty_1, cls_finite__insert_0, cls_min__max_Oinf__sup__distrib1_0, cls_the__inv__f__f_0, cls_min__max_Oinf__le1_0, cls_empty__is__image_1, cls_inj__image__eq__iff_0, cls_min__less__iff__conj_0, cls_image__mono_0, cls_insert__code_1, cls_fun__upd__apply_1, cls_le__funD_0, cls_fun__upd__image_1, cls_xt1_I12_J_0, cls_finite__subset__induct_2, cls_subset__image__iff_2, cls_min__max_Ole__sup__iff_2, cls_inj__on__image__Int_0, clsarity_bool__Lattices_Olower__semilattice, cls_Int__mono_0, cls_finite__vimageI_0, cls_linorder__neqE_0, cls_le__iff__inf_1, clsarity_fun__Orderings_Oorder, cls_image__Int_0, cls_Min__eqI_1, cls_vimage__Diff_0, cls_COMBK__def_0, cls_min__max_Osup__inf__absorb_0, cls_Int__insert__left_0, cls_insert__absorb_0, cls_Int__subset__iff_2, cls_le__inf__iff_1, cls_fold__graph__imp__finite_0, cls_min__less__iff__disj_2, cls_the__inv__into__onto_0, cls_mem__def_1, cls_fun__upd__image_0, clsarity_nat__Orderings_Olinorder, cls_empty__iff_0, cls_Min__le_0, cls_image__vimage__subset_0, cls_inj__on__image__set__diff_0, cls_min__less__iff__disj_0, cls_inf1E_1, cls_min__max_Oinf__sup__distrib2_0, cls_Diff__triv_0, cls_insert__iff_1, cls_le__maxI2_0, cls_insert__subset_0, cls_card__insert__if_0, cls_Int__absorb1_0, cls_finite__subset__induct_3, cls_fold__graph_H_Ointros_I2_J_0, cls_setsum__diff1__nat_1, cls_vimage__UNIV_0, cls_order__less__trans_0, cls_fold__graph_H_Ointros_I1_J_0, cls_inj__image__subset__iff_0, cls_Diff__insert_0, cls_set__rev__mp_0, cls_insert__Diff__if_1, cls_inf__left__commute_0, cls_inf__commute_0, cls_inj__image__mem__iff_0, cls_subset__insert__iff_2, cls_inj__on__image__iff_5, cls_Min__singleton_0, clsarity_bool__Finite__Set_Ofinite_Ofinite, cls_less__max__iff__disj_0, cls_finite__insert_1, clsarity_fun__Orderings_Otop, cls_less__max__iff__disj_2, cls_f__inv__into__f_0, clsarity_bool__HOL_Oord, cls_set__mp_0, cls_setsum__diff1_1, cls_finite__Int_1, cls_Int__empty__right_0, cls_min__max_Oless__infI2_0, cls_not__psubset__empty_0, cls_linorder__not__less_0, cls_psubset__insert__iff_8, cls_order__less__asym_0, cls_min__max_Ole__inf__iff_1, cls_order__eq__refl_0, cls_order__le__less_0, cls_rangeI_0, cls_order__less__asym_H_0, cls_rev__image__eqI_0, cls_linorder__antisym__conv1_0, cls_inj__on__insert_0, cls_image__subset__iff_2, cls_fun__upd__other_0, cls_linorder__antisym__conv2_0, cls_empty__is__image_0, cls_psubset__eq_1, clsarity_fun__Orderings_Obot, cls_f__the__inv__into__f_0, cls_finite__subset__induct_1, cls_Diff__UNIV_0, cls_the__inv__into__into_0, cls_min__max_Ole__infE_1, cls_insert__ident_0, cls_weak__coinduct_0, cls_inv__f__eq_0, cls_lessThan__subset__iff_1, cls_image__constant__conv_1, cls_vimageI_0, cls_psubset__insert__iff_5, cls_finite__Int_0, cls_psubset__trans_0, cls_inv__image__comp_0, clsarity_bool__Orderings_Oorder, cls_bot__least_0, cls_less__le__not__le_2, cls_min__max_Odistrib__inf__le_0, cls_xt1_I10_J_0, cls_le__maxI1_0, cls_Int__insert__right_1, cls_not__less__iff__gr__or__eq_0, cls_min__max_Ole__supE_0, cls_inf__top__right_0, cls_Max__mono_0, cls_min__max_Osup__least_0, cls_min__max_Ole__sup__iff_1, cls_lessThan__eq__iff_0, cls_singleton__iff_1, cls_min__max_Osup__left__idem_0, cls_subset__iff_0, cls_insert__code_2, cls_lessThan__iff_0, clsarity_fun__HOL_Oord, cls_Diff__idemp_0, cls_subset__empty_0, cls_rev__predicate1D_0, cls_inf__eq__top__eq1_0, cls_max__diff__distrib__left_0, cls_finite_0, cls_insert__Diff__single_0, cls_inv__into__image__cancel_0, cls_image__insert_0, cls_finite__Diff_0, cls_inv__into__f__f_0, cls_inf__absorb2_0, cls_le__max__iff__disj_1, cls_fold__graph_OinsertI_0, cls_inf__sup__ord_I2_J_0, cls_doubleton__eq__iff_2, cls_finite__subset__image_2, cls_min__max_Ole__infI2_0, cls_diff__single__insert_0, clsarity_fun__Finite__Set_Ofinite_Ofinite, cls_UNIV__not__empty_0, cls_min__max_Ole__iff__inf_1, cls_vimage__singleton__eq_1, cls_subset__insert__iff_3, cls_min__max_Oless__supI1_0, cls_fun__upd__triv_0, clsarity_nat__Orderings_Obot, cls_xt1_I8_J_0, cls_inf__sup__aci_I3_J_0, cls_set__eq__subset_2, cls_less__infI1_0, cls_Int__insert__left_1, cls_insert__subset_1, cls_psubset__insert__iff_4, cls_Min__eqI_0, clsarity_nat__Lattices_Olower__semilattice, cls_min__max_Ole__inf__iff_0, cls_inj__image__subset__iff_1, cls_ex__in__conv_0, cls_finite__subset__induct_4, cls_finite__surj_0, cls_min__max_Oinf__assoc_0, cls_vimage__const_1, cls_inj__on__image__iff_2, cls_Int__empty__left_0, cls_min__max_Oinf__idem_0, cls_le__inf__iff_0, cls_Int__subset__iff_1, cls_subset__iff__psubset__eq_0, cls_linorder__linear_0, cls_inj__on__the__inv__into_0, cls_min__max_Odistrib__sup__le_0, cls_inj__on__inv__into_0, cls_min__max_Oinf__left__idem_0, cls_min__max_Ole__supI_0, cls_fold__graph_OemptyI_0, clsarity_fun__Lattices_Olattice, cls_min__le__iff__disj_0, cls_min__max_Osup__idem_0, cls_not__leE_0, cls_Int__assoc_0, cls_inj__on__image__iff_6, cls_order__antisym_0, cls_order__trans_0, cls_psubset__insert__iff_9, cls_max__less__iff__conj_2, cls_subset__trans_0, cls_double__diff_0, cls_inf__le2_0, cls_image__empty_0, cls_finite__UNIV_0, cls_insertI1_0, cls_DiffI_0, cls_psubset__insert__iff_6, clsarity_bool__Orderings_Opreorder, cls_empty__not__insert_0, cls_insert__Diff1_0, cls_lessThan__subset__iff_0, cls_Diff__Int__distrib2_0, cls_image__constant__conv_0, cls_linorder__antisym__conv1_1, cls_inj__on__insert_1, clsarity_bool__Orderings_Obot, cls_mem__def_0, cls_linorder__not__le_1, cls_image__subsetI_1, cls_Diff__insert2_0, cls_min__max_Ole__sup__iff_0, cls_Int__commute_0, cls_empty__subsetI_0, cls_top__greatest_0, cls_fun__upd__twist_0, cls_image__subset__iff_1, cls_doubleton__eq__iff_0, cls_inf__sup__aci_I1_J_0, cls_subset__refl_0, cls_Max__singleton_0, cls_vimage__subsetI_0, cls_singletonE_0, cls_image__diff__subset_0, clsarity_nat__Lattices_Olattice, cls_inj__on__empty_0, cls_Int__Diff_0, cls_image__iff_2, cls_insertCI_0, cls_psubset__eq_0, cls_fun__upd__apply_0, cls_image__Int__subset_0, cls_le__inf__iff_2, cls_image__set__diff_0, cls_vimage__Int_0, cls_inj__on__iff_0, clsarity_nat__Orderings_Opreorder, cls_insert__Diff_0, cls_not__less__iff__gr__or__eq_1, cls_UNIV__I_0, cls_DiffE_0, cls_order__le__neq__trans_0, cls_le__infE_0, cls_top1I_0, cls_order__eq__iff_2, cls_le__infI1_0, cls_finite__subset__induct_0, cls_inf__assoc_0, cls_linorder__neqE__ordered__idom_0, cls_Int__lower2_0, cls_inj__vimage__image__eq_0, cls_insert__mono_0, cls_Int__UNIV__right_0, cls_less__le__not__le_1, cls_Max__ge_0, cls_bex__empty_0, cls_bot1E_0, cls_linorder__antisym__conv3_0, cls_min__max_Oinf__greatest_0, cls_Int__absorb_0, cls_subset__insertI2_0, cls_Diff__disjoint_0, cls_psubset__insert__iff_0, cls_min__max_Osup__absorb1_0, cls_psubset__insert__iff_1, cls_inf__eq__top__eq2_0, cls_vimage__const_0, cls_vimage__mono_0, cls_Int__left__absorb_0, cls_order__neq__le__trans_0, cls_doubleton__eq__iff_3, cls_finite__Diff__insert_1, cls_inj__on__fun__updI_0, cls_Diff__Int__distrib_0, cls_finite__Diff2_1, cls_Diff__mono_0, cls_order__le__less_1, cls_linorder__neq__iff_1, cls_psubset__subset__trans_0, cls_inj__on__def_0, cls_order__antisym__conv_0, cls_psubsetD_0, cls_max__less__iff__conj_1, cls_Int__lower1_0, clsarity_bool__Lattices_Olattice, cls_psubset__insert__iff_3, cls_injD_0, cls_finite__subset__image_1, cls_eq__eqI_0, cls_vimage__eq_1, cls_order__less__le_2, clsarity_bool__Lattices_Obounded__lattice, cls_inf__sup__ord_I1_J_0, cls_min__max_Ole__infI1_0, cls_le__infI_0, cls_min__max_Oinf__sup__absorb_0, cls_subset__insert__iff_4, cls_Int__subset__iff_0, cls_linorder__less__linear_0, cls_eq__card__imp__inj__on_0, cls_finite__subset_0, cls_vimageE_0, cls_insert__subset_2, cls_le__eqI_0, cls_subsetD_0, cls_finite__imageD_0, cls_insert__not__empty_0, cls_Int__left__commute_0, cls_inf__idem_0, clsarity_fun__Lattices_Obounded__lattice, clsarity_fun__Complete__Lattice_Ocomplete__lattice, cls_card__image_0, cls_min__max_Osup__inf__distrib2_0, cls_inf__bot__left_0, cls_inf1I_0, cls_min__max_Ole__supI1_0, cls_inj__on__image__iff_7, cls_card__bij__eq_0, cls_xt1_I11_J_0, cls_card__Diff__singleton__if_1, cls_fun__upd__idem_0, cls_min__max_Osup__left__commute_0, cls_finite__Diff__insert_0, cls_inf__sup__aci_I4_J_0, cls_vimage__singleton__eq_0, cls_min__max_Ole__inf__iff_2, cls_min__max_Ole__iff__sup_1, cls_min__less__iff__conj_2, cls_subset__singletonD_0, cls_Int__iff_2, cls_vimage__code_1, cls_min__max_Oinf__le2_0, cls_doubleton__eq__iff_1, cls_le__max__iff__disj_2, cls_fun__upd__idem__iff_0, cls_insert__absorb2_0, cls_inj__on__image__iff_1, cls_xt1_I6_J_0, cls_subset__insert__iff_0, cls_the__inv__into__f__eq_0, cls_inf__greatest_0, cls_inv__into__injective_0, cls_subset__psubset__trans_0, clsarity_bool__Complete__Lattice_Ocomplete__lattice, cls_inf__min_0, cls_setsum__diff1_0, cls_min__max_Oinf__absorb2_0, cls_linorder__not__le_0, cls_IntI_0, cls_min__max_Oinf__left__commute_0, cls_Diff__empty_0, cls_min__max_Osup__assoc_0, cls_le__iff__inf_0, cls_setsum__diff1__ring_0, cls_subset__insert_0, cls_emptyE_0, cls_fun__upd__same_0, cls_less__infI2_0, cls_eq__eqI_1, cls_comm__monoid__add_Ononempty__iff_2, cls_min__max_Oless__supI2_0, cls_less__fun__def_2, cls_order__less__irrefl_0, cls_Max__eqI_0, cls_subset__inj__on_0, cls_singleton__inject_0, cls_less__eqI_0, cls_vimageI2_0, cls_inj__on__image__iff_3, cls_IntE_1, cls_le__max__iff__disj_0, cls_min__le__iff__disj_1, cls_Int__greatest_0, cls_min__diff__distrib__left_0, cls_inj__onD_0, clsarity_fun__Orderings_Opreorder, cls_min__le__iff__disj_2, cls_IntE_0, cls_image__subsetI_0, cls_min__max_Ole__infI_0, cls_inj__on__contraD_0, cls_empty__fold__graphE_0, cls_finite__surj__inj_0, cls_le__infE_1, cls_finite_OemptyI_0, cls_card__eq__UNIV__imp__eq__UNIV_0, cls_Int__UNIV__left_0, cls_image__eqI_0, cls_the__inv__into__f__f_0, cls_subset__UNIV_0, cls_image__subset__iff_0, cls_inf__le1_0, cls_finite__imageI_0, cls_inf__left__idem_0, cls_doubleton__eq__iff_4, cls_Max__in_0, cls_Max__insert_0, cls_inj__on__diff_0, cls_inj__on__insert_2, cls_inv__into__into_0, cls_insertCI_1, cls_min__max_Ole__iff__inf_0, cls_min__max_Ole__iff__sup_0, cls_less__max__iff__disj_1, cls_insert__code_0, cls_le__eqI_1, cls_subset__insertI_0, cls_vimageD_0, cls_min__max_Ole__supI2_0, cls_order__less__imp__le_0, cls_DiffE_1, cls_max__less__iff__conj_0, cls_Diff__Int2_0, cls_inj__on__image__iff_0, cls_inv__f__f_0, cls_Diff__insert__absorb_0, cls_insert__image_0, cls_rev__finite__subset_0, cls_fun__upd__upd_0, cls_psubset__insert__iff_2, cls_Max__eqI_1, cls_disjoint__iff__not__equal_0, cls_image__vimage__eq_0, cls_inf__top__left_0, cls_vimage__empty_0, cls_gfp__upperbound_0, cls_endo__inj__surj_0, cls_insert__commute_0, cls_insert__iff_2, cls_le__infI2_0, cls_min__max_Ole__supE_1, clsarity_nat__Orderings_Oorder, cls_linorder__not__less_1, cls_image__is__empty_0, cls_Min__in_0, cls_psubset__insert__iff_7, cls_equalityE_0, cls_min__max_Osup__commute_0, cls_imageI_0, cls_inf__bot__right_0, cls_weak__coinduct__image_0, cls_less__eqI_1, cls_finite__Diff2_0, cls_order__less__le_1, cls_less__fun__def_0, cls_min__less__iff__conj_1, cls_xt1_I7_J_0, clsarity_bool__Orderings_Otop, cls_psubset__eq_2, cls_Min__antimono_0, cls_lessThan__iff_1, cls_image__inv__f__f_0, cls_subset__insert__iff_1, cls_min__less__iff__disj_1, cls_single__Diff__lessThan_0, cls_ball__empty_0, cls_finite__subset__image_0, cls_inv__into__f__eq_0, cls_Int__insert__right_0, cls_Diff__subset_0, cls_predicate1D_0, cls_inf1E_0, cls_empty__Diff_0, cls_fun__upd__idem__iff_1
% 10.92/3.35 % No. of inferences in proof: 1011
% 10.92/3.35 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2833 ms resp. 2203 ms w/o parsing
% 11.40/3.52 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 11.40/3.52 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------