TSTP Solution File: SCT071-1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SCT071-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n017.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 11:50:22 EDT 2023
% Result : Unsatisfiable 11.86s 3.49s
% Output : Refutation 12.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 486
% Syntax : Number of formulae : 922 ( 305 unt; 51 typ; 0 def)
% Number of atoms : 1759 ( 546 equ; 0 cnn)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 12754 ( 840 ~; 888 |; 0 &;11026 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 121 ( 121 >; 0 *; 0 +; 0 <<)
% Number of symbols : 53 ( 51 usr; 5 con; 0-5 aty)
% Number of variables : 2700 ( 0 ^;2700 !; 0 ?;2700 :)
% Comments :
%------------------------------------------------------------------------------
thf(v_thesis_____type,type,
v_thesis____: $o ).
thf(c_Set_Oinsert_type,type,
c_Set_Oinsert: $i > $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_Orderings_Oorder_type,type,
class_Orderings_Oorder: $i > $o ).
thf(c_lessequals_type,type,
c_lessequals: $i > $i > $i > $o ).
thf(c_Fun_Obij_type,type,
c_Fun_Obij: $i > $i > $i > $o ).
thf(c_Fun_Oid_type,type,
c_Fun_Oid: $i > $i ).
thf(c_Fun_Ocomp_type,type,
c_Fun_Ocomp: $i > $i > $i > $i > $i > $i ).
thf(hAPP_type,type,
hAPP: $i > $i > $i ).
thf(c_HOL_Ominus__class_Ominus_type,type,
c_HOL_Ominus__class_Ominus: $i > $i > $i > $i ).
thf(c_SetInterval_Oord__class_OlessThan_type,type,
c_SetInterval_Oord__class_OlessThan: $i > $i > $i ).
thf(c_SetInterval_Oord__class_OatLeastLessThan_type,type,
c_SetInterval_Oord__class_OatLeastLessThan: $i > $i > $i > $i ).
thf(tc_nat_type,type,
tc_nat: $i ).
thf(c_Hilbert__Choice_Oinv__into_type,type,
c_Hilbert__Choice_Oinv__into: $i > $i > $i > $i > $i ).
thf(c_Orderings_Otop__class_Otop_type,type,
c_Orderings_Otop__class_Otop: $i > $i ).
thf(c_HOL_Ouminus__class_Ouminus_type,type,
c_HOL_Ouminus__class_Ouminus: $i > $i ).
thf(c_Lattices_Olower__semilattice__class_Oinf_type,type,
c_Lattices_Olower__semilattice__class_Oinf: $i > $i > $i > $i ).
thf(c_Lattices_Oupper__semilattice__class_Osup_type,type,
c_Lattices_Oupper__semilattice__class_Osup: $i > $i > $i > $i ).
thf(class_Complete__Lattice_Ocomplete__lattice_type,type,
class_Complete__Lattice_Ocomplete__lattice: $i > $o ).
thf(c_Complete__Lattice_OSup__class_OSup_type,type,
c_Complete__Lattice_OSup__class_OSup: $i > $i > $i ).
thf(c_Fun_Osurj_type,type,
c_Fun_Osurj: $i > $i > $i > $o ).
thf(c_Finite__Set_Ofinite_type,type,
c_Finite__Set_Ofinite: $i > $i > $o ).
thf(class_Nat_Osemiring__char__0_type,type,
class_Nat_Osemiring__char__0: $i > $o ).
thf(c_Nat_Osemiring__1__class_Oof__nat_type,type,
c_Nat_Osemiring__1__class_Oof__nat: $i > $i > $i ).
thf(c_Fun_Oinj__on_type,type,
c_Fun_Oinj__on: $i > $i > $i > $i > $o ).
thf(c_Set_Ovimage_type,type,
c_Set_Ovimage: $i > $i > $i > $i > $i ).
thf(c_Set_Oimage_type,type,
c_Set_Oimage: $i > $i > $i > $i > $i ).
thf(c_Finite__Set_Ocard_type,type,
c_Finite__Set_Ocard: $i > $i > $i ).
thf(c_Fun_Obij__betw_type,type,
c_Fun_Obij__betw: $i > $i > $i > $i > $i > $o ).
thf(c_Fun_Othe__inv__into_type,type,
c_Fun_Othe__inv__into: $i > $i > $i > $i > $i ).
thf(c_Suc_type,type,
c_Suc: $i > $i ).
thf(c_List_Omap_type,type,
c_List_Omap: $i > $i > $i > $i > $i ).
thf(c_HOL_Ozero__class_Ozero_type,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
thf(c_COMBB_type,type,
c_COMBB: $i > $i > $i > $i > $i > $i ).
thf(class_Finite__Set_Ofinite_Ofinite_type,type,
class_Finite__Set_Ofinite_Ofinite: $i > $o ).
thf(c_Typedef_Otype__definition_type,type,
c_Typedef_Otype__definition: $i > $i > $i > $i > $i > $o ).
thf(class_Ring__and__Field_Osemiring__1_type,type,
class_Ring__and__Field_Osemiring__1: $i > $o ).
thf(c_List_Osko__SetInterval__Xex__bij__betw__nat__finite__1__1_type,type,
c_List_Osko__SetInterval__Xex__bij__betw__nat__finite__1__1: $i > $i > $i ).
thf(tc_Arrow__Order__Mirabelle_Oindi_type,type,
tc_Arrow__Order__Mirabelle_Oindi: $i ).
thf(c_ATP__Linkup_Osko__Fun__XinjI__1__1_type,type,
c_ATP__Linkup_Osko__Fun__XinjI__1__1: $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Fun__XinjI__1__2_type,type,
c_ATP__Linkup_Osko__Fun__XinjI__1__2: $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__imp__inv__eq__1__1_type,type,
c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__imp__inv__eq__1__1: $i > $i > $i > $i > $i ).
thf(c_List_OremoveAll_type,type,
c_List_OremoveAll: $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Fun__Xdatatype__injI__1__1_type,type,
c_ATP__Linkup_Osko__Fun__Xdatatype__injI__1__1: $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Fun__Xdatatype__injI__1__2_type,type,
c_ATP__Linkup_Osko__Fun__Xdatatype__injI__1__2: $i > $i > $i > $i ).
thf(c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1_type,type,
c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1: $i > $i > $i ).
thf(class_Ring__and__Field_Osemiring__0_type,type,
class_Ring__and__Field_Osemiring__0: $i > $o ).
thf(435,axiom,
! [A: $i] :
( ( ( c_Set_Oimage @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi @ tc_nat )
!= ( c_SetInterval_Oord__class_OatLeastLessThan @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Finite__Set_Ocard @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ tc_nat ) )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi @ tc_nat )
| v_thesis____ ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_that_0) ).
thf(1411,plain,
! [A: $i] :
( ( ( c_Set_Oimage @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi @ tc_nat )
!= ( c_SetInterval_Oord__class_OatLeastLessThan @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Finite__Set_Ocard @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi ) @ tc_nat ) )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi @ tc_nat )
| v_thesis____ ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(218,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ B ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__SucE_0) ).
thf(909,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ B ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(211,axiom,
! [A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ A @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__empty_2) ).
thf(893,plain,
! [A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ A @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(394,axiom,
! [B: $i,A: $i] : ( c_lessequals @ A @ A @ ( tc_fun @ B @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equalityE_0) ).
thf(1315,plain,
! [B: $i,A: $i] : ( c_lessequals @ A @ A @ ( tc_fun @ B @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(240,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ D @ A ) @ ( tc_fun @ A @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastLessThan @ D @ C @ A ) )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ivl__diff_0) ).
thf(962,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_HOL_Ominus__class_Ominus @ ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ D @ A ) @ ( tc_fun @ A @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastLessThan @ D @ C @ A ) )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(337,axiom,
( ( c_SetInterval_Oord__class_OlessThan @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_nat @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lessThan__0_0) ).
thf(1179,plain,
( ( c_SetInterval_Oord__class_OlessThan @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_nat @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(21,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
!= ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
| ( B = D )
| ( A = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_1) ).
thf(481,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)],[21]) ).
thf(94,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ D @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__Un_0) ).
thf(645,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ D @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(210,axiom,
class_Complete__Lattice_Ocomplete__lattice @ tc_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Complete__Lattice_Ocomplete__lattice) ).
thf(892,plain,
class_Complete__Lattice_Ocomplete__lattice @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(20,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/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_1) ).
thf(479,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)],[20]) ).
thf(302,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oimage @ ( c_Fun_Ocomp @ A @ B @ C @ D @ E ) @ F @ E @ D )
= ( c_Set_Oimage @ A @ ( c_Set_Oimage @ B @ F @ E @ C ) @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__compose_0) ).
thf(1105,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oimage @ ( c_Fun_Ocomp @ A @ B @ C @ D @ E ) @ F @ E @ D )
= ( c_Set_Oimage @ A @ ( c_Set_Oimage @ B @ F @ E @ C ) @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(256,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__subset__iff_0) ).
thf(1005,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(433,axiom,
! [B: $i,A: $i] :
( ( c_Fun_Osurj @ A @ B @ B )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ B @ B )
| ~ ( c_Finite__Set_Ofinite @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__UNIV__inj__surj_0) ).
thf(1406,plain,
! [B: $i,A: $i] :
( ( c_Fun_Osurj @ A @ B @ B )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ B @ B )
| ~ ( c_Finite__Set_Ofinite @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(111,axiom,
! [B: $i,A: $i] :
( ( A
= ( c_Suc @ B ) )
| ( c_lessequals @ A @ B @ tc_nat )
| ~ ( c_lessequals @ A @ ( c_Suc @ B ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__SucE_0) ).
thf(683,plain,
! [B: $i,A: $i] :
( ( A
= ( c_Suc @ B ) )
| ( c_lessequals @ A @ B @ tc_nat )
| ~ ( c_lessequals @ A @ ( c_Suc @ B ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(133,axiom,
! [B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ B @ ( tc_fun @ A @ tc_bool ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Compl__partition2_0) ).
thf(730,plain,
! [B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ B @ ( tc_fun @ A @ tc_bool ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(284,axiom,
class_Finite__Set_Ofinite_Ofinite @ tc_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Finite__Set_Ofinite_Ofinite) ).
thf(1068,plain,
class_Finite__Set_Ofinite_Ofinite @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(252,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ D @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__Int_0) ).
thf(994,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ D @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(138,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ A ) @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__eq__Suc__le_1) ).
thf(741,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ A ) @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(375,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/sandbox2/benchmark/theBenchmark.p',cls_inv__into__image__cancel_0) ).
thf(1269,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)],[375]) ).
thf(203,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/sandbox2/benchmark/theBenchmark.p',cls_image__vimage__subset_0) ).
thf(878,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)],[203]) ).
thf(39,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Set_Oinsert @ A @ B @ C ) @ C )
| ~ ( c_Finite__Set_Ofinite @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__insert_1) ).
thf(523,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)],[39]) ).
thf(65,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( c_Fun_Oid @ A ) @ B )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_id__apply_0) ).
thf(582,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( c_Fun_Oid @ A ) @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(348,axiom,
c_Finite__Set_Ofinite @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__indi_0) ).
thf(1205,plain,
c_Finite__Set_Ofinite @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ tc_bool ) ) @ tc_Arrow__Order__Mirabelle_Oindi,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(6,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/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_1) ).
thf(449,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)],[6]) ).
thf(80,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ B ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__complement_0) ).
thf(614,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ B ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(108,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__empty_0) ).
thf(677,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)],[108]) ).
thf(289,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_HOL_Ominus__class_Ominus @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
= C )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ C @ A @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__diff_0) ).
thf(1078,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)],[289]) ).
thf(50,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ B @ C )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__is__Un_0) ).
thf(550,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ B @ C )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(377,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( c_lessequals @ ( c_Finite__Set_Ocard @ B @ C ) @ ( c_Finite__Set_Ocard @ A @ C ) @ tc_nat )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_card__seteq_0) ).
thf(1275,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( c_lessequals @ ( c_Finite__Set_Ocard @ B @ C ) @ ( c_Finite__Set_Ocard @ A @ C ) @ tc_nat )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(16,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ C @ A )
| ( c_lessequals @ D @ C @ A )
| ~ ( c_lessequals @ ( c_SetInterval_Oord__class_OatLeastLessThan @ C @ D @ A ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ E @ A ) @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastLessThan__subset__iff_0) ).
thf(472,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ C @ A )
| ( c_lessequals @ D @ C @ A )
| ~ ( c_lessequals @ ( c_SetInterval_Oord__class_OatLeastLessThan @ C @ D @ A ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ E @ A ) @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(361,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Set_Oimage @ A @ B @ C @ D ) @ ( c_Set_Oimage @ A @ E @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ B @ E @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__mono_0) ).
thf(1233,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)],[361]) ).
thf(399,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/sandbox2/benchmark/theBenchmark.p',cls_injD_0) ).
thf(1327,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)],[399]) ).
thf(233,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_HOL_Ominus__class_Ominus @ B @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
= B )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__partition_0) ).
thf(945,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_HOL_Ominus__class_Ominus @ B @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
= B )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(282,axiom,
! [B: $i,A: $i] :
( ( c_lessequals @ A @ B @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__le__mono_0) ).
thf(1063,plain,
! [B: $i,A: $i] :
( ( c_lessequals @ A @ B @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(411,axiom,
! [A: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat_Osimps_I2_J_0) ).
thf(1354,plain,
! [A: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(405,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/sandbox2/benchmark/theBenchmark.p',cls_inj__on__inv__into_0) ).
thf(1342,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)],[405]) ).
thf(141,axiom,
! [A: $i] : ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ A ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_zero__less__Suc_0) ).
thf(747,plain,
! [A: $i] : ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ A ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(181,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ A @ tc_bool ) ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Compl__Int_0) ).
thf(829,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ A @ tc_bool ) ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(344,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/sandbox2/benchmark/theBenchmark.p',cls_inv__f__eq_0) ).
thf(1196,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)],[344]) ).
thf(157,axiom,
! [A: $i] :
( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Compl__UNIV__eq_0) ).
thf(782,plain,
! [A: $i] :
( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ ( 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)],[157]) ).
thf(123,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ C )
| ~ ( c_Finite__Set_Ofinite @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__Diff_0) ).
thf(709,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)],[123]) ).
thf(187,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_SetInterval_Oord__class_OlessThan @ B @ A ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A ) @ ( tc_fun @ A @ tc_bool ) )
= ( c_SetInterval_Oord__class_OlessThan @ C @ A ) )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ivl__disj__un_I8_J_0) ).
thf(841,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_SetInterval_Oord__class_OlessThan @ B @ A ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A ) @ ( tc_fun @ A @ tc_bool ) )
= ( c_SetInterval_Oord__class_OlessThan @ C @ A ) )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(413,axiom,
! [B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__UNIV__left_0) ).
thf(1359,plain,
! [B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(424,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Finite__Set_Ocard @ A @ B ) @ ( c_Finite__Set_Ocard @ C @ D ) @ tc_nat )
| ~ ( c_Finite__Set_Ofinite @ C @ D )
| ~ ( c_lessequals @ ( c_Set_Oimage @ E @ A @ B @ D ) @ C @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ E @ A @ B @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_card__inj__on__le_0) ).
thf(1386,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Finite__Set_Ocard @ A @ B ) @ ( c_Finite__Set_Ocard @ C @ D ) @ tc_nat )
| ~ ( c_Finite__Set_Ofinite @ C @ D )
| ~ ( c_lessequals @ ( c_Set_Oimage @ E @ A @ B @ D ) @ C @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ E @ A @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(1,negated_conjecture,
~ v_thesis____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(436,plain,
~ v_thesis____,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(373,axiom,
! [C: $i,B: $i,A: $i] : ( c_Fun_Oinj__on @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B @ C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__empty_0) ).
thf(1265,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)],[373]) ).
thf(365,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ B @ C )
| ( ( hAPP @ A @ ( c_ATP__Linkup_Osko__Fun__XinjI__1__1 @ A @ B @ C ) )
= ( hAPP @ A @ ( c_ATP__Linkup_Osko__Fun__XinjI__1__2 @ A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_injI_0) ).
thf(1243,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ B @ C )
| ( ( hAPP @ A @ ( c_ATP__Linkup_Osko__Fun__XinjI__1__1 @ A @ B @ C ) )
= ( hAPP @ A @ ( c_ATP__Linkup_Osko__Fun__XinjI__1__2 @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(312,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oimage @ A @ B @ C @ D ) @ ( c_Set_Oimage @ A @ E @ C @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ ( c_Set_Oimage @ A @ ( c_HOL_Ominus__class_Ominus @ B @ E @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) @ ( tc_fun @ D @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__diff__subset_0) ).
thf(1127,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)],[312]) ).
thf(244,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) )
| ~ ( c_lessequals @ D @ A @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Int__assoc__eq_1) ).
thf(973,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) )
| ~ ( c_lessequals @ D @ A @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(207,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
| ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__empty_1) ).
thf(885,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
| ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(130,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ B @ tc_bool ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__Un_0) ).
thf(724,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ B @ tc_bool ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(382,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oimage @ A @ ( c_Set_Ovimage @ A @ B @ C @ D ) @ C @ D )
= ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Set_Oimage @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__vimage__eq_0) ).
thf(1287,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oimage @ A @ ( c_Set_Ovimage @ A @ B @ C @ D ) @ C @ D )
= ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Set_Oimage @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(127,axiom,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ B ) @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__eq__eq_1) ).
thf(719,plain,
! [B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ B ) @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(159,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ A @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__subset__iff_1) ).
thf(785,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ A @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(221,axiom,
! [B: $i,A: $i] :
( ( ( c_Suc @ A )
!= ( c_Suc @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat_Oinject_0) ).
thf(917,plain,
! [B: $i,A: $i] :
( ( ( c_Suc @ A )
!= ( c_Suc @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(168,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
!= ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A ) )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastLessThan__empty__iff2_0) ).
thf(802,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
!= ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A ) )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(342,axiom,
! [B: $i,A: $i] :
( ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ B @ B )
| ~ ( c_Fun_Osurj @ A @ B @ B )
| ~ ( c_Finite__Set_Ofinite @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__UNIV__surj__inj_0) ).
thf(1191,plain,
! [B: $i,A: $i] :
( ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ B @ B )
| ~ ( c_Fun_Osurj @ A @ B @ B )
| ~ ( c_Finite__Set_Ofinite @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(280,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ D @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__Int__distrib_0) ).
thf(1059,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ D @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(11,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D )
= ( c_Set_Oinsert @ B @ ( c_Set_Oinsert @ A @ C @ D ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__commute_0) ).
thf(460,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)],[11]) ).
thf(400,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_Lattices_Oupper__semilattice__class_Osup @ B @ E @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__Un_0) ).
thf(1330,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_Lattices_Oupper__semilattice__class_Osup @ B @ E @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(372,axiom,
c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__0__eq_1) ).
thf(1264,plain,
c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(67,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_lessequals @ B @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).
thf(587,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_lessequals @ B @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(82,axiom,
! [B: $i,A: $i] :
( ( c_Set_Ovimage @ ( c_Fun_Oid @ A ) @ B @ A @ A )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__id_0) ).
thf(619,plain,
! [B: $i,A: $i] :
( ( c_Set_Ovimage @ ( c_Fun_Oid @ A ) @ B @ A @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(215,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ A ) @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__lessD_0) ).
thf(902,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ A ) @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(421,axiom,
~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_neq0__conv_1) ).
thf(1379,plain,
~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(396,axiom,
! [B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__UNIV__right_0) ).
thf(1319,plain,
! [B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(205,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__Un__distrib2_0) ).
thf(881,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(307,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
| ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__empty_0) ).
thf(1115,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
| ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(300,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Diff__cancel2_0) ).
thf(1100,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(360,axiom,
class_Nat_Osemiring__char__0 @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Nat_Osemiring__char__0) ).
thf(1232,plain,
class_Nat_Osemiring__char__0 @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(76,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).
thf(606,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)],[76]) ).
thf(407,axiom,
! [B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ A @ ( tc_fun @ B @ tc_bool ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__absorb_0) ).
thf(1347,plain,
! [B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ A @ ( tc_fun @ B @ tc_bool ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(18,axiom,
! [A: $i] :
( ( c_Hilbert__Choice_Oinv__into @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Fun_Oid @ A ) @ A @ A )
= ( c_Fun_Oid @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inv__id_0) ).
thf(475,plain,
! [A: $i] :
( ( c_Hilbert__Choice_Oinv__into @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Fun_Oid @ A ) @ A @ A )
= ( c_Fun_Oid @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(161,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Ovimage @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ E @ D )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Ovimage @ A @ B @ E @ D ) @ ( c_Set_Ovimage @ A @ C @ E @ D ) @ ( tc_fun @ E @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__Un_0) ).
thf(789,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Ovimage @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ E @ D )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( 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)],[161]) ).
thf(69,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ C @ A )
| ( c_lessequals @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__linear_0) ).
thf(591,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)],[69]) ).
thf(419,axiom,
! [B: $i,A: $i] :
( ( ( c_Finite__Set_Ocard @ A @ B )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( c_Finite__Set_Ofinite @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_card__eq__0__iff_2) ).
thf(1373,plain,
! [B: $i,A: $i] :
( ( ( c_Finite__Set_Ocard @ A @ B )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ( c_Finite__Set_Ofinite @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(84,axiom,
! [B: $i,A: $i] :
( ( c_Set_Oimage @ ( c_Fun_Oid @ A ) @ B @ A @ A )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__id_0) ).
thf(623,plain,
! [B: $i,A: $i] :
( ( c_Set_Oimage @ ( c_Fun_Oid @ A ) @ B @ A @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(323,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_Lattices_Oupper__semilattice__class_Osup @ E @ B @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__Un_1) ).
thf(1151,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_Lattices_Oupper__semilattice__class_Osup @ E @ B @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(339,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/sandbox2/benchmark/theBenchmark.p',cls_image__set__diff_0) ).
thf(1183,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)],[339]) ).
thf(271,axiom,
! [B: $i,A: $i] :
( ( class_Finite__Set_Ofinite_Ofinite @ ( tc_fun @ A @ B ) )
| ~ ( class_Finite__Set_Ofinite_Ofinite @ B )
| ~ ( class_Finite__Set_Ofinite_Ofinite @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Finite__Set_Ofinite_Ofinite) ).
thf(1040,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)],[271]) ).
thf(304,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ C )
| ~ ( c_Finite__Set_Ofinite @ A @ C )
| ~ ( c_Finite__Set_Ofinite @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__Diff2_1) ).
thf(1109,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)],[304]) ).
thf(316,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/sandbox2/benchmark/theBenchmark.p',cls_vimage__subsetI_0) ).
thf(1136,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)],[316]) ).
thf(184,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( c_lessequals @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastLessThan__empty_0) ).
thf(834,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( c_lessequals @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(423,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_ATP__Linkup_Osko__Fun__Xdatatype__injI__1__1 @ A @ B @ C )
!= ( c_ATP__Linkup_Osko__Fun__Xdatatype__injI__1__2 @ A @ B @ C ) )
| ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_datatype__injI_1) ).
thf(1383,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_ATP__Linkup_Osko__Fun__Xdatatype__injI__1__1 @ A @ B @ C )
!= ( c_ATP__Linkup_Osko__Fun__Xdatatype__injI__1__2 @ A @ B @ C ) )
| ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(61,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_1) ).
thf(574,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)],[61]) ).
thf(237,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Fun_Ocomp @ ( c_Hilbert__Choice_Oinv__into @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ B @ A @ C ) @ B @ C @ A @ A )
= ( c_Fun_Oid @ A ) )
| ~ ( c_Fun_Oinj__on @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__iff_0) ).
thf(956,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Fun_Ocomp @ ( c_Hilbert__Choice_Oinv__into @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ B @ A @ C ) @ B @ C @ A @ A )
= ( c_Fun_Oid @ A ) )
| ~ ( 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)],[237]) ).
thf(197,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ D @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__subset__iff_0) ).
thf(866,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ D @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(286,axiom,
! [B: $i,A: $i] :
( ( c_lessequals @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_termination__basic__simps_I5_J_0) ).
thf(1072,plain,
! [B: $i,A: $i] :
( ( c_lessequals @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(428,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/sandbox2/benchmark/theBenchmark.p',cls_inv__image__comp_0) ).
thf(1394,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)],[428]) ).
thf(409,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Oinj__on @ ( c_Fun_Ocomp @ A @ B @ C @ D @ E ) @ F @ E @ D )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Set_Oimage @ B @ F @ E @ C ) @ C @ D )
| ~ ( c_Fun_Oinj__on @ B @ F @ E @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comp__inj__on_0) ).
thf(1351,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Oinj__on @ ( c_Fun_Ocomp @ A @ B @ C @ D @ E ) @ F @ E @ D )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Set_Oimage @ B @ F @ E @ C ) @ C @ D )
| ~ ( c_Fun_Oinj__on @ B @ F @ E @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(250,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
!= ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) )
| ( c_lessequals @ D @ A @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Int__assoc__eq_0) ).
thf(988,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
!= ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) )
| ( c_lessequals @ D @ A @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(346,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__assoc_0) ).
thf(1201,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(190,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( c_lessequals @ B @ A @ tc_nat )
| ~ ( c_lessequals @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__antisym_0) ).
thf(849,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( c_lessequals @ B @ A @ tc_nat )
| ~ ( c_lessequals @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(32,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Set_Oinsert @ B @ C @ A ) @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Complete__Lattice_OSup__class_OSup @ C @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sup__insert_0) ).
thf(507,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Set_Oinsert @ B @ C @ A ) @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Complete__Lattice_OSup__class_OSup @ C @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(74,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/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__less_0) ).
thf(602,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)],[74]) ).
thf(247,axiom,
! [A: $i] : ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ A ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gr0__conv__Suc_1) ).
thf(981,plain,
! [A: $i] : ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ A ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(150,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_SetInterval_Oord__class_OlessThan @ B @ A ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A ) @ ( tc_fun @ A @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ivl__disj__int_I2_J_0) ).
thf(766,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_SetInterval_Oord__class_OlessThan @ B @ A ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A ) @ ( tc_fun @ A @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(202,axiom,
! [A: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ ( tc_fun @ A @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__Compl__self__eq_1) ).
thf(877,plain,
! [A: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( 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)],[202]) ).
thf(115,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ( c_HOL_Oord__class_Oless @ B @ A @ tc_nat )
| ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neqE__nat_0) ).
thf(692,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ( c_HOL_Oord__class_Oless @ B @ A @ tc_nat )
| ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(287,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ B ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ B @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__eq_0) ).
thf(1074,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ B ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ B @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(349,axiom,
! [A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gr0I_0) ).
thf(1206,plain,
! [A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
| ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(101,axiom,
! [B: $i,A: $i] :
( ( c_lessequals @ ( c_Suc @ A ) @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__eq__Suc__le_0) ).
thf(661,plain,
! [B: $i,A: $i] :
( ( c_lessequals @ ( c_Suc @ A ) @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(389,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Fun_Osurj @ ( c_Hilbert__Choice_Oinv__into @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ B @ A @ C ) @ C @ A )
| ~ ( c_Fun_Oinj__on @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__imp__surj__inv_0) ).
thf(1306,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Fun_Osurj @ ( c_Hilbert__Choice_Oinv__into @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ B @ A @ C ) @ C @ A )
| ~ ( 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)],[389]) ).
thf(345,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Fun_Oinj__on @ ( c_Hilbert__Choice_Oinv__into @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ B @ A @ C ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) @ C @ A )
| ~ ( c_Fun_Osurj @ B @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_surj__imp__inj__inv_0) ).
thf(1199,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Fun_Oinj__on @ ( c_Hilbert__Choice_Oinv__into @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ B @ A @ C ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) @ C @ A )
| ~ ( c_Fun_Osurj @ B @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(172,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ( A = B )
| ~ ( c_lessequals @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__less__le_2) ).
thf(810,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ( A = B )
| ~ ( c_lessequals @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(403,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Set_Oimage @ ( c_COMBB @ A @ B @ C @ D @ E ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_bool ) ) @ E @ D ) @ D )
| ~ ( c_Finite__Set_Ofinite @ ( c_Set_Oimage @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_bool ) ) @ E @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__range__imageI_0) ).
thf(1338,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Set_Oimage @ ( c_COMBB @ A @ B @ C @ D @ E ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_bool ) ) @ E @ D ) @ D )
| ~ ( c_Finite__Set_Ofinite @ ( c_Set_Oimage @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_bool ) ) @ E @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(125,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Obij__betw @ ( c_Fun_Ocomp @ A @ B @ C @ D @ E ) @ F @ G @ E @ D )
| ~ ( c_Fun_Obij__betw @ A @ H @ G @ C @ D )
| ~ ( c_Fun_Obij__betw @ B @ F @ H @ E @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bij__betw__trans_0) ).
thf(714,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Obij__betw @ ( c_Fun_Ocomp @ A @ B @ C @ D @ E ) @ F @ G @ E @ D )
| ~ ( c_Fun_Obij__betw @ A @ H @ G @ C @ D )
| ~ ( c_Fun_Obij__betw @ B @ F @ H @ E @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(34,axiom,
! [A: $i] : ( c_Fun_Osurj @ ( c_Fun_Oid @ A ) @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_surj__id_0) ).
thf(512,plain,
! [A: $i] : ( c_Fun_Osurj @ ( c_Fun_Oid @ A ) @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(231,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ ( c_SetInterval_Oord__class_OlessThan @ B @ A ) @ ( c_SetInterval_Oord__class_OlessThan @ C @ A ) @ ( tc_fun @ A @ tc_bool ) )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lessThan__subset__iff_1) ).
thf(942,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)],[231]) ).
thf(48,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/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__le_0) ).
thf(546,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)],[48]) ).
thf(163,axiom,
! [B: $i,A: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__subsetI_0) ).
thf(793,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)],[163]) ).
thf(324,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Fun_Oinj__on @ A @ B @ C @ D )
| ( c_Fun_Obij__betw @ A @ B @ ( c_Set_Oimage @ A @ B @ C @ D ) @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bij__betw__def_2) ).
thf(1153,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Fun_Oinj__on @ A @ B @ C @ D )
| ( c_Fun_Obij__betw @ A @ B @ ( c_Set_Oimage @ A @ B @ C @ D ) @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(148,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ C )
| ~ ( c_Finite__Set_Ofinite @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__Int_0) ).
thf(761,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ C )
| ~ ( c_Finite__Set_Ofinite @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(391,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/sandbox2/benchmark/theBenchmark.p',cls_subset__UNIV_0) ).
thf(1311,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)],[391]) ).
thf(43,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Set_Oinsert @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__insert__left_0) ).
thf(534,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Set_Oinsert @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(166,axiom,
! [B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Finite__Set_Ocard @ A @ B ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_card__gt__0__iff_1) ).
thf(798,plain,
! [B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Finite__Set_Ocard @ A @ B ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(329,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ( c_lessequals @ ( c_Set_Oimage @ D @ A @ C @ E ) @ ( c_Set_Oimage @ D @ B @ C @ E ) @ ( tc_fun @ E @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__image__iff_2) ).
thf(1163,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)],[329]) ).
thf(356,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Fun_Obij @ A @ B @ C )
| ~ ( c_Fun_Osurj @ A @ B @ C )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bijI_0) ).
thf(1223,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Fun_Obij @ A @ B @ C )
| ~ ( c_Fun_Osurj @ A @ B @ C )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(272,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Ovimage @ A @ B @ C @ D )
= ( c_Set_Oimage @ ( c_Hilbert__Choice_Oinv__into @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) @ A @ C @ D ) @ B @ D @ C ) )
| ~ ( c_Fun_Obij @ A @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bij__vimage__eq__inv__image_0) ).
thf(1042,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Ovimage @ A @ B @ C @ D )
= ( c_Set_Oimage @ ( c_Hilbert__Choice_Oinv__into @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) @ A @ C @ D ) @ B @ D @ C ) )
| ~ ( c_Fun_Obij @ A @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(369,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Fun_Ocomp @ ( c_Fun_Ocomp @ A @ ( c_Hilbert__Choice_Oinv__into @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ C @ B @ D ) @ B @ E @ D ) @ C @ D @ E @ B )
= A )
| ~ ( c_Fun_Oinj__on @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ B @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_o__inv__o__cancel_0) ).
thf(1255,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Fun_Ocomp @ ( c_Fun_Ocomp @ A @ ( c_Hilbert__Choice_Oinv__into @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ C @ B @ D ) @ B @ E @ D ) @ C @ D @ E @ B )
= A )
| ~ ( c_Fun_Oinj__on @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(334,axiom,
! [B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__UNIV__left_0) ).
thf(1174,plain,
! [B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(176,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Set_Oimage @ B @ C @ D @ A ) ) @ ( c_Set_Oimage @ B @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ D @ tc_bool ) ) @ C ) @ D @ A ) @ ( tc_fun @ A @ tc_bool ) )
| ~ ( c_Fun_Osurj @ B @ D @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_surj__Compl__image__subset_0) ).
thf(820,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Set_Oimage @ B @ C @ D @ A ) ) @ ( c_Set_Oimage @ B @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ D @ tc_bool ) ) @ C ) @ D @ A ) @ ( tc_fun @ A @ tc_bool ) )
| ~ ( c_Fun_Osurj @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(55,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/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_0) ).
thf(561,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)],[55]) ).
thf(87,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ ( c_HOL_Ominus__class_Ominus @ B @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ ( tc_fun @ C @ tc_bool ) ) @ C )
= ( c_Set_Oinsert @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__Diff__single_0) ).
thf(630,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)],[87]) ).
thf(418,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/sandbox2/benchmark/theBenchmark.p',cls_inj__vimage__image__eq_0) ).
thf(1370,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)],[418]) ).
thf(363,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Omap @ A @ B @ C @ D )
!= ( c_List_Omap @ A @ E @ C @ D ) )
| ( B = E )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__injective_0) ).
thf(1238,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Omap @ A @ B @ C @ D )
!= ( c_List_Omap @ A @ E @ C @ D ) )
| ( B = E )
| ~ ( 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)],[363]) ).
thf(263,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Set_Oimage @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oimage @ A @ B @ D @ E ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ ( tc_fun @ E @ tc_bool ) ) @ ( tc_fun @ E @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__Int__subset_0) ).
thf(1021,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Set_Oimage @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oimage @ A @ B @ D @ E ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ ( tc_fun @ E @ tc_bool ) ) @ ( tc_fun @ E @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(155,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ A ) @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__trans__Suc_0) ).
thf(778,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ A ) @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ C @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(310,axiom,
! [A: $i] : ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ A ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lessI_0) ).
thf(1123,plain,
! [A: $i] : ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ A ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(195,axiom,
! [B: $i,A: $i] :
( ( c_lessequals @ ( c_Suc @ A ) @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__leI_0) ).
thf(862,plain,
! [B: $i,A: $i] :
( ( c_lessequals @ ( c_Suc @ A ) @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(353,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/sandbox2/benchmark/theBenchmark.p',cls_finite__vimageI_0) ).
thf(1217,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)],[353]) ).
thf(72,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/sandbox2/benchmark/theBenchmark.p',cls_order__le__less_1) ).
thf(598,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)],[72]) ).
thf(14,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/sandbox2/benchmark/theBenchmark.p',cls_order__less__le_2) ).
thf(467,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)],[14]) ).
thf(416,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/sandbox2/benchmark/theBenchmark.p',cls_inv__f__f_0) ).
thf(1365,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)],[416]) ).
thf(85,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Fun_Ocomp @ A @ ( c_Fun_Oid @ B ) @ B @ C @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_o__id_0) ).
thf(625,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Fun_Ocomp @ A @ ( c_Fun_Oid @ B ) @ B @ C @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(204,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ C )
| ~ ( c_Finite__Set_Ofinite @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__Int_1) ).
thf(879,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ C )
| ~ ( c_Finite__Set_Ofinite @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(191,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/sandbox2/benchmark/theBenchmark.p',cls_subset__insert__iff_4) ).
thf(852,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)],[191]) ).
thf(103,axiom,
! [B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ B @ tc_bool ) ) @ A ) @ ( tc_fun @ B @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Compl__disjoint_0) ).
thf(665,plain,
! [B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ B @ tc_bool ) ) @ A ) @ ( tc_fun @ B @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(327,axiom,
! [A: $i] :
~ ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_gr__implies__not0_0) ).
thf(1159,plain,
! [A: $i] :
~ ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(26,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( B = C )
| ~ ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__antisym__conv_0) ).
thf(493,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)],[26]) ).
thf(146,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ C )
| ~ ( c_Finite__Set_Ofinite @ B @ C )
| ~ ( c_Finite__Set_Ofinite @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__Un_2) ).
thf(757,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ C )
| ~ ( c_Finite__Set_Ofinite @ B @ C )
| ~ ( c_Finite__Set_Ofinite @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(313,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ( c_HOL_Oord__class_Oless @ B @ A @ tc_nat )
| ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__neq__iff_0) ).
thf(1128,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ( c_HOL_Oord__class_Oless @ B @ A @ tc_nat )
| ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(384,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/sandbox2/benchmark/theBenchmark.p',cls_card__eq__UNIV__imp__eq__UNIV_0) ).
thf(1291,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)],[384]) ).
thf(259,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_COMBB @ A @ B @ C @ D @ E ) @ F )
= ( hAPP @ A @ ( hAPP @ B @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBB__def_0) ).
thf(1012,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_COMBB @ A @ B @ C @ D @ E ) @ F )
= ( hAPP @ A @ ( hAPP @ B @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(189,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__greatest_0) ).
thf(847,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(57,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
!= ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
| ( B = D )
| ( B = E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_3) ).
thf(566,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)],[57]) ).
thf(22,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ ( tc_fun @ A @ tc_bool ) )
| ~ ( c_lessequals @ C @ B @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Compl__subset__Compl__iff_1) ).
thf(484,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ ( tc_fun @ A @ tc_bool ) )
| ~ ( c_lessequals @ C @ B @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(431,axiom,
! [A: $i] :
( ( c_SetInterval_Oord__class_OatLeastLessThan @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_nat @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastLessThan0_0) ).
thf(1402,plain,
! [A: $i] :
( ( c_SetInterval_Oord__class_OatLeastLessThan @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_nat @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(63,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
!= ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
| ( A = E )
| ( A = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_0) ).
thf(578,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)],[63]) ).
thf(117,axiom,
! [B: $i,A: $i] :
( ( c_lessequals @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat )
| ~ ( c_lessequals @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__le__mono_1) ).
thf(697,plain,
! [B: $i,A: $i] :
( ( c_lessequals @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat )
| ~ ( c_lessequals @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(309,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( c_SetInterval_Oord__class_OlessThan @ B @ A ) @ ( c_SetInterval_Oord__class_OlessThan @ C @ A ) @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lessThan__subset__iff_0) ).
thf(1121,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)],[309]) ).
thf(298,axiom,
! [B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__empty__left_0) ).
thf(1096,plain,
! [B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( 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)],[298]) ).
thf(317,axiom,
! [B: $i,A: $i] : ( c_Finite__Set_Ofinite @ ( c_SetInterval_Oord__class_OatLeastLessThan @ A @ B @ tc_nat ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__atLeastLessThan_0) ).
thf(1138,plain,
! [B: $i,A: $i] : ( c_Finite__Set_Ofinite @ ( c_SetInterval_Oord__class_OatLeastLessThan @ A @ B @ tc_nat ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(70,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ B @ C )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__not__empty_0) ).
thf(593,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)],[70]) ).
thf(199,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
= A )
| ~ ( c_lessequals @ B @ A @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__absorb2_0) ).
thf(869,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
= A )
| ~ ( c_lessequals @ B @ A @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(78,axiom,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ A @ C ) @ ( tc_fun @ C @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insertI_0) ).
thf(610,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)],[78]) ).
thf(308,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastLessThan__empty__iff_0) ).
thf(1118,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(201,axiom,
! [A: $i] :
( ( c_Suc @ A )
!= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__n__not__n_0) ).
thf(874,plain,
! [A: $i] :
( ( c_Suc @ A )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(320,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ A @ B @ C @ D )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) )
| ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__is__empty_0) ).
thf(1143,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)],[320]) ).
thf(96,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Obij__betw @ ( c_Hilbert__Choice_Oinv__into @ A @ B @ C @ D ) @ E @ A @ D @ C )
| ~ ( c_Fun_Obij__betw @ B @ A @ E @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bij__betw__inv__into_0) ).
thf(650,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Obij__betw @ ( c_Hilbert__Choice_Oinv__into @ A @ B @ C @ D ) @ E @ A @ D @ C )
| ~ ( c_Fun_Obij__betw @ B @ A @ E @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(234,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ C @ D @ A ) @ ( tc_fun @ A @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ivl__disj__int_I11_J_0) ).
thf(948,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ C @ D @ A ) @ ( tc_fun @ A @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(305,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ A @ tc_bool ) ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Compl__Diff__eq_0) ).
thf(1111,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ A @ tc_bool ) ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ C @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(358,axiom,
! [A: $i] :
( ( c_Suc @ A )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat_Osimps_I3_J_0) ).
thf(1227,plain,
! [A: $i] :
( ( c_Suc @ A )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(193,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/sandbox2/benchmark/theBenchmark.p',cls_vimage__mono_0) ).
thf(857,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)],[193]) ).
thf(429,axiom,
! [A: $i] :
( ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_lessequals @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__0__eq_0) ).
thf(1397,plain,
! [A: $i] :
( ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_lessequals @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(24,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/sandbox2/benchmark/theBenchmark.p',cls_order__le__less_0) ).
thf(488,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)],[24]) ).
thf(414,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Finite__Set_Ocard @ A @ B ) @ ( c_Finite__Set_Ocard @ C @ B ) @ tc_nat )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ C @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_card__mono_0) ).
thf(1361,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Finite__Set_Ocard @ A @ B ) @ ( c_Finite__Set_Ocard @ C @ B ) @ tc_nat )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(227,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
!= B )
| ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__Un__eq_1) ).
thf(933,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
!= B )
| ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(52,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).
thf(554,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)],[52]) ).
thf(112,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ A @ C @ ( tc_fun @ B @ tc_bool ) ) @ B )
| ~ ( c_Finite__Set_Ofinite @ C @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__Diff2_0) ).
thf(686,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)],[112]) ).
thf(352,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ A @ ( c_Set_Oimage @ ( c_Hilbert__Choice_Oinv__into @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ A @ B @ C ) @ D @ C @ B ) @ B @ C )
= D )
| ~ ( c_Fun_Osurj @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__surj__f__inv__f_0) ).
thf(1214,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ A @ ( c_Set_Oimage @ ( c_Hilbert__Choice_Oinv__into @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ A @ B @ C ) @ D @ C @ B ) @ B @ C )
= D )
| ~ ( c_Fun_Osurj @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(261,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__Diff_0) ).
thf(1016,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)],[261]) ).
thf(325,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oimage @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B @ C )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__empty_0) ).
thf(1155,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)],[325]) ).
thf(266,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ B ) @ tc_nat )
| ~ ( c_lessequals @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc__eq__le_1) ).
thf(1028,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ B ) @ tc_nat )
| ~ ( c_lessequals @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(291,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Fun_Osurj @ A @ B @ C )
| ~ ( c_Fun_Obij @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bij__def_1) ).
thf(1082,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Fun_Osurj @ A @ B @ C )
| ~ ( c_Fun_Obij @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(109,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ A ) @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__le__eq_0) ).
thf(679,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ A ) @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(243,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ B ) @ tc_nat )
| ~ ( c_lessequals @ B @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__less__Suc__eq_0) ).
thf(970,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ B ) @ tc_nat )
| ~ ( c_lessequals @ B @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(185,axiom,
! [B: $i,A: $i] :
( ( c_lessequals @ A @ B @ tc_nat )
| ( c_lessequals @ B @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__le__linear_0) ).
thf(837,plain,
! [B: $i,A: $i] :
( ( c_lessequals @ A @ B @ tc_nat )
| ( c_lessequals @ B @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(398,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/sandbox2/benchmark/theBenchmark.p',cls_inj__on__iff__eq__card_0) ).
thf(1324,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)],[398]) ).
thf(95,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( hAPP @ ( c_Hilbert__Choice_Oinv__into @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ A @ B @ C ) @ D ) )
= D )
| ~ ( c_Fun_Osurj @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_surj__f__inv__f_0) ).
thf(647,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( hAPP @ ( c_Hilbert__Choice_Oinv__into @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ A @ B @ C ) @ D ) )
= D )
| ~ ( c_Fun_Osurj @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(249,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ A ) @ B @ tc_nat )
| ( ( c_Suc @ A )
= B )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__lessI_0) ).
thf(985,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ A ) @ B @ tc_nat )
| ( ( c_Suc @ A )
= B )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(119,axiom,
! [B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__empty__left_0) ).
thf(701,plain,
! [B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(386,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( hAPP @ B @ ( c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__imp__inv__eq__1__1 @ A @ B @ C @ D ) ) )
!= ( c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__imp__inv__eq__1__1 @ A @ B @ C @ D ) )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) @ C @ D )
| ( ( c_Hilbert__Choice_Oinv__into @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) @ A @ C @ D )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__imp__inv__eq_0) ).
thf(1297,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( hAPP @ B @ ( c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__imp__inv__eq__1__1 @ A @ B @ C @ D ) ) )
!= ( c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__imp__inv__eq__1__1 @ A @ B @ C @ D ) )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) @ C @ D )
| ( ( c_Hilbert__Choice_Oinv__into @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) @ A @ C @ D )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(374,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ A @ B @ C @ D )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_bool ) ) )
| ~ ( c_Typedef_Otype__definition @ E @ A @ B @ D @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_type__definition_OAbs__image_0) ).
thf(1266,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ A @ B @ C @ D )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_bool ) ) )
| ~ ( c_Typedef_Otype__definition @ E @ A @ B @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(275,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Set_Oimage @ A @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ B @ D ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ D @ tc_bool ) ) @ ( c_Set_Oimage @ A @ C @ B @ D ) ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ B @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__image__Compl__subset_0) ).
thf(1050,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Set_Oimage @ A @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ B @ D ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ D @ tc_bool ) ) @ ( c_Set_Oimage @ A @ C @ B @ D ) ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(128,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__subset__conv_0) ).
thf(721,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(255,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_Suc @ A ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ B @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__antisym_0) ).
thf(1002,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_Suc @ A ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ B @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(58,axiom,
! [B: $i,A: $i] :
( ( class_Orderings_Oorder @ ( tc_fun @ A @ B ) )
| ~ ( class_Orderings_Oorder @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Oorder) ).
thf(569,plain,
! [B: $i,A: $i] :
( ( class_Orderings_Oorder @ ( tc_fun @ A @ B ) )
| ~ ( class_Orderings_Oorder @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(366,axiom,
! [B: $i,A: $i] :
( ( ( c_Finite__Set_Ocard @ A @ B )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_Finite__Set_Ofinite @ A @ B )
| ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_card__eq__0__iff_0) ).
thf(1246,plain,
! [B: $i,A: $i] :
( ( ( c_Finite__Set_Ocard @ A @ B )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_Finite__Set_Ofinite @ A @ B )
| ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(36,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( c_lessequals @ D @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I6_J_0) ).
thf(515,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)],[36]) ).
thf(367,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( c_lessequals @ B @ A @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__eq__subset_2) ).
thf(1249,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)],[367]) ).
thf(314,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/sandbox2/benchmark/theBenchmark.p',cls_finite__UNIV_0) ).
thf(1131,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)],[314]) ).
thf(98,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ D @ E @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ E @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__mono_0) ).
thf(654,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)],[98]) ).
thf(30,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ C @ A )
| ( c_lessequals @ B @ D @ A )
| ~ ( c_lessequals @ ( c_SetInterval_Oord__class_OatLeastLessThan @ D @ B @ A ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ E @ C @ A ) @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastLessThan__subset__iff_1) ).
thf(503,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ C @ A )
| ( c_lessequals @ B @ D @ A )
| ~ ( c_lessequals @ ( c_SetInterval_Oord__class_OatLeastLessThan @ D @ B @ A ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ E @ C @ A ) @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(427,axiom,
class_Ring__and__Field_Osemiring__0 @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__0) ).
thf(1393,plain,
class_Ring__and__Field_Osemiring__0 @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(364,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__left__absorb_0) ).
thf(1241,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(169,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_Finite__Set_Ofinite @ ( c_Set_Ovimage @ C @ A @ D @ B ) @ D )
| ~ ( c_Fun_Obij @ C @ D @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__vimage__iff_0) ).
thf(805,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_Finite__Set_Ofinite @ ( c_Set_Ovimage @ C @ A @ D @ B ) @ D )
| ~ ( c_Fun_Obij @ C @ D @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(222,axiom,
! [B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ A )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ A )
| ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__compl_0) ).
thf(921,plain,
! [B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ A )
| ~ ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ A )
| ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(46,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( B = C )
| ~ ( c_lessequals @ C @ B @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__antisym_0) ).
thf(541,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)],[46]) ).
thf(277,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ tc_nat )
| ~ ( c_lessequals @ C @ B @ tc_nat )
| ~ ( c_lessequals @ A @ C @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__trans_0) ).
thf(1054,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ tc_nat )
| ~ ( c_lessequals @ C @ B @ tc_nat )
| ~ ( c_lessequals @ A @ C @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(332,axiom,
! [A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Finite__Set_Ocard @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ tc_nat )
| ~ ( c_Finite__Set_Ofinite @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__UNIV__card__ge__0_0) ).
thf(1170,plain,
! [A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Finite__Set_Ocard @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ tc_nat )
| ~ ( c_Finite__Set_Ofinite @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(269,axiom,
! [B: $i,A: $i] :
( ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_Suc @ A ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__eq_1) ).
thf(1035,plain,
! [B: $i,A: $i] :
( ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ B @ ( c_Suc @ A ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(54,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
!= ( c_Set_Oinsert @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__not__insert_0) ).
thf(558,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)],[54]) ).
thf(107,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Fun_Ocomp @ A @ B @ C @ D @ E )
!= ( c_Fun_Ocomp @ F @ G @ H @ D @ E ) )
| ( ( hAPP @ A @ ( hAPP @ B @ I ) )
= ( hAPP @ F @ ( hAPP @ G @ I ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_o__eq__dest_0) ).
thf(674,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Fun_Ocomp @ A @ B @ C @ D @ E )
!= ( c_Fun_Ocomp @ F @ G @ H @ D @ E ) )
| ( ( hAPP @ A @ ( hAPP @ B @ I ) )
= ( hAPP @ F @ ( hAPP @ G @ I ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(331,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_Lattices_Oupper__semilattice__class_Osup @ B @ E @ ( tc_fun @ C @ tc_bool ) ) @ C @ D )
| ( B = E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__Un__image__eq__iff_0) ).
thf(1167,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_Lattices_Oupper__semilattice__class_Osup @ B @ E @ ( tc_fun @ C @ tc_bool ) ) @ C @ D )
| ( B = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(208,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Oinj__on @ A @ B @ C @ D )
| ~ ( c_Fun_Obij__betw @ A @ B @ E @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bij__betw__def_0) ).
thf(888,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Oinj__on @ A @ B @ C @ D )
| ~ ( c_Fun_Obij__betw @ A @ B @ E @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(224,axiom,
! [B: $i,A: $i] :
( ~ ( class_Finite__Set_Ofinite_Ofinite @ A )
| ( c_Finite__Set_Ofinite @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite_0) ).
thf(926,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)],[224]) ).
thf(293,axiom,
! [B: $i,A: $i] :
( ( c_lessequals @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ B ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc__eq__le_0) ).
thf(1086,plain,
! [B: $i,A: $i] :
( ( c_lessequals @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ B ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(229,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__subset__conv_1) ).
thf(938,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(153,axiom,
! [B: $i,A: $i] :
( ( ( c_SetInterval_Oord__class_OatLeastLessThan @ A @ ( c_Suc @ B ) @ tc_nat )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_nat @ tc_bool ) ) )
| ( c_lessequals @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastLessThanSuc_1) ).
thf(773,plain,
! [B: $i,A: $i] :
( ( ( c_SetInterval_Oord__class_OatLeastLessThan @ A @ ( c_Suc @ B ) @ tc_nat )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ tc_nat @ tc_bool ) ) )
| ( c_lessequals @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(164,axiom,
! [B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__empty__right_0) ).
thf(794,plain,
! [B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(217,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
| ( ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__triv_0) ).
thf(906,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
| ( ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(378,axiom,
! [B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__UNIV__right_0) ).
thf(1278,plain,
! [B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(140,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_lessequals @ A @ ( c_Set_Oimage @ C @ D @ E @ B ) @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__surj_0) ).
thf(745,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)],[140]) ).
thf(60,axiom,
! [B: $i,A: $i] : ( c_Fun_Oinj__on @ ( c_Fun_Oid @ A ) @ B @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__id_0) ).
thf(573,plain,
! [B: $i,A: $i] : ( c_Fun_Oinj__on @ ( c_Fun_Oid @ A ) @ B @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(4,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( B = C )
| ( c_HOL_Oord__class_Oless @ C @ B @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_0) ).
thf(444,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)],[4]) ).
thf(241,axiom,
! [B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ B @ tc_bool ) ) @ A ) @ ( tc_fun @ B @ tc_bool ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Compl__partition_0) ).
thf(965,plain,
! [B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ B @ tc_bool ) ) @ A ) @ ( tc_fun @ B @ tc_bool ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(143,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_HOL_Ominus__class_Ominus @ B @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Diff__cancel_0) ).
thf(750,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_HOL_Ominus__class_Ominus @ B @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(35,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
= ( c_Set_Oinsert @ B @ ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_4) ).
thf(513,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)],[35]) ).
thf(321,axiom,
! [A: $i] :
( ( c_SetInterval_Oord__class_OatLeastLessThan @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
= ( c_SetInterval_Oord__class_OlessThan @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeast0LessThan_0) ).
thf(1146,plain,
! [A: $i] :
( ( c_SetInterval_Oord__class_OatLeastLessThan @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat )
= ( c_SetInterval_Oord__class_OlessThan @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(354,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_Fun_Oinj__on @ C @ A @ B @ D )
| ~ ( c_Finite__Set_Ofinite @ ( c_Set_Oimage @ C @ A @ B @ D ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__imageD_0) ).
thf(1219,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)],[354]) ).
thf(178,axiom,
! [A: $i] :
~ ( c_HOL_Oord__class_Oless @ A @ A @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__less__le_1) ).
thf(824,plain,
! [A: $i] :
~ ( c_HOL_Oord__class_Oless @ A @ A @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(66,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_SetInterval_Oord__class_OlessThan @ B @ A )
!= ( c_SetInterval_Oord__class_OlessThan @ C @ A ) )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_lessThan__eq__iff_0) ).
thf(584,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)],[66]) ).
thf(175,axiom,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ A @ ( tc_fun @ C @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__lower1_0) ).
thf(819,plain,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ A @ ( tc_fun @ C @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(216,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/sandbox2/benchmark/theBenchmark.p',cls_Diff__UNIV_0) ).
thf(904,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)],[216]) ).
thf(257,axiom,
! [B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sup__singleton_0) ).
thf(1007,plain,
! [B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( c_Complete__Lattice_OSup__class_OSup @ ( 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)],[257]) ).
thf(134,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A ) )
| ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastLessThan__empty__iff2_1) ).
thf(732,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A ) )
| ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(425,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/sandbox2/benchmark/theBenchmark.p',cls_inj__image__subset__iff_0) ).
thf(1388,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)],[425]) ).
thf(139,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ B @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__least_0) ).
thf(743,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ B @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(311,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ A @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ B @ D )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ D @ tc_bool ) ) @ ( c_Set_Oimage @ A @ C @ B @ D ) ) )
| ~ ( c_Fun_Obij @ A @ B @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bij__image__Compl__eq_0) ).
thf(1124,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ A @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ B @ D )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ D @ tc_bool ) ) @ ( c_Set_Oimage @ A @ C @ B @ D ) ) )
| ~ ( c_Fun_Obij @ A @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(179,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ C )
| ~ ( c_Finite__Set_Ofinite @ B @ C )
| ~ ( c_Finite__Set_Ofinite @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__UnI_0) ).
thf(826,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ C )
| ~ ( c_Finite__Set_Ofinite @ B @ C )
| ~ ( c_Finite__Set_Ofinite @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(124,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_atLeastLessThan__empty__iff_1) ).
thf(711,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
| ( c_HOL_Oord__class_Oless @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(92,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Fun_Obij @ ( c_Hilbert__Choice_Oinv__into @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ B @ A @ C ) @ C @ A )
| ~ ( c_Fun_Obij @ B @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bij__imp__bij__inv_0) ).
thf(641,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Fun_Obij @ ( c_Hilbert__Choice_Oinv__into @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ B @ A @ C ) @ C @ A )
| ~ ( c_Fun_Obij @ B @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(318,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ B @ A @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__commute_0) ).
thf(1139,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ B @ A @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(228,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__subset__iff_2) ).
thf(936,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(392,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__commute_0) ).
thf(1312,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(28,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/sandbox2/benchmark/theBenchmark.p',cls_order__le__neq__trans_0) ).
thf(498,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)],[28]) ).
thf(401,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E )
= ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oimage @ A @ B @ D @ E ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ ( tc_fun @ E @ tc_bool ) ) )
| ~ ( c_lessequals @ C @ F @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ B @ F @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ A @ F @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__image__set__diff_0) ).
thf(1332,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)],[401]) ).
thf(296,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Int__distrib2_0) ).
thf(1092,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(295,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Set_Oimage @ B @ C @ D @ E ) @ ( tc_fun @ E @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Set_Ovimage @ B @ A @ D @ E ) @ C @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_Fun_Osurj @ B @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__subsetD_0) ).
thf(1090,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Set_Oimage @ B @ C @ D @ E ) @ ( tc_fun @ E @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Set_Ovimage @ B @ A @ D @ E ) @ C @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_Fun_Osurj @ B @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(370,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/sandbox2/benchmark/theBenchmark.p',cls_eq__card__imp__inj__on_0) ).
thf(1258,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)],[370]) ).
thf(106,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_Fun_Osurj @ C @ D @ B )
| ~ ( c_Finite__Set_Ofinite @ ( c_Set_Ovimage @ C @ A @ D @ B ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__vimageD_0) ).
thf(672,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_Fun_Osurj @ C @ D @ B )
| ~ ( c_Finite__Set_Ofinite @ ( c_Set_Ovimage @ C @ A @ D @ B ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(79,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C )
!= ( c_Set_Oinsert @ D @ ( c_Set_Oinsert @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) @ C ) )
| ( A = E )
| ( B = E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_2) ).
thf(611,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)],[79]) ).
thf(160,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_Obij @ A @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__subset__eq_1) ).
thf(787,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_Obij @ A @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(279,axiom,
! [A: $i] : ( c_lessequals @ ( c_Suc @ A ) @ ( c_Suc @ A ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__Suc__eq_2) ).
thf(1058,plain,
! [A: $i] : ( c_lessequals @ ( c_Suc @ A ) @ ( c_Suc @ A ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(303,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ A @ ( hAPP @ B @ C ) )
= ( hAPP @ ( c_Fun_Ocomp @ A @ B @ D @ E @ F ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_o__eq__dest__lhs_0) ).
thf(1107,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ A @ ( hAPP @ B @ C ) )
= ( hAPP @ ( c_Fun_Ocomp @ A @ B @ D @ E @ F ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(350,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Omap @ A @ B @ C @ D )
!= ( c_List_Omap @ 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/sandbox2/benchmark/theBenchmark.p',cls_inj__map__eq__map_0) ).
thf(1209,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Omap @ A @ B @ C @ D )
!= ( c_List_Omap @ 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)],[350]) ).
thf(182,axiom,
! [A: $i] : ( c_Finite__Set_Ofinite @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite_OemptyI_0) ).
thf(831,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)],[182]) ).
thf(380,axiom,
! [B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ A @ ( tc_fun @ B @ tc_bool ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__absorb_0) ).
thf(1282,plain,
! [B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ A @ ( tc_fun @ B @ tc_bool ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(158,axiom,
! [A: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ A @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__empty_1) ).
thf(784,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)],[158]) ).
thf(274,axiom,
! [A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ A @ tc_nat )
| ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ A ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__less__Suc__eq_1) ).
thf(1048,plain,
! [A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ A @ tc_nat )
| ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ A ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(408,axiom,
! [A: $i] :
~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Finite__Set_Ocard @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_card__gt__0__iff_0) ).
thf(1349,plain,
! [A: $i] :
~ ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Finite__Set_Ocard @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(253,axiom,
! [B: $i,A: $i] :
( ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
| ~ ( c_lessequals @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__empty_0) ).
thf(996,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)],[253]) ).
thf(7,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/sandbox2/benchmark/theBenchmark.p',cls_subset__singletonD_0) ).
thf(451,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)],[7]) ).
thf(136,axiom,
! [B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__empty__right_0) ).
thf(737,plain,
! [B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Orderings_Obot__class_Obot @ ( 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)],[136]) ).
thf(81,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/sandbox2/benchmark/theBenchmark.p',cls_order__neq__le__trans_0) ).
thf(616,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)],[81]) ).
thf(420,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
!= ( c_Set_Oimage @ B @ C @ D @ A ) )
| ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__is__image_0) ).
thf(1376,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)],[420]) ).
thf(246,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ E @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ B @ E @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__mono_0) ).
thf(979,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ E @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ B @ E @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(75,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/sandbox2/benchmark/theBenchmark.p',cls_subset__insertI2_0) ).
thf(604,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)],[75]) ).
thf(110,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ D @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__Un__distrib_0) ).
thf(681,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ D @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(434,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ B @ C )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) )
| ~ ( c_Fun_Osurj @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_surj__range_0) ).
thf(1408,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ B @ C )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) )
| ~ ( c_Fun_Osurj @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(209,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ C @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__finite__subset_0) ).
thf(890,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)],[209]) ).
thf(19,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ D @ A )
| ~ ( c_HOL_Oord__class_Oless @ D @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_xt1_I10_J_0) ).
thf(477,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)],[19]) ).
thf(51,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ C )
| ~ ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ D @ B @ C ) @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__Diff__insert_0) ).
thf(552,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)],[51]) ).
thf(174,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_lessequals @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__eq__less__or__eq_0) ).
thf(816,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_lessequals @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(131,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/sandbox2/benchmark/theBenchmark.p',cls_vimage__empty_0) ).
thf(726,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)],[131]) ).
thf(83,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/sandbox2/benchmark/theBenchmark.p',cls_not__leE_0) ).
thf(621,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)],[83]) ).
thf(38,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/sandbox2/benchmark/theBenchmark.p',cls_xt1_I11_J_0) ).
thf(520,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)],[38]) ).
thf(212,axiom,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__lower2_0) ).
thf(895,plain,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(220,axiom,
! [B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ B @ ( tc_fun @ A @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Compl__disjoint2_0) ).
thf(915,plain,
! [B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ B @ ( tc_fun @ A @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(406,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ B @ C )
| ( ( hAPP @ A @ ( c_ATP__Linkup_Osko__Fun__Xdatatype__injI__1__1 @ A @ B @ C ) )
= ( hAPP @ A @ ( c_ATP__Linkup_Osko__Fun__Xdatatype__injI__1__2 @ A @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_datatype__injI_0) ).
thf(1344,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ B @ C )
| ( ( hAPP @ A @ ( c_ATP__Linkup_Osko__Fun__Xdatatype__injI__1__1 @ A @ B @ C ) )
= ( hAPP @ A @ ( c_ATP__Linkup_Osko__Fun__Xdatatype__injI__1__2 @ A @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(151,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Int__crazy_0) ).
thf(769,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(264,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Hilbert__Choice_Oinv__into @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Fun_Ocomp @ B @ C @ D @ E @ A ) @ A @ E )
= ( c_Fun_Ocomp @ ( c_Hilbert__Choice_Oinv__into @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ C @ A @ D ) @ ( c_Hilbert__Choice_Oinv__into @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_bool ) ) @ B @ D @ E ) @ D @ A @ E ) )
| ~ ( c_Fun_Obij @ C @ A @ D )
| ~ ( c_Fun_Obij @ B @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_o__inv__distrib_0) ).
thf(1022,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Hilbert__Choice_Oinv__into @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Fun_Ocomp @ B @ C @ D @ E @ A ) @ A @ E )
= ( c_Fun_Ocomp @ ( c_Hilbert__Choice_Oinv__into @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ C @ A @ D ) @ ( c_Hilbert__Choice_Oinv__into @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_bool ) ) @ B @ D @ E ) @ D @ A @ E ) )
| ~ ( c_Fun_Obij @ C @ A @ D )
| ~ ( c_Fun_Obij @ B @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(105,axiom,
! [B: $i,A: $i] :
( ( ( c_Suc @ A )
!= ( c_Suc @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__inject_0) ).
thf(668,plain,
! [B: $i,A: $i] :
( ( ( c_Suc @ A )
!= ( c_Suc @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(336,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/sandbox2/benchmark/theBenchmark.p',cls_vimage__UNIV_0) ).
thf(1177,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)],[336]) ).
thf(422,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__left__commute_0) ).
thf(1381,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(12,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/sandbox2/benchmark/theBenchmark.p',cls_single__Diff__lessThan_0) ).
thf(462,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)],[12]) ).
thf(281,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ A @ ( tc_fun @ B @ tc_bool ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__Un_1) ).
thf(1061,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ A @ ( tc_fun @ B @ tc_bool ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(219,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Finite__Set_Ocard @ ( c_Set_Oinsert @ A @ B @ C ) @ C )
= ( c_Suc @ ( c_Finite__Set_Ocard @ ( 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_Finite__Set_Ofinite @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_card__insert_0) ).
thf(912,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Finite__Set_Ocard @ ( c_Set_Oinsert @ A @ B @ C ) @ C )
= ( c_Suc @ ( c_Finite__Set_Ocard @ ( 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_Finite__Set_Ofinite @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(238,axiom,
! [A: $i] :
( ~ ( c_lessequals @ A @ A @ tc_nat )
| ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ A ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__less__Suc__eq_1) ).
thf(959,plain,
! [A: $i] :
( ~ ( c_lessequals @ A @ A @ tc_nat )
| ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ A ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(198,axiom,
! [A: $i] : ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ A ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc__eq_2) ).
thf(868,plain,
! [A: $i] : ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ A ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(156,axiom,
! [B: $i,A: $i] :
( ( c_lessequals @ ( c_Suc @ A ) @ B @ tc_nat )
| ( c_lessequals @ B @ A @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__eq__eq_0) ).
thf(780,plain,
! [B: $i,A: $i] :
( ( c_lessequals @ ( c_Suc @ A ) @ B @ tc_nat )
| ( c_lessequals @ B @ A @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(306,axiom,
! [B: $i,A: $i] :
( ( c_lessequals @ A @ B @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ A ) @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__leD_0) ).
thf(1113,plain,
! [B: $i,A: $i] :
( ( c_lessequals @ A @ B @ tc_nat )
| ~ ( c_lessequals @ ( c_Suc @ A ) @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(301,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oimage @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E ) @ ( c_Set_Oimage @ A @ ( c_HOL_Ominus__class_Ominus @ C @ B @ ( tc_fun @ D @ tc_bool ) ) @ D @ E ) @ ( tc_fun @ E @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_bool ) ) )
| ~ ( c_Fun_Oinj__on @ A @ C @ D @ E )
| ~ ( c_Fun_Oinj__on @ A @ B @ D @ E )
| ( c_Fun_Oinj__on @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__Un_3) ).
thf(1102,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oimage @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E ) @ ( c_Set_Oimage @ A @ ( c_HOL_Ominus__class_Ominus @ C @ B @ ( tc_fun @ D @ tc_bool ) ) @ D @ E ) @ ( tc_fun @ E @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_bool ) ) )
| ~ ( c_Fun_Oinj__on @ A @ C @ D @ E )
| ~ ( c_Fun_Oinj__on @ A @ B @ D @ E )
| ( c_Fun_Oinj__on @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(100,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
| ~ ( c_lessequals @ A @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_bool ) ) @ B ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_disjoint__eq__subset__Compl_1) ).
thf(658,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
| ~ ( c_lessequals @ A @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_bool ) ) @ B ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(90,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Hilbert__Choice_Oinv__into @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Hilbert__Choice_Oinv__into @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ C @ B @ A ) @ A @ B )
= C )
| ~ ( c_Fun_Obij @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inv__inv__eq_0) ).
thf(636,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Hilbert__Choice_Oinv__into @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Hilbert__Choice_Oinv__into @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ C @ B @ A ) @ A @ B )
= C )
| ~ ( c_Fun_Obij @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(116,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Ovimage @ ( c_Fun_Ocomp @ A @ B @ C @ D @ E ) @ F @ E @ D )
= ( c_Set_Ovimage @ B @ ( c_Set_Ovimage @ A @ F @ C @ D ) @ E @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__compose_0) ).
thf(695,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Ovimage @ ( c_Fun_Ocomp @ A @ B @ C @ D @ E ) @ F @ E @ D )
= ( c_Set_Ovimage @ B @ ( c_Set_Ovimage @ A @ F @ C @ D ) @ E @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(9,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Fun_Ocomp @ A @ B @ C @ D @ E )
!= ( c_Fun_Ocomp @ ( c_Fun_Oid @ D ) @ F @ D @ D @ E ) )
| ( ( hAPP @ A @ ( hAPP @ B @ G ) )
= ( hAPP @ F @ G ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_o__eq__id__dest_0) ).
thf(455,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Fun_Ocomp @ A @ B @ C @ D @ E )
!= ( c_Fun_Ocomp @ ( c_Fun_Oid @ D ) @ F @ D @ D @ E ) )
| ( ( hAPP @ A @ ( hAPP @ B @ G ) )
= ( hAPP @ F @ G ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(206,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oimage @ A @ ( c_Set_Oimage @ B @ C @ D @ E ) @ E @ F )
= ( c_Set_Oimage @ ( c_COMBB @ A @ B @ E @ F @ D ) @ C @ D @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__image_0) ).
thf(883,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oimage @ A @ ( c_Set_Oimage @ B @ C @ D @ E ) @ E @ F )
= ( c_Set_Oimage @ ( c_COMBB @ A @ B @ E @ F @ D ) @ C @ D @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(335,axiom,
class_Ring__and__Field_Osemiring__1 @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Ring__and__Field_Osemiring__1) ).
thf(1176,plain,
class_Ring__and__Field_Osemiring__1 @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(77,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Finite__Set_Ocard @ A @ B ) @ ( c_Finite__Set_Ocard @ ( c_Set_Oinsert @ C @ A @ B ) @ B ) @ tc_nat )
| ~ ( c_Finite__Set_Ofinite @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_card__insert__le_0) ).
thf(608,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Finite__Set_Ocard @ A @ B ) @ ( c_Finite__Set_Ocard @ ( c_Set_Oinsert @ C @ A @ B ) @ B ) @ tc_nat )
| ~ ( c_Finite__Set_Ofinite @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(31,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Set_Oinsert @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__insert__right_0) ).
thf(505,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Set_Oinsert @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(2,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B )
!= ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) )
| ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_singleton__inject_0) ).
thf(438,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)],[2]) ).
thf(288,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ B @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__subset__iff_2) ).
thf(1076,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ B @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(290,axiom,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__upper1_0) ).
thf(1081,plain,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(404,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ B @ C )
| ~ ( c_Fun_Obij @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bij__def_0) ).
thf(1340,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ B @ C )
| ~ ( c_Fun_Obij @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(262,axiom,
! [A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A )
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sup__empty_0) ).
thf(1018,plain,
! [A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A )
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(347,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Oinj__on @ A @ ( c_Set_Oimage @ B @ C @ D @ E ) @ E @ F )
| ~ ( c_Fun_Oinj__on @ ( c_Fun_Ocomp @ A @ B @ E @ F @ D ) @ C @ D @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__imageI_0) ).
thf(1203,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Oinj__on @ A @ ( c_Set_Oimage @ B @ C @ D @ E ) @ E @ F )
| ~ ( c_Fun_Oinj__on @ ( c_Fun_Ocomp @ A @ B @ E @ F @ D ) @ C @ D @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(68,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_bool ) ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_bool ) ) @ A ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Compl__subset__Compl__iff_0) ).
thf(589,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_bool ) ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_bool ) ) @ A ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(42,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( B = C )
| ~ ( c_lessequals @ C @ B @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__eq__iff_2) ).
thf(531,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)],[42]) ).
thf(232,axiom,
! [A: $i] : ( c_Finite__Set_Ofinite @ ( c_SetInterval_Oord__class_OlessThan @ A @ tc_nat ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__lessThan_0) ).
thf(944,plain,
! [A: $i] : ( c_Finite__Set_Ofinite @ ( c_SetInterval_Oord__class_OlessThan @ A @ tc_nat ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(102,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ A @ tc_bool ) ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Compl__Un_0) ).
thf(663,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ A @ tc_bool ) ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(49,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_Finite__Set_Ofinite @ ( c_Set_Oinsert @ C @ A @ B ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__insert_0) ).
thf(548,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)],[49]) ).
thf(10,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/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__less_1) ).
thf(458,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)],[10]) ).
thf(338,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/sandbox2/benchmark/theBenchmark.p',cls_inj__on__the__inv__into_0) ).
thf(1181,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)],[338]) ).
thf(154,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Osurj @ ( c_Fun_Ocomp @ A @ B @ C @ D @ E ) @ E @ D )
| ~ ( c_Fun_Osurj @ A @ C @ D )
| ~ ( c_Fun_Osurj @ B @ E @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comp__surj_0) ).
thf(776,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Osurj @ ( c_Fun_Ocomp @ A @ B @ C @ D @ E ) @ E @ D )
| ~ ( c_Fun_Osurj @ A @ C @ D )
| ~ ( c_Fun_Osurj @ B @ E @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(40,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( B = C )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv3_0) ).
thf(525,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)],[40]) ).
thf(114,axiom,
! [A: $i] :
( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Compl__empty__eq_0) ).
thf(690,plain,
! [A: $i] :
( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(265,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( hAPP @ B @ C ) )
= C )
| ~ ( c_Typedef_Otype__definition @ B @ A @ D @ E @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_type__definition_ORep__inverse_0) ).
thf(1025,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( hAPP @ B @ C ) )
= C )
| ~ ( c_Typedef_Otype__definition @ B @ A @ D @ E @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(200,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__subset__iff_1) ).
thf(872,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(121,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__Int__distrib2_0) ).
thf(705,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(137,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ B ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__SucI_0) ).
thf(739,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ B ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(417,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__trans_0) ).
thf(1368,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)],[417]) ).
thf(359,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oimage @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ A @ B @ D @ E ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ ( tc_fun @ E @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__Un_0) ).
thf(1230,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oimage @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ A @ B @ D @ E ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ ( tc_fun @ E @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(299,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_bool ) ) @ B ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__eq_0) ).
thf(1098,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_bool ) ) @ B ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(357,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Oinj__on @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E )
| ~ ( c_Fun_Oinj__on @ A @ B @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__diff_0) ).
thf(1225,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)],[357]) ).
thf(430,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__left__commute_0) ).
thf(1400,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(122,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ D @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Int__distrib_0) ).
thf(707,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ D @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(236,axiom,
! [B: $i,A: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Complete__Lattice_Ocomplete__lattice @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Complete__Lattice_Ocomplete__lattice) ).
thf(954,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)],[236]) ).
thf(368,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/sandbox2/benchmark/theBenchmark.p',cls_card__image_0) ).
thf(1252,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)],[368]) ).
thf(387,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/sandbox2/benchmark/theBenchmark.p',cls_inj__image__eq__iff_0) ).
thf(1300,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)],[387]) ).
thf(162,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc__eq__0__disj_3) ).
thf(791,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(3,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( c_HOL_Oord__class_Oless @ C @ B @ A )
| ( C = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__neqE_0) ).
thf(441,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)],[3]) ).
thf(362,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ A @ B @ C @ C )
= B )
| ~ ( c_Fun_Oinj__on @ A @ B @ C @ C )
| ~ ( c_lessequals @ ( c_Set_Oimage @ A @ B @ C @ C ) @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_endo__inj__surj_0) ).
thf(1235,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)],[362]) ).
thf(93,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Obij__betw @ ( c_Fun_Othe__inv__into @ A @ B @ C @ D ) @ E @ A @ D @ C )
| ~ ( c_Fun_Obij__betw @ B @ A @ E @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bij__betw__the__inv__into_0) ).
thf(643,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Obij__betw @ ( c_Fun_Othe__inv__into @ A @ B @ C @ D ) @ E @ A @ D @ C )
| ~ ( c_Fun_Obij__betw @ B @ A @ E @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(47,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Ovimage @ A @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D @ B )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ D @ tc_bool ) ) @ ( c_Set_Ovimage @ A @ C @ D @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__Compl_0) ).
thf(544,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Ovimage @ A @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D @ B )
= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ D @ tc_bool ) ) @ ( c_Set_Ovimage @ A @ C @ D @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(341,axiom,
! [A: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Zero__neq__Suc_0) ).
thf(1188,plain,
! [A: $i] :
( ( c_HOL_Ozero__class_Ozero @ tc_nat )
!= ( c_Suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(340,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Fun_Obij @ A @ B @ C )
| ~ ( c_Fun_Osurj @ A @ B @ C )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bij__def_2) ).
thf(1186,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Fun_Obij @ A @ B @ C )
| ~ ( c_Fun_Osurj @ A @ B @ C )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(15,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/sandbox2/benchmark/theBenchmark.p',cls_insert__mono_0) ).
thf(470,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)],[15]) ).
thf(62,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C )
= ( c_Set_Oinsert @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__absorb2_0) ).
thf(576,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)],[62]) ).
thf(235,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Set_Oinsert @ B @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ A ) @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sup__binary_0) ).
thf(951,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Set_Oinsert @ B @ ( c_Set_Oinsert @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A ) @ A ) @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(171,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ E @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ B @ E @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__mono_0) ).
thf(808,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ E @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ B @ E @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(432,axiom,
! [A: $i] :
( ( c_Finite__Set_Ocard @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_card__empty_0) ).
thf(1404,plain,
! [A: $i] :
( ( c_Finite__Set_Ocard @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ A )
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(120,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Set_Ovimage @ A @ B @ C @ D ) @ C )
| ~ ( c_Finite__Set_Ofinite @ B @ D )
| ~ ( c_Fun_Obij @ A @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__vimage__iff_1) ).
thf(703,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Set_Ovimage @ A @ B @ C @ D ) @ C )
| ~ ( c_Finite__Set_Ofinite @ B @ D )
| ~ ( c_Fun_Obij @ A @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(319,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__left__absorb_0) ).
thf(1141,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(99,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Set_Oimage @ B @ C @ D @ E ) @ ( tc_fun @ E @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Set_Ovimage @ B @ A @ D @ E ) @ C @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_Fun_Obij @ B @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__subset__eq_0) ).
thf(656,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Set_Oimage @ B @ C @ D @ E ) @ ( tc_fun @ E @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Set_Ovimage @ B @ A @ D @ E ) @ C @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_Fun_Obij @ B @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(276,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ A @ B @ C @ D @ E ) @ F )
= ( hAPP @ A @ ( hAPP @ B @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_o__apply_0) ).
thf(1052,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Fun_Ocomp @ A @ B @ C @ D @ E ) @ F )
= ( hAPP @ A @ ( hAPP @ B @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(196,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__less__eq_0) ).
thf(864,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(297,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( 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 ) @ tc_nat )
| ~ ( c_Finite__Set_Ofinite @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_card__Diff1__le_0) ).
thf(1094,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( 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 ) @ tc_nat )
| ~ ( c_Finite__Set_Ofinite @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(59,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__insert2_0) ).
thf(571,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)],[59]) ).
thf(376,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/sandbox2/benchmark/theBenchmark.p',cls_the__inv__f__f_0) ).
thf(1272,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)],[376]) ).
thf(194,axiom,
! [B: $i,A: $i] :
( ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
| ~ ( c_lessequals @ A @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ B @ tc_bool ) ) @ A ) @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__Compl__self__eq_0) ).
thf(859,plain,
! [B: $i,A: $i] :
( ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
| ~ ( c_lessequals @ A @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ B @ tc_bool ) ) @ A ) @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(251,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ A @ B @ C @ D )
= E )
| ~ ( c_Fun_Obij__betw @ A @ B @ E @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bij__betw__def_1) ).
thf(991,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ A @ B @ C @ D )
= E )
| ~ ( c_Fun_Obij__betw @ A @ B @ E @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(355,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Fun_Oinj__on @ A @ B @ C @ C )
| ~ ( c_lessequals @ B @ ( c_Set_Oimage @ A @ B @ C @ C ) @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__surj__inj_0) ).
thf(1221,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)],[355]) ).
thf(381,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/sandbox2/benchmark/theBenchmark.p',cls_image__inv__f__f_0) ).
thf(1284,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)],[381]) ).
thf(410,axiom,
! [B: $i,A: $i] : ( c_lessequals @ A @ A @ ( tc_fun @ B @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__refl_0) ).
thf(1353,plain,
! [B: $i,A: $i] : ( c_lessequals @ A @ A @ ( tc_fun @ B @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(73,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/sandbox2/benchmark/theBenchmark.p',cls_linorder__not__le_1) ).
thf(600,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)],[73]) ).
thf(13,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__insert_0) ).
thf(465,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)],[13]) ).
thf(86,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ B )
!= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ C ) )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Compl__eq__Compl__iff_0) ).
thf(627,plain,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ B )
!= ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ C ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(53,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/sandbox2/benchmark/theBenchmark.p',cls_insert__subset_1) ).
thf(556,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)],[53]) ).
thf(64,axiom,
class_Orderings_Olinorder @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
thf(581,plain,
class_Orderings_Olinorder @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(147,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_HOL_Ominus__class_Ominus @ B @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__disjoint_0) ).
thf(759,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_HOL_Ominus__class_Ominus @ B @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(152,axiom,
! [B: $i,A: $i] :
( ( c_lessequals @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_nat__less__le_0) ).
thf(771,plain,
! [B: $i,A: $i] :
( ( c_lessequals @ A @ B @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(395,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oimage @ A @ B @ D @ E ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ ( tc_fun @ E @ tc_bool ) ) )
| ~ ( c_lessequals @ C @ F @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ B @ F @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ A @ F @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__image__Int_0) ).
thf(1316,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( 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)],[395]) ).
thf(292,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Finite__Set_Ocard @ ( c_Set_Oimage @ A @ B @ C @ D ) @ D ) @ ( c_Finite__Set_Ocard @ B @ C ) @ tc_nat )
| ~ ( c_Finite__Set_Ofinite @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_card__image__le_0) ).
thf(1084,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Finite__Set_Ocard @ ( c_Set_Oimage @ A @ B @ C @ D ) @ D ) @ ( c_Finite__Set_Ocard @ B @ C ) @ tc_nat )
| ~ ( c_Finite__Set_Ofinite @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(226,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Ovimage @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ E @ D )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Ovimage @ A @ B @ E @ D ) @ ( c_Set_Ovimage @ A @ C @ E @ D ) @ ( tc_fun @ E @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__Int_0) ).
thf(931,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Ovimage @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ E @ D )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( 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)],[226]) ).
thf(45,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/sandbox2/benchmark/theBenchmark.p',cls_inj__on__insert_0) ).
thf(539,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)],[45]) ).
thf(326,axiom,
! [A: $i] :
~ ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less0_0) ).
thf(1157,plain,
! [A: $i] :
~ ( c_HOL_Oord__class_Oless @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(397,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_ATP__Linkup_Osko__Fun__XinjI__1__1 @ A @ B @ C )
!= ( c_ATP__Linkup_Osko__Fun__XinjI__1__2 @ A @ B @ C ) )
| ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_injI_1) ).
thf(1321,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_ATP__Linkup_Osko__Fun__XinjI__1__1 @ A @ B @ C )
!= ( c_ATP__Linkup_Osko__Fun__XinjI__1__2 @ A @ B @ C ) )
| ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(245,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Finite__Set_Ocard @ A @ B )
= ( c_Finite__Set_Ocard @ C @ D ) )
| ~ ( c_Fun_Obij__betw @ E @ A @ C @ B @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bij__betw__same__card_0) ).
thf(976,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Finite__Set_Ocard @ A @ B )
= ( c_Finite__Set_Ocard @ C @ D ) )
| ~ ( c_Fun_Obij__betw @ E @ A @ C @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(113,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Omap @ A @ ( c_List_Omap @ B @ C @ D @ E ) @ E @ F )
= ( c_List_Omap @ ( c_Fun_Ocomp @ A @ B @ E @ F @ D ) @ C @ D @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__map_0) ).
thf(688,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Omap @ A @ ( c_List_Omap @ B @ C @ D @ E ) @ E @ F )
= ( c_List_Omap @ ( c_Fun_Ocomp @ A @ B @ E @ F @ D ) @ C @ D @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(258,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Diff__Int_0) ).
thf(1010,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(426,axiom,
! [A: $i] :
( ( c_Suc @ A )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__neq__Zero_0) ).
thf(1390,plain,
! [A: $i] :
( ( c_Suc @ A )
!= ( c_HOL_Ozero__class_Ozero @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(383,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Oinj__on @ A @ B @ C @ D )
| ~ ( c_lessequals @ B @ E @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_Fun_Oinj__on @ A @ E @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__inj__on_0) ).
thf(1289,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)],[383]) ).
thf(188,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
| ( c_lessequals @ A @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_bool ) ) @ B ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_disjoint__eq__subset__Compl_0) ).
thf(844,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
| ( c_lessequals @ A @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ C @ tc_bool ) ) @ B ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(118,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Obij @ ( c_Fun_Ocomp @ A @ B @ C @ D @ E ) @ E @ D )
| ~ ( c_Fun_Obij @ A @ C @ D )
| ~ ( c_Fun_Obij @ B @ E @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bij__comp_0) ).
thf(699,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Obij @ ( c_Fun_Ocomp @ A @ B @ C @ D @ E ) @ E @ D )
| ~ ( c_Fun_Obij @ A @ C @ D )
| ~ ( c_Fun_Obij @ B @ E @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(37,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/sandbox2/benchmark/theBenchmark.p',cls_xt1_I12_J_0) ).
thf(517,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)],[37]) ).
thf(97,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Ovimage @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ E @ D )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Ovimage @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ E @ D ) @ ( c_Set_Ovimage @ A @ C @ E @ D ) @ ( tc_fun @ E @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_vimage__insert_0) ).
thf(652,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Ovimage @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ E @ D )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Ovimage @ A @ ( c_Set_Oinsert @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) @ D ) @ E @ D ) @ ( c_Set_Ovimage @ A @ C @ E @ D ) @ ( tc_fun @ E @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(88,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/sandbox2/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_0) ).
thf(632,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)],[88]) ).
thf(239,axiom,
! [A: $i] : ( c_lessequals @ A @ A @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__imp__le_0) ).
thf(961,plain,
! [A: $i] : ( c_lessequals @ A @ A @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(173,axiom,
! [A: $i] :
( A
!= ( c_Suc @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_n__not__Suc__n_0) ).
thf(813,plain,
! [A: $i] :
( A
!= ( c_Suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(213,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ A @ ( c_Set_Ovimage @ A @ B @ C @ D ) @ C @ D )
= B )
| ~ ( c_Fun_Osurj @ A @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_surj__image__vimage__eq_0) ).
thf(896,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ A @ ( c_Set_Ovimage @ A @ B @ C @ D ) @ C @ D )
= B )
| ~ ( c_Fun_Osurj @ A @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(142,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ A @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( tc_fun @ B @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ A @ C @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__Compl_0) ).
thf(748,plain,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ A @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( tc_fun @ B @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ A @ C @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(267,axiom,
! [A: $i] :
( ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc0_0) ).
thf(1030,plain,
! [A: $i] :
( ( A
= ( c_HOL_Ozero__class_Ozero @ tc_nat ) )
| ~ ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(33,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ~ ( c_HOL_Oord__class_Oless @ B @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_order__less__le_1) ).
thf(510,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)],[33]) ).
thf(390,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/sandbox2/benchmark/theBenchmark.p',cls_the__inv__into__onto_0) ).
thf(1308,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)],[390]) ).
thf(343,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( 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/sandbox2/benchmark/theBenchmark.p',cls_image__Int_0) ).
thf(1193,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( 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)],[343]) ).
thf(351,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/sandbox2/benchmark/theBenchmark.p',cls_inj__image__subset__iff_1) ).
thf(1212,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)],[351]) ).
thf(149,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Fun_Ocomp @ A @ ( c_Hilbert__Choice_Oinv__into @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ A @ B @ C ) @ B @ C @ C )
!= ( c_Fun_Oid @ C ) )
| ( c_Fun_Osurj @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_surj__iff_1) ).
thf(763,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Fun_Ocomp @ A @ ( c_Hilbert__Choice_Oinv__into @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ A @ B @ C ) @ B @ C @ C )
!= ( c_Fun_Oid @ C ) )
| ( c_Fun_Osurj @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(214,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) )
= A )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__absorb2_0) ).
thf(899,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) )
= A )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(183,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ B )
= ( c_HOL_Ominus__class_Ominus @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Compl__eq__Diff__UNIV_0) ).
thf(832,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ B )
= ( c_HOL_Ominus__class_Ominus @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(44,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_HOL_Oord__class_Oless @ B @ C @ A )
| ( C = B )
| ( c_HOL_Oord__class_Oless @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__less__linear_0) ).
thf(536,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)],[44]) ).
thf(273,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ B ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__less__less__Suc__eq_0) ).
thf(1045,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( c_HOL_Oord__class_Oless @ A @ ( c_Suc @ B ) @ tc_nat )
| ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(104,axiom,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ A @ ( tc_fun @ C @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__subset_0) ).
thf(667,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)],[104]) ).
thf(385,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( c_lessequals @ B @ A @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equalityI_0) ).
thf(1294,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)],[385]) ).
thf(126,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ( A = B )
| ~ ( c_lessequals @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__neq__implies__less_0) ).
thf(716,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat )
| ( A = B )
| ~ ( c_lessequals @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(328,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__assoc_0) ).
thf(1161,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(167,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Ocomp @ A @ ( c_Fun_Ocomp @ B @ C @ D @ E @ F ) @ E @ G @ F )
= ( c_Fun_Ocomp @ ( c_Fun_Ocomp @ A @ B @ E @ G @ D ) @ C @ D @ G @ F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_o__assoc_0) ).
thf(800,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Fun_Ocomp @ A @ ( c_Fun_Ocomp @ B @ C @ D @ E @ F ) @ E @ G @ F )
= ( c_Fun_Ocomp @ ( c_Fun_Ocomp @ A @ B @ E @ G @ D ) @ C @ D @ G @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(315,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/sandbox2/benchmark/theBenchmark.p',cls_UNIV__not__empty_0) ).
thf(1133,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)],[315]) ).
thf(254,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Fun_Ocomp @ A @ ( c_Hilbert__Choice_Oinv__into @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ A @ B @ C ) @ B @ C @ C )
= ( c_Fun_Oid @ C ) )
| ~ ( c_Fun_Osurj @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_surj__iff_0) ).
thf(999,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Fun_Ocomp @ A @ ( c_Hilbert__Choice_Oinv__into @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ A @ B @ C ) @ B @ C @ C )
= ( c_Fun_Oid @ C ) )
| ~ ( c_Fun_Osurj @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(144,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Finite__Set_Ocard @ A @ B ) @ tc_nat )
| ~ ( c_Finite__Set_Ofinite @ A @ B )
| ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_card__gt__0__iff_2) ).
thf(752,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Finite__Set_Ocard @ A @ B ) @ tc_nat )
| ~ ( c_Finite__Set_Ofinite @ A @ B )
| ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(5,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/sandbox2/benchmark/theBenchmark.p',cls_xt1_I8_J_0) ).
thf(447,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)],[5]) ).
thf(379,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
= ( c_Set_Oimage @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__is__image_1) ).
thf(1280,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)],[379]) ).
thf(242,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
!= ( hAPP @ A @ C ) )
| ~ ( c_Typedef_Otype__definition @ A @ D @ E @ F @ G )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_type__definition_ORep__inject_0) ).
thf(967,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
!= ( hAPP @ A @ C ) )
| ~ ( c_Typedef_Otype__definition @ A @ D @ E @ F @ G )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(322,axiom,
! [A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ A )
= ( c_Orderings_Otop__class_Otop @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sup__UNIV_0) ).
thf(1148,plain,
! [A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ A )
= ( c_Orderings_Otop__class_Otop @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(135,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ A @ A @ ( tc_fun @ B @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__cancel_0) ).
thf(735,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)],[135]) ).
thf(192,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) )
= B )
| ~ ( c_lessequals @ B @ A @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__absorb1_0) ).
thf(854,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) )
= B )
| ~ ( c_lessequals @ B @ A @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(388,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/sandbox2/benchmark/theBenchmark.p',cls_card__bij__eq_0) ).
thf(1303,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)],[388]) ).
thf(56,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/sandbox2/benchmark/theBenchmark.p',cls_image__insert_0) ).
thf(564,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)],[56]) ).
thf(170,axiom,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__upper2_0) ).
thf(807,plain,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(402,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Omap @ A @ ( c_List_OremoveAll @ B @ C @ D ) @ D @ E )
= ( c_List_OremoveAll @ ( hAPP @ A @ B ) @ ( c_List_Omap @ A @ C @ D @ E ) @ E ) )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_bool ) ) @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_map__removeAll__inj_0) ).
thf(1335,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Omap @ A @ ( c_List_OremoveAll @ B @ C @ D ) @ D @ E )
= ( c_List_OremoveAll @ ( hAPP @ A @ B ) @ ( c_List_Omap @ A @ C @ D @ E ) @ E ) )
| ~ ( 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)],[402]) ).
thf(278,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__Int2_0) ).
thf(1056,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(268,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Set_Oimage @ A @ B @ C @ D ) @ D )
| ~ ( c_Finite__Set_Ofinite @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__imageI_0) ).
thf(1033,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)],[268]) ).
thf(180,axiom,
! [A: $i] : ( c_lessequals @ A @ A @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__refl_0) ).
thf(828,plain,
! [A: $i] : ( c_lessequals @ A @ A @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(89,axiom,
class_Orderings_Oorder @ tc_bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Oorder) ).
thf(635,plain,
class_Orderings_Oorder @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(283,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oimage @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E ) @ ( c_Set_Oimage @ A @ ( c_HOL_Ominus__class_Ominus @ C @ B @ ( tc_fun @ D @ tc_bool ) ) @ D @ E ) @ ( tc_fun @ E @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_bool ) ) )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__on__Un_2) ).
thf(1065,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oimage @ A @ ( c_HOL_Ominus__class_Ominus @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E ) @ ( c_Set_Oimage @ A @ ( c_HOL_Ominus__class_Ominus @ C @ B @ ( tc_fun @ D @ tc_bool ) ) @ D @ E ) @ ( tc_fun @ E @ tc_bool ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_bool ) ) )
| ~ ( c_Fun_Oinj__on @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(330,axiom,
! [B: $i,A: $i] :
( ( c_Fun_Obij__betw @ ( c_List_Osko__SetInterval__Xex__bij__betw__nat__finite__1__1 @ A @ B ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Finite__Set_Ocard @ A @ B ) @ tc_nat ) @ A @ tc_nat @ B )
| ~ ( c_Finite__Set_Ofinite @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ex__bij__betw__nat__finite_0) ).
thf(1165,plain,
! [B: $i,A: $i] :
( ( c_Fun_Obij__betw @ ( c_List_Osko__SetInterval__Xex__bij__betw__nat__finite__1__1 @ A @ B ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Finite__Set_Ocard @ A @ B ) @ tc_nat ) @ A @ tc_nat @ B )
| ~ ( c_Finite__Set_Ofinite @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(165,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_Finite__Set_Ofinite @ C @ B )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__subset_0) ).
thf(796,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)],[165]) ).
thf(225,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
= B )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__absorb1_0) ).
thf(928,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
= B )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(415,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oimage @ ( c_COMBB @ A @ B @ C @ D @ E ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_bool ) ) @ E @ D )
= ( c_Set_Oimage @ A @ ( c_Set_Oimage @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_bool ) ) @ E @ C ) @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_range__composition_0) ).
thf(1363,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oimage @ ( c_COMBB @ A @ B @ C @ D @ E ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_bool ) ) @ E @ D )
= ( c_Set_Oimage @ A @ ( c_Set_Oimage @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ E @ tc_bool ) ) @ E @ C ) @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(393,axiom,
! [A: $i] : ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le0_0) ).
thf(1314,plain,
! [A: $i] : ( c_lessequals @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(333,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) )
= ( c_HOL_Ominus__class_Ominus @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__idemp_0) ).
thf(1172,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)],[333]) ).
thf(17,axiom,
class_Orderings_Oorder @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).
thf(474,plain,
class_Orderings_Oorder @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(186,axiom,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__mono_0) ).
thf(839,plain,
! [B: $i,A: $i] :
( ( c_HOL_Oord__class_Oless @ ( c_Suc @ A ) @ ( c_Suc @ B ) @ tc_nat )
| ~ ( c_HOL_Oord__class_Oless @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(132,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_HOL_Ominus__class_Ominus @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__Diff_0) ).
thf(728,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_HOL_Ominus__class_Ominus @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(371,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ B @ C )
= D )
| ~ ( c_Typedef_Otype__definition @ A @ E @ D @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_type__definition_ORep__range_0) ).
thf(1261,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ B @ C )
= D )
| ~ ( c_Typedef_Otype__definition @ A @ E @ D @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(71,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ D )
| ~ ( c_Finite__Set_Ofinite @ ( c_HOL_Ominus__class_Ominus @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__Diff__insert_1) ).
thf(596,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)],[71]) ).
thf(41,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Nat_Osemiring__char__0 @ A )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ C @ A ) )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__eq__iff_0) ).
thf(528,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Nat_Osemiring__char__0 @ A )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ B @ A )
!= ( c_Nat_Osemiring__1__class_Oof__nat @ C @ A ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(412,axiom,
! [B: $i,A: $i] :
( ( c_Fun_Obij__betw @ ( c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1 @ A @ B ) @ A @ ( c_SetInterval_Oord__class_OatLeastLessThan @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Finite__Set_Ocard @ A @ B ) @ tc_nat ) @ B @ tc_nat )
| ~ ( c_Finite__Set_Ofinite @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ex__bij__betw__finite__nat_0) ).
thf(1357,plain,
! [B: $i,A: $i] :
( ( c_Fun_Obij__betw @ ( c_List_Osko__SetInterval__Xex__bij__betw__finite__nat__1__1 @ A @ B ) @ A @ ( c_SetInterval_Oord__class_OatLeastLessThan @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Finite__Set_Ocard @ A @ B ) @ tc_nat ) @ B @ tc_nat )
| ~ ( c_Finite__Set_Ofinite @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(129,axiom,
c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__Suc0_1) ).
thf(723,plain,
c_HOL_Oord__class_Oless @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ ( c_Suc @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(177,axiom,
! [A: $i] :
~ ( c_HOL_Oord__class_Oless @ A @ A @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_less__not__refl_0) ).
thf(822,plain,
! [A: $i] :
~ ( c_HOL_Oord__class_Oless @ A @ A @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(248,axiom,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_of__nat__0_0) ).
thf(982,plain,
! [A: $i] :
( ~ ( class_Ring__and__Field_Osemiring__1 @ A )
| ( ( c_Nat_Osemiring__1__class_Oof__nat @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ A )
= ( c_HOL_Ozero__class_Ozero @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(29,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ ( tc_fun @ A @ tc_bool ) )
| ~ ( c_lessequals @ C @ B @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Compl__anti__mono_0) ).
thf(501,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ C ) @ ( tc_fun @ A @ tc_bool ) )
| ~ ( c_lessequals @ C @ B @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(23,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Fun_Ocomp @ ( c_Fun_Oid @ A ) @ B @ A @ A @ C )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_id__o_0) ).
thf(486,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Fun_Ocomp @ ( c_Fun_Oid @ A ) @ B @ A @ A @ C )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(230,axiom,
! [B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ A )
| ~ ( c_Finite__Set_Ofinite @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ A )
| ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__compl_1) ).
thf(940,plain,
! [B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( hAPP @ ( c_HOL_Ouminus__class_Ouminus @ ( tc_fun @ A @ tc_bool ) ) @ B ) @ A )
| ~ ( c_Finite__Set_Ofinite @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ A )
| ~ ( c_Finite__Set_Ofinite @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(223,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( hAPP @ B @ C ) )
!= ( hAPP @ D @ ( hAPP @ E @ F ) ) )
| ( ( hAPP @ ( c_Fun_Ocomp @ A @ B @ G @ H @ I ) @ C )
= ( hAPP @ ( c_Fun_Ocomp @ D @ E @ J @ H @ K ) @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comp__cong_0) ).
thf(923,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( hAPP @ B @ C ) )
!= ( hAPP @ D @ ( hAPP @ E @ F ) ) )
| ( ( hAPP @ ( c_Fun_Ocomp @ A @ B @ G @ H @ I ) @ C )
= ( hAPP @ ( c_Fun_Ocomp @ D @ E @ J @ H @ K ) @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(270,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Fun_Ocomp @ ( c_Hilbert__Choice_Oinv__into @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ B @ A @ C ) @ B @ C @ A @ A )
!= ( c_Fun_Oid @ A ) )
| ( c_Fun_Oinj__on @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inj__iff_1) ).
thf(1037,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Fun_Ocomp @ ( c_Hilbert__Choice_Oinv__into @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ B @ A @ C ) @ B @ C @ A @ A )
!= ( c_Fun_Oid @ A ) )
| ( 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)],[270]) ).
thf(91,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ A @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Diff_0) ).
thf(639,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_HOL_Ominus__class_Ominus @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_HOL_Ominus__class_Ominus @ A @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( c_HOL_Ominus__class_Ominus @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(145,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/sandbox2/benchmark/theBenchmark.p',cls_vimage__Diff_0) ).
thf(755,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)],[145]) ).
thf(260,axiom,
! [A: $i] :
~ ( c_lessequals @ ( c_Suc @ A ) @ A @ tc_nat ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Suc__n__not__le__n_0) ).
thf(1014,plain,
! [A: $i] :
~ ( c_lessequals @ ( c_Suc @ A ) @ A @ tc_nat ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(25,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/sandbox2/benchmark/theBenchmark.p',cls_xt1_I7_J_0) ).
thf(491,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)],[25]) ).
thf(294,axiom,
! [B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Suc @ B ) @ tc_nat )
| ~ ( c_lessequals @ A @ B @ tc_nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__SucI_0) ).
thf(1088,plain,
! [B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Suc @ B ) @ tc_nat )
| ~ ( c_lessequals @ A @ B @ tc_nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(27,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ A @ B @ C ) @ ( c_Set_Oinsert @ A @ D @ C ) @ ( tc_fun @ C @ tc_bool ) )
= ( c_Set_Oinsert @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__inter__insert_0) ).
thf(496,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ A @ B @ C ) @ ( c_Set_Oinsert @ A @ D @ C ) @ ( tc_fun @ C @ tc_bool ) )
= ( c_Set_Oinsert @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(8,axiom,
! [A: $i] : ( c_Fun_Obij @ ( c_Fun_Oid @ A ) @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bij__id_0) ).
thf(454,plain,
! [A: $i] : ( c_Fun_Obij @ ( c_Fun_Oid @ A ) @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(285,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ C @ D @ A ) @ ( tc_fun @ A @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ D @ A ) )
| ~ ( c_lessequals @ C @ D @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ivl__disj__un_I17_J_0) ).
thf(1069,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ C @ A ) @ ( c_SetInterval_Oord__class_OatLeastLessThan @ C @ D @ A ) @ ( tc_fun @ A @ tc_bool ) )
= ( c_SetInterval_Oord__class_OatLeastLessThan @ B @ D @ A ) )
| ~ ( c_lessequals @ C @ D @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(1646,plain,
$false,
inference(e,[status(thm)],[1411,909,893,1315,962,1179,481,645,892,479,1105,1005,1406,683,730,1068,994,741,1269,878,523,582,1205,449,614,677,1078,550,1275,472,1233,1327,945,1063,1354,1342,747,829,1196,782,709,841,1359,1386,436,1265,1243,1127,973,885,724,1287,719,785,917,802,1191,1059,460,1330,1264,587,619,902,1379,1319,881,1115,1100,1232,606,1347,475,789,591,1373,623,1151,1183,1040,1109,1136,834,1383,574,956,866,1072,1394,1351,988,1201,849,507,602,981,766,877,692,1074,1206,661,1306,1199,810,1338,714,512,942,546,793,1153,761,1311,534,798,1163,1223,1042,1255,1174,820,561,630,1370,1238,1021,778,1123,862,1217,598,467,1365,625,879,852,665,1159,493,757,1128,1291,1012,847,566,484,1402,578,697,1121,1096,1138,593,869,610,1118,874,1143,650,948,1111,1227,857,1397,488,1361,933,554,686,1214,1016,1155,1028,1082,679,970,837,1324,647,985,701,1297,1266,1050,721,1002,569,1246,515,1249,1131,654,503,1393,1241,805,921,541,1054,1170,1035,558,674,1167,888,926,1086,938,773,794,906,1278,745,573,444,965,750,513,1146,1219,824,584,819,904,1007,732,1388,743,1124,826,711,641,1139,936,1312,498,1332,1092,1090,1258,672,611,787,1058,1107,1209,831,1282,784,1048,1349,996,451,737,616,1376,979,604,681,1408,890,477,552,816,726,621,520,895,915,1344,769,1022,668,1177,1381,462,1061,912,959,868,780,1113,1102,658,636,695,455,883,1176,608,505,438,1076,1081,1340,1018,1203,589,531,944,663,548,458,1181,776,525,690,1025,872,705,739,1368,1230,1098,1225,1400,707,954,1252,1300,791,441,1235,643,544,1188,1186,470,576,951,808,1404,703,1141,656,1052,864,1094,571,1272,859,991,1221,1284,1353,600,465,627,556,581,759,771,1316,1084,931,539,1157,1321,976,688,1010,1390,1289,844,699,517,652,632,961,813,896,748,1030,510,1308,1193,1212,763,899,832,536,1045,667,1294,716,1161,800,1133,999,752,447,1280,967,1148,735,854,1303,564,807,1335,1056,1033,828,635,1065,1165,796,928,1363,1314,1172,474,839,728,1261,596,528,1357,723,822,982,501,486,940,923,1037,639,755,1014,491,1088,496,454,1069]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SCT071-1 : TPTP v8.1.2. Released v4.1.0.
% 0.13/0.16 % Command : run_Leo-III %s %d
% 0.16/0.36 % Computer : n017.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Thu May 18 14:54:31 EDT 2023
% 0.16/0.37 % CPUTime :
% 0.99/0.85 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.85/1.10 % [INFO] Parsing done (248ms).
% 1.85/1.11 % [INFO] Running in sequential loop mode.
% 2.51/1.33 % [INFO] eprover registered as external prover.
% 2.51/1.33 % [INFO] cvc4 registered as external prover.
% 2.51/1.34 % [INFO] Scanning for conjecture ...
% 2.75/1.46 % [INFO] Found a conjecture and 836 axioms. Running axiom selection ...
% 3.73/1.63 % [INFO] Axiom selection finished. Selected 434 axioms (removed 402 axioms).
% 4.30/1.79 % [INFO] Problem is propositional (TPTP CNF).
% 4.30/1.80 % [INFO] Type checking passed.
% 4.39/1.80 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 11.86/3.48 % External prover 'e' found a proof!
% 11.86/3.48 % [INFO] Killing All external provers ...
% 11.86/3.48 % Time passed: 2956ms (effective reasoning time: 2367ms)
% 11.86/3.48 % 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)>
% 11.86/3.49 % Axioms used in derivation (434): cls_Int__Un__distrib_0, cls_linorder__antisym__conv2_1, cls_Int__absorb2_0, cls_surj__iff_0, cls_ivl__disj__un_I8_J_0, cls_le__0__eq_1, cls_finite__UNIV__card__ge__0_0, cls_Diff__cancel_0, cls_surj__f__inv__f_0, cls_xt1_I9_J_0, cls_atLeast0LessThan_0, cls_Compl__subset__Compl__iff_1, cls_ex__bij__betw__nat__finite_0, cls_Compl__Diff__eq_0, cls_inj__iff_1, cls_Un__Diff_0, cls_eq__imp__le_0, cls_order__eq__iff_0, cls_Suc__mono_0, cls_card__empty_0, cls_of__nat__0_0, cls_insert__inter__insert_0, cls_Un__subset__iff_0, cls_Suc__inject_0, cls_finite__atLeastLessThan_0, cls_equalityI_0, cls_bij__betw__the__inv__into_0, cls_inj__on__iff__eq__card_0, cls_inj__on__Un_2, cls_id__o_0, cls_xt1_I12_J_0, cls_subset__empty_1, cls_subset__image__iff_2, cls_finite__insert_0, cls_the__inv__f__f_0, cls_inj__on__image__Int_0, cls_empty__is__image_1, cls_inj__image__eq__iff_0, cls_image__mono_0, cls_Un__empty__left_0, cls_termination__basic__simps_I5_J_0, cls_Diff__eq_0, cls_Suc__n__not__n_0, cls_atLeastLessThan__subset__iff_1, cls_card__insert_0, cls_finite__vimageI_0, cls_linorder__neqE_0, cls_less__antisym_0, cls_vimage__Diff_0, cls_Un__upper1_0, cls_Un__commute_0, cls_image__Int_0, cls_Int__mono_0, cls_bij__betw__def_0, cls_card__gt__0__iff_1, clsarity_fun__Orderings_Oorder, cls_finite__Un_2, cls_Diff__Un_0, cls_card__eq__0__iff_2, cls_finite__vimage__iff_1, cls_Int__Un__distrib2_0, clsarity_nat__Orderings_Olinorder, cls_Suc__lessI_0, cls_finite__vimageD_0, cls_Int__subset__iff_2, cls_less__Suc__eq_2, cls_o__eq__id__dest_0, cls_the__inv__into__onto_0, cls_not__less__eq_1, cls_Diff__subset__conv_0, cls_image__vimage__subset_0, cls_inj__on__image__set__diff_0, cls_Diff__triv_0, cls_vimage__UNIV_0, cls_Int__absorb1_0, cls_inj__image__subset__iff_0, cls_Diff__insert_0, cls_inj__on__Un__image__eq__iff_0, cls_datatype__injI_0, cls_gr0I_0, cls_vimage__Compl_0, cls_inj__image__Compl__subset_0, cls_inv__inv__eq_0, cls_vimage__compose_0, cls_finite__insert_1, cls_bij__betw__inv__into_0, cls_Compl__partition_0, cls_COMBB__def_0, cls_le__0__eq_0, cls_disjoint__eq__subset__Compl_0, cls_Un__left__commute_0, clsarity_bool__Finite__Set_Ofinite_Ofinite, cls_finite__Int_1, cls_Int__empty__right_0, cls_Suc__le__mono_0, cls_Un__empty_2, cls_le__antisym_0, cls_Un__subset__iff_1, cls_finite__UNIV__inj__surj_0, clsarity_nat__Ring__and__Field_Osemiring__0, cls_Un__Int__distrib2_0, cls_gr__implies__not0_0, cls_vimage__insert_0, cls_linorder__not__less_0, cls_atLeastLessThan__empty__iff2_0, cls_ivl__disj__int_I11_J_0, cls_empty__is__image_0, cls_order__le__less_0, cls_inj__on__Un_3, cls_finite__UNIV__surj__inj_0, cls_linorder__antisym__conv1_0, cls_range__composition_0, cls_card__seteq_0, cls_Diff__UNIV_0, cls_bij__betw__def_1, cls_linorder__antisym__conv2_0, cls_inj__on__insert_0, cls_finite__range__imageI_0, cls_type__definition_ORep__inject_0, cls_Sup__UNIV_0, cls_Un__empty__right_0, cls_image__id_0, cls_inv__f__eq_0, cls_lessThan__subset__iff_1, cls_finite__Int_0, cls_id__apply_0, cls_Un__absorb2_0, cls_linorder__neqE__nat_0, cls_inv__image__comp_0, clsarity_bool__Orderings_Oorder, cls_Suc__leI_0, cls_Un__UNIV__right_0, cls_vimage__id_0, cls_xt1_I10_J_0, cls_Un__upper2_0, cls_Compl__disjoint2_0, cls_not__less__iff__gr__or__eq_0, cls_Sup__singleton_0, cls_comp__inj__on_0, cls_inj__iff_0, cls_bij__betw__trans_0, cls_bij__betw__same__card_0, cls_lessThan__eq__iff_0, cls_bij__def_2, cls_inj__on__imageI_0, cls_finite_0, cls_card__gt__0__iff_2, cls_surj__image__vimage__eq_0, cls_Compl__Un_0, cls_Diff__idemp_0, cls_subset__empty_0, cls_not__less__eq__eq_1, cls_subset__Compl__self__eq_1, cls_insert__Diff__single_0, cls_inv__into__image__cancel_0, cls_image__insert_0, clsarity_fun__Finite__Set_Ofinite_Ofinite, cls_Suc__neq__Zero_0, cls_UNIV__not__empty_0, cls_Compl__disjoint_0, cls_Sup__binary_0, cls_type__definition_ORep__inverse_0, cls_vimage__Un_0, cls_finite__Diff_0, cls_Un__insert__left_0, cls_less__Suc__eq__le_1, cls_doubleton__eq__iff_2, cls_Compl__partition2_0, cls_inj__image__subset__iff_1, cls_xt1_I8_J_0, cls_Compl__anti__mono_0, cls_finite__surj_0, cls_finite__UnI_0, cls_Un__mono_0, cls_Compl__UNIV__eq_0, cls_finite__vimage__iff_0, cls_insert__subset_1, cls_Int__empty__left_0, clsarity_nat__Nat_Osemiring__char__0, cls_Int__subset__iff_1, cls_set__eq__subset_2, cls_of__nat__eq__iff_0, cls_bij__def_1, cls_vimage__subset__eq_0, cls_inj__on__the__inv__into_0, cls_inj__imp__inv__eq_0, cls_inj__on__inv__into_0, cls_type__definition_ORep__range_0, cls_bij__betw__def_2, cls_Un__subset__iff_2, cls_le__SucE_0, cls_Suc__le__mono_1, cls_linorder__linear_0, cls_Un__empty_0, cls_atLeastLessThan__empty__iff_1, cls_not__leE_0, cls_datatype__injI_1, cls_lessI_0, cls_Int__assoc_0, cls_order__antisym_0, cls_card__image__le_0, cls_less__Suc__eq__0__disj_3, cls_subset__trans_0, cls_double__diff_0, cls_Compl__eq__Compl__iff_0, cls_insert__is__Un_0, cls_image__empty_0, cls_finite__UNIV_0, cls_Compl__subset__Compl__iff_0, cls_linorder__antisym__conv1_1, cls_Un__Int__crazy_0, cls_atLeastLessThan0_0, cls_subset__Compl__self__eq_0, cls_empty__not__insert_0, cls_card__insert__le_0, cls_lessThan__subset__iff_0, cls_Diff__Int__distrib2_0, cls_surj__range_0, cls_inv__id_0, cls_empty__subsetI_0, cls_neq0__conv_1, cls_bijI_0, cls_doubleton__eq__iff_0, cls_Un__absorb1_0, cls_bij__comp_0, cls_Diff__insert2_0, cls_finite__lessThan_0, cls_not__less__less__Suc__eq_0, cls_le__trans_0, cls_Compl__eq__Diff__UNIV_0, cls_linorder__not__le_1, cls_Int__commute_0, cls_Un__UNIV__left_0, cls_subset__refl_0, cls_vimage__subsetI_0, cls_image__diff__subset_0, cls_inj__on__empty_0, cls_Int__Diff_0, cls_order__le__neq__trans_0, cls_card__mono_0, cls_image__Int__subset_0, cls_vimage__Int_0, cls_image__Un_0, cls_not__less__iff__gr__or__eq_1, cls_Suc__le__eq_0, cls_image__set__diff_0, cls_map__map_0, cls_Un__Diff__cancel_0, cls_order__eq__iff_2, cls_less__not__refl_0, cls_linorder__antisym__conv3_0, cls_Int__absorb_0, cls_inj__vimage__image__eq_0, cls_insert__mono_0, cls_gr0__conv__Suc_1, cls_Int__UNIV__right_0, cls_vimage__subsetD_0, cls_Un__Diff__cancel2_0, cls_ivl__diff_0, cls_Int__lower2_0, cls_o__eq__dest_0, cls_Un__assoc_0, cls_Diff__disjoint_0, cls_o__eq__dest__lhs_0, cls_finite__Diff__insert_1, cls_Un__absorb_0, cls_nat_Oinject_0, cls_order__antisym__conv_0, cls_image__surj__f__inv__f_0, cls_less__SucE_0, cls_inj__on__Un_0, cls_subset__insertI2_0, cls_vimage__mono_0, cls_Int__left__absorb_0, cls_card__inj__on__le_0, cls_order__neq__le__trans_0, cls_doubleton__eq__iff_3, cls_Compl__Int_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_Int__lower1_0, cls_card__eq__0__iff_0, cls_not__less__less__Suc__eq_1, cls_less__eq__Suc__le_0, cls_Un__Int__distrib_0, cls_subset__insert__iff_4, cls_Int__subset__iff_0, cls_linorder__less__linear_0, cls_injD_0, cls_vimage__subset__eq_1, cls_nat_Osimps_I2_J_0, cls_Zero__neq__Suc_0, cls_finite__compl_1, cls_Suc__lessD_0, cls_order__less__le_2, cls_nat__neq__iff_0, cls_le__less__Suc__eq_0, cls_finite__subset_0, cls_type__definition_OAbs__image_0, cls_card__image_0, cls_less__eq__Suc__le_1, cls_bij__id_0, cls_o__id_0, cls_finite__imageD_0, cls_less__Suc__eq__le_0, cls_injI_1, cls_insert__not__empty_0, cls_Int__left__commute_0, clsarity_fun__Complete__Lattice_Ocomplete__lattice, cls_eq__card__imp__inj__on_0, cls_le0_0, cls_card__bij__eq_0, cls_finite__Un_0, cls_xt1_I11_J_0, cls_insert__absorb2_0, cls_less__Suc0_0, cls_finite__Diff__insert_0, cls_Sup__insert_0, cls_xt1_I6_J_0, cls_ex__bij__betw__finite__nat_0, cls_subset__singletonD_0, cls_Un__Int__assoc__eq_1, cls_finite__indi_0, cls_inj__on__id_0, cls_doubleton__eq__iff_1, cls_nat__less__le_0, cls_Sup__empty_0, cls_atLeastLessThan__empty__iff2_1, cls_nat_Osimps_I3_J_0, cls_less__trans__Suc_0, cls_le__Suc__eq_2, clsarity_bool__Complete__Lattice_Ocomplete__lattice, cls_Diff__empty_0, cls_nat__less__le_2, cls_comp__surj_0, cls_not__less__eq_0, cls_nat__le__linear_0, cls_Un__left__absorb_0, cls_linorder__not__le_0, cls_comp__cong_0, cls_Suc__n__not__le__n_0, cls_Diff__Int_0, cls_atLeastLessThan__empty_0, cls_Un__empty_1, cls_surj__iff_1, cls_inj__map__eq__map_0, cls_o__inv__o__cancel_0, cls_o__inv__distrib_0, cls_Diff__Compl_0, cls_surj__id_0, cls_subset__inj__on_0, cls_singleton__inject_0, cls_Suc__leD_0, cls_bij__def_0, cls_n__not__Suc__n_0, cls_atLeastLessThan__subset__iff_0, cls_Un__least_0, cls_double__complement_0, cls_Int__greatest_0, cls_less__SucI_0, cls_subset__Un__eq_1, cls_finite__surj__inj_0, cls_finite_OemptyI_0, cls_card__eq__UNIV__imp__eq__UNIV_0, cls_Int__UNIV__left_0, cls_inj__on__diff_0, cls_doubleton__eq__iff_4, cls_atLeastLessThan__empty__iff_0, cls_not__less0_0, cls_card__Diff1__le_0, cls_bij__image__Compl__eq_0, cls_subset__UNIV_0, cls_finite__imageI_0, cls_surj__imp__inj__inv_0, cls_injI_0, cls_Diff__subset__conv_1, cls_map__removeAll__inj_0, cls_card__gt__0__iff_0, cls_that_0, cls_Un__Diff__Int_0, cls_Suc__less__eq_0, cls_subset__insertI_0, cls_lessThan__0_0, cls_Diff__Int2_0, cls_inv__f__f_0, clsarity_nat__Ring__and__Field_Osemiring__1, cls_Diff__partition_0, cls_rev__finite__subset_0, cls_finite__Un_1, cls_image__vimage__eq_0, cls_le__less__Suc__eq_1, cls_inj__on__Un_1, cls_less__Suc0_1, cls_Un__Int__assoc__eq_0, cls_endo__inj__surj_0, cls_map__injective_0, cls_insert__commute_0, cls_image__image_0, cls_atLeastLessThanSuc_1, cls_le__eq__less__or__eq_0, cls_vimage__empty_0, clsarity_nat__Orderings_Oorder, cls_xt1_I7_J_0, cls_image__compose_0, cls_linorder__not__less_1, cls_image__is__empty_0, cls_zero__less__Suc_0, cls_le__neq__implies__less_0, cls_bij__imp__bij__inv_0, cls_equalityE_0, cls_ivl__disj__un_I17_J_0, cls_finite__compl_0, cls_ivl__disj__int_I2_J_0, cls_finite__Diff2_0, cls_order__less__le_1, cls_nat__less__le_1, cls_Un__insert__right_0, cls_bij__vimage__eq__inv__image_0, cls_disjoint__eq__subset__Compl_1, cls_o__apply_0, cls_Compl__empty__eq_0, cls_le__SucI_0, cls_not__less__eq__eq_0, cls_inj__imp__surj__inv_0, cls_Diff__subset_0, cls_empty__Diff_0, cls_o__assoc_0, cls_image__inv__f__f_0, cls_surj__Compl__image__subset_0, cls_le__refl_0, cls_single__Diff__lessThan_0
% 11.86/3.49 % No. of inferences in proof: 871
% 11.86/3.49 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2956 ms resp. 2367 ms w/o parsing
% 12.37/3.65 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 12.37/3.65 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------