TSTP Solution File: SCT020-1 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SCT020-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n013.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 11:50:06 EDT 2023
% Result : Unsatisfiable 104.51s 21.03s
% Output : Refutation 105.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 836
% Syntax : Number of formulae : 1548 ( 421 unt; 125 typ; 0 def)
% Number of atoms : 2982 ( 685 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 26665 (1432 ~;1559 |; 0 &;23674 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 11 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 301 ( 301 >; 0 *; 0 +; 0 <<)
% Number of symbols : 127 ( 125 usr; 11 con; 0-7 aty)
% Number of variables : 5010 ( 0 ^;5010 !; 0 ?;5010 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_Relation_Otrans_type,type,
c_Relation_Otrans: $i > $i > $o ).
thf(hAPP_type,type,
hAPP: $i > $i > $i ).
thf(v_P_type,type,
v_P: $i ).
thf(tc_Arrow__Order__Mirabelle_Oalt_type,type,
tc_Arrow__Order__Mirabelle_Oalt: $i ).
thf(c_Relation_Oirrefl_type,type,
c_Relation_Oirrefl: $i > $i > $o ).
thf(c_Relation_Ototal__on_type,type,
c_Relation_Ototal__on: $i > $i > $i > $o ).
thf(c_Orderings_Otop__class_Otop_type,type,
c_Orderings_Otop__class_Otop: $i > $i ).
thf(tc_fun_type,type,
tc_fun: $i > $i > $i ).
thf(tc_bool_type,type,
tc_bool: $i ).
thf(hBOOL_type,type,
hBOOL: $i > $o ).
thf(c_in_type,type,
c_in: $i > $i > $i > $i ).
thf(c_Pair_type,type,
c_Pair: $i > $i > $i > $i > $i ).
thf(v_a_type,type,
v_a: $i ).
thf(v_b_type,type,
v_b: $i ).
thf(v_F_type,type,
v_F: $i > $i ).
thf(tc_prod_type,type,
tc_prod: $i > $i > $i ).
thf(v_i_type,type,
v_i: $i ).
thf(v_x_type,type,
v_x: $i ).
thf(v_Pa_type,type,
v_Pa: $i > $i ).
thf(c_Relation_Orel__comp_type,type,
c_Relation_Orel__comp: $i > $i > $i > $i > $i > $i ).
thf(c_Relation_Oconverse_type,type,
c_Relation_Oconverse: $i > $i > $i > $i ).
thf(c_Equiv__Relations_Oequiv_type,type,
c_Equiv__Relations_Oequiv: $i > $i > $i > $o ).
thf(c_Relation_ODomain_type,type,
c_Relation_ODomain: $i > $i > $i > $i ).
thf(c_Relation_Osym_type,type,
c_Relation_Osym: $i > $i > $o ).
thf(c_Transitive__Closure_Otrancl_type,type,
c_Transitive__Closure_Otrancl: $i > $i > $i ).
thf(c_Relation_OId_type,type,
c_Relation_OId: $i > $i ).
thf(c_Wellfounded_Owf_type,type,
c_Wellfounded_Owf: $i > $i > $o ).
thf(c_Wellfounded_Oacyclic_type,type,
c_Wellfounded_Oacyclic: $i > $i > $o ).
thf(class_Orderings_Obot_type,type,
class_Orderings_Obot: $i > $o ).
thf(c_lessequals_type,type,
c_lessequals: $i > $i > $i > $o ).
thf(c_Orderings_Obot__class_Obot_type,type,
c_Orderings_Obot__class_Obot: $i > $i ).
thf(c_Relation_Oantisym_type,type,
c_Relation_Oantisym: $i > $i > $o ).
thf(c_Relation_OId__on_type,type,
c_Relation_OId__on: $i > $i > $i ).
thf(c_Transitive__Closure_Ortrancl_type,type,
c_Transitive__Closure_Ortrancl: $i > $i > $i ).
thf(c_Relation_Orefl__on_type,type,
c_Relation_Orefl__on: $i > $i > $i > $o ).
thf(c_Relation_ORange_type,type,
c_Relation_ORange: $i > $i > $i > $i ).
thf(class_Orderings_Oorder_type,type,
class_Orderings_Oorder: $i > $o ).
thf(c_Relation_Oinv__image_type,type,
c_Relation_Oinv__image: $i > $i > $i > $i > $i ).
thf(c_Relation_Osingle__valued_type,type,
c_Relation_Osingle__valued: $i > $i > $i > $o ).
thf(c_Set_Oimage_type,type,
c_Set_Oimage: $i > $i > $i > $i > $i ).
thf(c_COMBB_type,type,
c_COMBB: $i > $i > $i > $i > $i > $i ).
thf(v_r_type,type,
v_r: $i ).
thf(t_a_type,type,
t_a: $i ).
thf(t_b_type,type,
t_b: $i ).
thf(class_Orderings_Opreorder_type,type,
class_Orderings_Opreorder: $i > $o ).
thf(class_Orderings_Olinorder_type,type,
class_Orderings_Olinorder: $i > $o ).
thf(c_Complete__Lattice_Ocomplete__lattice__class_OINFI_type,type,
c_Complete__Lattice_Ocomplete__lattice__class_OINFI: $i > $i > $i > $i > $i ).
thf(c_Relation_OImage_type,type,
c_Relation_OImage: $i > $i > $i > $i ).
thf(c_Set_Oinsert_type,type,
c_Set_Oinsert: $i > $i > $i ).
thf(class_Lattices_Olower__semilattice_type,type,
class_Lattices_Olower__semilattice: $i > $o ).
thf(c_Lattices_Olower__semilattice__class_Oinf_type,type,
c_Lattices_Olower__semilattice__class_Oinf: $i > $i > $i ).
thf(c_Lattices_Oupper__semilattice__class_Osup_type,type,
c_Lattices_Oupper__semilattice__class_Osup: $i > $i > $i ).
thf(c_HOL_Ominus__class_Ominus_type,type,
c_HOL_Ominus__class_Ominus: $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Set__Xball__UNIV__1__2_type,type,
c_ATP__Linkup_Osko__Set__Xball__UNIV__1__2: $i > $i > $i ).
thf(class_Lattices_Oupper__semilattice_type,type,
class_Lattices_Oupper__semilattice: $i > $o ).
thf(class_Lattices_Olattice_type,type,
class_Lattices_Olattice: $i > $o ).
thf(c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1_type,type,
c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1: $i > $i > $i > $i ).
thf(c_Wellfounded_Oacc_type,type,
c_Wellfounded_Oacc: $i > $i > $i ).
thf(v_sko__Wellfounded__Xacc__Xinducts__1_type,type,
v_sko__Wellfounded__Xacc__Xinducts__1: $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Relation__Xtrans__def__1__1_type,type,
c_ATP__Linkup_Osko__Relation__Xtrans__def__1__1: $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Relation__Xtrans__def__1__3_type,type,
c_ATP__Linkup_Osko__Relation__Xtrans__def__1__3: $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(class_Orderings_Otop_type,type,
class_Orderings_Otop: $i > $o ).
thf(class_Lattices_Obounded__lattice_type,type,
class_Lattices_Obounded__lattice: $i > $o ).
thf(c_Product__Type_OSigma_type,type,
c_Product__Type_OSigma: $i > $i > $i > $i > $i ).
thf(c_COMBK_type,type,
c_COMBK: $i > $i > $i > $i ).
thf(c_Order__Relation_Ostrict__linear__order__on_type,type,
c_Order__Relation_Ostrict__linear__order__on: $i > $i > $i > $o ).
thf(c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1_type,type,
c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1: $i > $i > $i ).
thf(class_Lattices_Odistrib__lattice_type,type,
class_Lattices_Odistrib__lattice: $i > $o ).
thf(c_Arrow__Order__Mirabelle_Omktop_type,type,
c_Arrow__Order__Mirabelle_Omktop: $i > $i > $i ).
thf(c_FunDef_Oin__rel_type,type,
c_FunDef_Oin__rel: $i > $i > $i > $i > $i > $o ).
thf(c_split_type,type,
c_split: $i > $i > $i > $i > $i ).
thf(class_HOL_Ominus_type,type,
class_HOL_Ominus: $i > $o ).
thf(c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1_type,type,
c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1: $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1_type,type,
c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1: $i > $i > $i > $i > $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Relation__Xtrans__def__1__2_type,type,
c_ATP__Linkup_Osko__Relation__Xtrans__def__1__2: $i > $i > $i ).
thf(class_OrderedGroup_Oab__group__add_type,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
thf(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1_type,type,
c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1: $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Relation__XImage__iff__1__1_type,type,
c_ATP__Linkup_Osko__Relation__XImage__iff__1__1: $i > $i > $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Relation__XtransI__1__1_type,type,
c_ATP__Linkup_Osko__Relation__XtransI__1__1: $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Relation__XtransI__1__3_type,type,
c_ATP__Linkup_Osko__Relation__XtransI__1__3: $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1_type,type,
c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1: $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Relation__XDomainE__1__1_type,type,
c_ATP__Linkup_Osko__Relation__XDomainE__1__1: $i > $i > $i > $i > $i ).
thf(c_Arrow__Order__Mirabelle_Omkbot_type,type,
c_Arrow__Order__Mirabelle_Omkbot: $i > $i > $i ).
thf(class_OrderedGroup_Opordered__ab__group__add_type,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
thf(c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1_type,type,
c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1: $i > $i > $i > $i > $i ).
thf(class_HOL_Oord_type,type,
class_HOL_Oord: $i > $o ).
thf(c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1_type,type,
c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1: $i > $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1_type,type,
c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1: $i > $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1_type,type,
c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1: $i > $i > $i > $i ).
thf(v_sko__Transitive__Closure__Xtrancl__Xcases__1_type,type,
v_sko__Transitive__Closure__Xtrancl__Xcases__1: $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Set__XUNIV__witness__1__1_type,type,
c_ATP__Linkup_Osko__Set__XUNIV__witness__1__1: $i > $i ).
thf(c_ATP__Linkup_Osko__Relation__Xtotal__on__def__1__2_type,type,
c_ATP__Linkup_Osko__Relation__Xtotal__on__def__1__2: $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1_type,type,
c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1: $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1_type,type,
c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1: $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Complete__Lattice__XINTER__UNIV__conv__1__1_type,type,
c_ATP__Linkup_Osko__Complete__Lattice__XINTER__UNIV__conv__1__1: $i > $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1_type,type,
c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1: $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1_type,type,
c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1: $i > $i > $i > $i > $i ).
thf(c_Nitpick_Orefl_H_type,type,
c_Nitpick_Orefl_H: $i > $i > $o ).
thf(c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1_type,type,
c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1: $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__2_type,type,
c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__2: $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Set__Xball__UNIV__1__1_type,type,
c_ATP__Linkup_Osko__Set__Xball__UNIV__1__1: $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Relation__Xtotal__on__def__1__1_type,type,
c_ATP__Linkup_Osko__Relation__Xtotal__on__def__1__1: $i > $i > $i > $i ).
thf(c_List_Osko__Recdef__Xtfl__wf__induct__1__1_type,type,
c_List_Osko__Recdef__Xtfl__wf__induct__1__1: $i > $i > $i > $i ).
thf(c_Recdef_Ocut_type,type,
c_Recdef_Ocut: $i > $i > $i > $i > $i > $i ).
thf(c_List_Osko__Recdef__Xcuts__eq__1__1_type,type,
c_List_Osko__Recdef__Xcuts__eq__1__1: $i > $i > $i > $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1_type,type,
c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1: $i > $i > $i > $i > $i ).
thf(v_sko__Wellfounded__Xacc__Xinduct__1_type,type,
v_sko__Wellfounded__Xacc__Xinduct__1: $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Complete__Lattice__XINTER__UNIV__conv__2__1_type,type,
c_ATP__Linkup_Osko__Complete__Lattice__XINTER__UNIV__conv__2__1: $i > $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Set__XUNIV__eq__I__1__1_type,type,
c_ATP__Linkup_Osko__Set__XUNIV__eq__I__1__1: $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Relation__XId__onE__1__1_type,type,
c_ATP__Linkup_Osko__Relation__XId__onE__1__1: $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Relation__XImageE__1__1_type,type,
c_ATP__Linkup_Osko__Relation__XImageE__1__1: $i > $i > $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1_type,type,
c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1: $i > $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1_type,type,
c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1: $i > $i > $i > $i ).
thf(c_Equiv__Relations_Ocongruent2_type,type,
c_Equiv__Relations_Ocongruent2: $i > $i > $i > $i > $i > $i > $o ).
thf(c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1_type,type,
c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1: $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Relation__XRange__iff__1__1_type,type,
c_ATP__Linkup_Osko__Relation__XRange__iff__1__1: $i > $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Relation__XtransI__1__2_type,type,
c_ATP__Linkup_Osko__Relation__XtransI__1__2: $i > $i > $i ).
thf(c_Equiv__Relations_Ocongruent_type,type,
c_Equiv__Relations_Ocongruent: $i > $i > $i > $i > $o ).
thf(c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1_type,type,
c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1: $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__1_type,type,
c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__1: $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Relation__XRangeE__1__1_type,type,
c_ATP__Linkup_Osko__Relation__XRangeE__1__1: $i > $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Relation__XIdE__1__1_type,type,
c_ATP__Linkup_Osko__Relation__XIdE__1__1: $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Wellfounded__Xwf__acc__iff__1__1_type,type,
c_ATP__Linkup_Osko__Wellfounded__Xwf__acc__iff__1__1: $i > $i > $i ).
thf(676,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Relation_OImage @ A @ B @ B ) @ ( hAPP @ ( c_Set_Oinsert @ C @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) )
!= ( hAPP @ ( c_Relation_OImage @ A @ B @ B ) @ ( hAPP @ ( c_Set_Oinsert @ D @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) ) )
| ~ ( c_Equiv__Relations_Oequiv @ E @ A @ B )
| ( hBOOL @ ( c_in @ ( c_Pair @ C @ D @ B @ B ) @ A @ ( tc_prod @ B @ B ) ) )
| ~ ( hBOOL @ ( c_in @ D @ E @ B ) )
| ~ ( hBOOL @ ( c_in @ C @ E @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__class__eq__iff_3) ).
thf(2163,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Relation_OImage @ A @ B @ B ) @ ( hAPP @ ( c_Set_Oinsert @ C @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) )
!= ( hAPP @ ( c_Relation_OImage @ A @ B @ B ) @ ( hAPP @ ( c_Set_Oinsert @ D @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) ) )
| ~ ( c_Equiv__Relations_Oequiv @ E @ A @ B )
| ( hBOOL @ ( c_in @ ( c_Pair @ C @ D @ B @ B ) @ A @ ( tc_prod @ B @ B ) ) )
| ~ ( hBOOL @ ( c_in @ D @ E @ B ) )
| ~ ( hBOOL @ ( c_in @ C @ E @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[676]) ).
thf(157,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Relation_ODomain @ B @ C @ D ) @ C ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ E @ C @ D ) @ B @ ( tc_prod @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__iff_1) ).
thf(1036,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Relation_ODomain @ B @ C @ D ) @ C ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ E @ C @ D ) @ B @ ( tc_prod @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(646,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( hAPP @ B @ C ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ C @ E @ F ) )
| ~ ( c_lessequals @ A @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ B @ F @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__subset__iff_0) ).
thf(2094,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( hAPP @ B @ C ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ C @ E @ F ) )
| ~ ( c_lessequals @ A @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ B @ F @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[646]) ).
thf(27,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Orel__comp @ ( c_Relation_OId @ A ) @ B @ A @ A @ C )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Id__O__R_0) ).
thf(760,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Orel__comp @ ( c_Relation_OId @ A ) @ B @ A @ A @ C )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(477,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
= ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XId__onE__1__1 @ B @ A @ C ) @ ( c_ATP__Linkup_Osko__Relation__XId__onE__1__1 @ B @ A @ C ) @ C @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_Relation_OId__on @ B @ C ) @ ( tc_prod @ C @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Id__onE_1) ).
thf(1729,plain,
! [C: $i,B: $i,A: $i] :
( ( A
= ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XId__onE__1__1 @ B @ A @ C ) @ ( c_ATP__Linkup_Osko__Relation__XId__onE__1__1 @ B @ A @ C ) @ C @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_Relation_OId__on @ B @ C ) @ ( tc_prod @ C @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).
thf(557,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1 @ A @ C @ D ) ) )
| ~ ( c_Wellfounded_Owf @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__induct__rule_1) ).
thf(1899,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1 @ A @ C @ D ) ) )
| ~ ( c_Wellfounded_Owf @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).
thf(92,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Set_Oinsert @ A @ B ) @ ( hAPP @ ( c_Set_Oinsert @ C @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) )
!= ( hAPP @ ( c_Set_Oinsert @ D @ B ) @ ( hAPP @ ( c_Set_Oinsert @ E @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) ) )
| ( A = E )
| ( C = E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_2) ).
thf(893,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Set_Oinsert @ A @ B ) @ ( hAPP @ ( c_Set_Oinsert @ C @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) )
!= ( hAPP @ ( c_Set_Oinsert @ D @ B ) @ ( hAPP @ ( c_Set_Oinsert @ E @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) ) )
| ( A = E )
| ( C = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(534,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ( hBOOL @ ( c_in @ D @ A @ C ) )
| ~ ( c_lessequals @ A @ ( hAPP @ ( c_Set_Oinsert @ D @ C ) @ B ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_1) ).
thf(1850,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ( hBOOL @ ( c_in @ D @ A @ C ) )
| ~ ( c_lessequals @ A @ ( hAPP @ ( c_Set_Oinsert @ D @ C ) @ B ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).
thf(595,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/sandbox/benchmark/theBenchmark.p',cls_Sup__empty_0) ).
thf(1982,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)],[595]) ).
thf(113,axiom,
! [B: $i,A: $i] : ( c_Relation_Oirrefl @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ ( c_Relation_OId @ B ) ) @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_irrefl__diff__Id_0) ).
thf(941,plain,
! [B: $i,A: $i] : ( c_Relation_Oirrefl @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ ( c_Relation_OId @ B ) ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(220,axiom,
! [B: $i,A: $i] :
( ( class_HOL_Oord @ ( tc_fun @ A @ B ) )
| ~ ( class_HOL_Oord @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__HOL_Oord) ).
thf(1179,plain,
! [B: $i,A: $i] :
( ( class_HOL_Oord @ ( tc_fun @ A @ B ) )
| ~ ( class_HOL_Oord @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(274,axiom,
! [B: $i,A: $i] : ( hBOOL @ ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ ( c_Relation_OId @ B ) @ ( tc_prod @ B @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IdI_0) ).
thf(1295,plain,
! [B: $i,A: $i] : ( hBOOL @ ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ ( c_Relation_OId @ B ) @ ( tc_prod @ B @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(414,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( c_lessequals @ ( hAPP @ ( c_Set_Oinsert @ A @ C ) @ D ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_0) ).
thf(1586,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( c_lessequals @ ( hAPP @ ( c_Set_Oinsert @ A @ C ) @ D ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(51,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Osym @ A @ B )
| ~ ( c_Equiv__Relations_Oequiv @ C @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv_Osym_0) ).
thf(809,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Osym @ A @ B )
| ~ ( c_Equiv__Relations_Oequiv @ C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(151,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( hAPP @ ( c_split @ B @ C @ D @ ( tc_fun @ E @ tc_bool ) ) @ ( c_Pair @ F @ G @ C @ D ) ) @ E ) )
| ~ ( hBOOL @ ( c_in @ A @ ( hAPP @ ( hAPP @ B @ F ) @ G ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__splitI_0) ).
thf(1024,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( hAPP @ ( c_split @ B @ C @ D @ ( tc_fun @ E @ tc_bool ) ) @ ( c_Pair @ F @ G @ C @ D ) ) @ E ) )
| ~ ( hBOOL @ ( c_in @ A @ ( hAPP @ ( hAPP @ B @ F ) @ G ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(358,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Set_Oinsert @ A @ B ) @ C )
= ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ ( c_Set_Oinsert @ A @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) @ ( tc_fun @ B @ tc_bool ) ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__is__Un_0) ).
thf(1469,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Set_Oinsert @ A @ B ) @ C )
= ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ ( c_Set_Oinsert @ A @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) @ ( tc_fun @ B @ tc_bool ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(313,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Set_Oinsert @ A @ B ) @ ( hAPP @ ( c_Set_Oinsert @ C @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) )
!= ( hAPP @ ( c_Set_Oinsert @ D @ B ) @ ( hAPP @ ( c_Set_Oinsert @ E @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) ) )
| ( A = E )
| ( A = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_0) ).
thf(1369,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Set_Oinsert @ A @ B ) @ ( hAPP @ ( c_Set_Oinsert @ C @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) )
!= ( hAPP @ ( c_Set_Oinsert @ D @ B ) @ ( hAPP @ ( c_Set_Oinsert @ E @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) ) )
| ( A = E )
| ( A = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(225,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ ( tc_fun @ B @ tc_bool ) ) @ D ) )
= ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A @ ( tc_fun @ B @ tc_bool ) ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Un_0) ).
thf(1190,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ ( tc_fun @ B @ tc_bool ) ) @ D ) )
= ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A @ ( tc_fun @ B @ tc_bool ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(653,axiom,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Ortrancl @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ ( c_Relation_OId @ B ) ) @ B )
= ( c_Transitive__Closure_Ortrancl @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__reflcl_0) ).
thf(2109,plain,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Ortrancl @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ ( c_Relation_OId @ B ) ) @ B )
= ( c_Transitive__Closure_Ortrancl @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[653]) ).
thf(351,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_split @ A @ B @ C @ D ) @ ( c_Pair @ E @ F @ B @ C ) )
= ( hAPP @ ( hAPP @ A @ E ) @ F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Product__Type_Osplit_0) ).
thf(1454,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_split @ A @ B @ C @ D ) @ ( c_Pair @ E @ F @ B @ C ) )
= ( hAPP @ ( hAPP @ A @ E ) @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(618,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( hAPP @ ( c_Relation_OImage @ B @ C @ D ) @ E ) @ D ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ F @ A @ C @ D ) @ B @ ( tc_prod @ C @ D ) ) )
| ~ ( hBOOL @ ( c_in @ F @ E @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__ImageI_0) ).
thf(2031,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( hAPP @ ( c_Relation_OImage @ B @ C @ D ) @ E ) @ D ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ F @ A @ C @ D ) @ B @ ( tc_prod @ C @ D ) ) )
| ~ ( hBOOL @ ( c_in @ F @ E @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[618]) ).
thf(400,axiom,
! [A: $i] : ( c_Relation_Orefl__on @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Relation_OId @ A ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__Id_0) ).
thf(1559,plain,
! [A: $i] : ( c_Relation_Orefl__on @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Relation_OId @ A ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(189,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Set_Oinsert @ A @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
!= ( hAPP @ ( c_Set_Oinsert @ C @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) )
| ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__inject_0) ).
thf(1105,plain,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Set_Oinsert @ A @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
!= ( hAPP @ ( c_Set_Oinsert @ C @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(248,axiom,
! [B: $i,A: $i] :
( ( class_Orderings_Obot @ ( tc_fun @ A @ B ) )
| ~ ( class_Orderings_Obot @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Obot) ).
thf(1237,plain,
! [B: $i,A: $i] :
( ( class_Orderings_Obot @ ( tc_fun @ A @ B ) )
| ~ ( class_Orderings_Obot @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(70,axiom,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Ortrancl @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ B )
= ( c_Transitive__Closure_Ortrancl @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__idemp_0) ).
thf(846,plain,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Ortrancl @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ B )
= ( c_Transitive__Closure_Ortrancl @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(581,axiom,
! [B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( c_Complete__Lattice_OSup__class_OSup @ ( hAPP @ ( c_Set_Oinsert @ B @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sup__singleton_0) ).
thf(1950,plain,
! [B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( c_Complete__Lattice_OSup__class_OSup @ ( hAPP @ ( c_Set_Oinsert @ B @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).
thf(395,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( hAPP @ ( c_Relation_OImage @ A @ B @ C ) @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ ( tc_fun @ B @ tc_bool ) ) @ E ) ) @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( hAPP @ ( c_Relation_OImage @ A @ B @ C ) @ D ) @ ( tc_fun @ C @ tc_bool ) ) @ ( hAPP @ ( c_Relation_OImage @ A @ B @ C ) @ E ) ) @ ( tc_fun @ C @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__Int__subset_0) ).
thf(1549,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( hAPP @ ( c_Relation_OImage @ A @ B @ C ) @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ ( tc_fun @ B @ tc_bool ) ) @ E ) ) @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( hAPP @ ( c_Relation_OImage @ A @ B @ C ) @ D ) @ ( tc_fun @ C @ tc_bool ) ) @ ( hAPP @ ( c_Relation_OImage @ A @ B @ C ) @ E ) ) @ ( tc_fun @ C @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(398,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ ( c_Relation_Oconverse @ E @ D @ C ) @ ( tc_prod @ C @ D ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ B @ A @ D @ C ) @ E @ ( tc_prod @ D @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converseI_0) ).
thf(1554,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ ( c_Relation_Oconverse @ E @ D @ C ) @ ( tc_prod @ C @ D ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ B @ A @ D @ C ) @ E @ ( tc_prod @ D @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(191,axiom,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A ) @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__idem_0) ).
thf(1110,plain,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A ) @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(638,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__1 @ A @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ C ) )
| ~ ( hBOOL @ ( c_in @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bex__UNIV_0) ).
thf(2077,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__1 @ A @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ C ) )
| ~ ( hBOOL @ ( c_in @ C @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[638]) ).
thf(129,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Product__Type_OSigma @ ( hAPP @ ( c_Set_Oinsert @ A @ B ) @ C ) @ ( c_COMBK @ ( hAPP @ ( c_Set_Oinsert @ D @ E ) @ F ) @ ( tc_fun @ E @ tc_bool ) @ B ) @ B @ E )
= ( hAPP @ ( c_Set_Oinsert @ ( c_Pair @ A @ D @ B @ E ) @ ( tc_prod @ B @ E ) ) @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Product__Type_OSigma @ C @ ( c_COMBK @ ( hAPP @ ( c_Set_Oinsert @ D @ E ) @ F ) @ ( tc_fun @ E @ tc_bool ) @ B ) @ B @ E ) @ ( tc_fun @ ( tc_prod @ B @ E ) @ tc_bool ) ) @ ( c_Product__Type_OSigma @ ( hAPP @ ( c_Set_Oinsert @ A @ B ) @ C ) @ ( c_COMBK @ F @ ( tc_fun @ E @ tc_bool ) @ B ) @ B @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__times__insert_0) ).
thf(977,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Product__Type_OSigma @ ( hAPP @ ( c_Set_Oinsert @ A @ B ) @ C ) @ ( c_COMBK @ ( hAPP @ ( c_Set_Oinsert @ D @ E ) @ F ) @ ( tc_fun @ E @ tc_bool ) @ B ) @ B @ E )
= ( hAPP @ ( c_Set_Oinsert @ ( c_Pair @ A @ D @ B @ E ) @ ( tc_prod @ B @ E ) ) @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Product__Type_OSigma @ C @ ( c_COMBK @ ( hAPP @ ( c_Set_Oinsert @ D @ E ) @ F ) @ ( tc_fun @ E @ tc_bool ) @ B ) @ B @ E ) @ ( tc_fun @ ( tc_prod @ B @ E ) @ tc_bool ) ) @ ( c_Product__Type_OSigma @ ( hAPP @ ( c_Set_Oinsert @ A @ B ) @ C ) @ ( c_COMBK @ F @ ( tc_fun @ E @ tc_bool ) @ B ) @ B @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(568,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Relation_Orel__comp @ A @ B @ C @ D @ E ) @ ( c_Product__Type_OSigma @ F @ ( c_COMBK @ G @ ( tc_fun @ E @ tc_bool ) @ C ) @ C @ E ) @ ( tc_fun @ ( tc_prod @ C @ E ) @ tc_bool ) )
| ~ ( c_lessequals @ B @ ( c_Product__Type_OSigma @ H @ ( c_COMBK @ G @ ( tc_fun @ E @ tc_bool ) @ D ) @ D @ E ) @ ( tc_fun @ ( tc_prod @ D @ E ) @ tc_bool ) )
| ~ ( c_lessequals @ A @ ( c_Product__Type_OSigma @ F @ ( c_COMBK @ H @ ( tc_fun @ D @ tc_bool ) @ C ) @ C @ D ) @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__comp__subset__Sigma_0) ).
thf(1924,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Relation_Orel__comp @ A @ B @ C @ D @ E ) @ ( c_Product__Type_OSigma @ F @ ( c_COMBK @ G @ ( tc_fun @ E @ tc_bool ) @ C ) @ C @ E ) @ ( tc_fun @ ( tc_prod @ C @ E ) @ tc_bool ) )
| ~ ( c_lessequals @ B @ ( c_Product__Type_OSigma @ H @ ( c_COMBK @ G @ ( tc_fun @ E @ tc_bool ) @ D ) @ D @ E ) @ ( tc_fun @ ( tc_prod @ D @ E ) @ tc_bool ) )
| ~ ( c_lessequals @ A @ ( c_Product__Type_OSigma @ F @ ( c_COMBK @ H @ ( tc_fun @ D @ tc_bool ) @ C ) @ C @ D ) @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).
thf(708,axiom,
! [B: $i,A: $i] :
~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ A @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ B @ A ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mkbot_1) ).
thf(2231,plain,
! [B: $i,A: $i] :
~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ A @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ B @ A ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[708]) ).
thf(514,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( hAPP @ ( c_HOL_Ominus__class_Ominus @ B @ A ) @ C )
!= ( hAPP @ ( c_HOL_Ominus__class_Ominus @ D @ A ) @ D ) )
| ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__eqI_1) ).
thf(1808,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( hAPP @ ( c_HOL_Ominus__class_Ominus @ B @ A ) @ C )
!= ( hAPP @ ( c_HOL_Ominus__class_Ominus @ D @ A ) @ D ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).
thf(232,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ E @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ E @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl__into__trancl_0) ).
thf(1205,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ E @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ E @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(205,axiom,
! [B: $i,A: $i] :
( ( c_Relation_Otrans @ A @ B )
| ( hBOOL @ ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__Xtrans__def__1__1 @ A @ B ) @ ( c_ATP__Linkup_Osko__Relation__Xtrans__def__1__2 @ A @ B ) @ B @ B ) @ A @ ( tc_prod @ B @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__def_1) ).
thf(1142,plain,
! [B: $i,A: $i] :
( ( c_Relation_Otrans @ A @ B )
| ( hBOOL @ ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__Xtrans__def__1__1 @ A @ B ) @ ( c_ATP__Linkup_Osko__Relation__Xtrans__def__1__2 @ A @ B ) @ B @ B ) @ A @ ( tc_prod @ B @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(85,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ A @ C @ D ) @ ( c_Wellfounded_Oacc @ C @ D ) @ D ) )
| ~ ( hBOOL @ ( c_in @ B @ ( c_Wellfounded_Oacc @ C @ D ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__induct_0) ).
thf(878,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ A @ C @ D ) @ ( c_Wellfounded_Oacc @ C @ D ) @ D ) )
| ~ ( hBOOL @ ( c_in @ B @ ( c_Wellfounded_Oacc @ C @ D ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(590,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ A @ C @ D ) @ ( c_Wellfounded_Oacc @ C @ D ) @ D ) )
| ~ ( hBOOL @ ( c_in @ B @ ( c_Wellfounded_Oacc @ C @ D ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__induct__rule_0) ).
thf(1971,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ A @ C @ D ) @ ( c_Wellfounded_Oacc @ C @ D ) @ D ) )
| ~ ( hBOOL @ ( c_in @ B @ ( c_Wellfounded_Oacc @ C @ D ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).
thf(366,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( c_Set_Oinsert @ A @ B ) @ C ) @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_Set_Oinsert @ A @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) )
= C )
| ( hBOOL @ ( c_in @ A @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__insert__absorb_0) ).
thf(1486,plain,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( c_Set_Oinsert @ A @ B ) @ C ) @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_Set_Oinsert @ A @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) )
= C )
| ( hBOOL @ ( c_in @ A @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(211,axiom,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Orderings_Obot__class_Obot @ A ) @ A ) @ B )
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__bot__left_0) ).
thf(1158,plain,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Orderings_Obot__class_Obot @ A ) @ A ) @ B )
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(28,axiom,
! [B: $i,A: $i] :
( ( c_Relation_ODomain @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ B @ B )
= ( c_Relation_ODomain @ A @ B @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__domain_0) ).
thf(762,plain,
! [B: $i,A: $i] :
( ( c_Relation_ODomain @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ B @ B )
= ( c_Relation_ODomain @ A @ B @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(657,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ C ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ C @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ A @ D @ E ) @ E @ E ) @ D @ ( tc_prod @ E @ E ) ) )
| ~ ( hBOOL @ ( c_in @ B @ ( c_Wellfounded_Oacc @ D @ E ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__induct_1) ).
thf(2117,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ C ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ C @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ A @ D @ E ) @ E @ E ) @ D @ ( tc_prod @ E @ E ) ) )
| ~ ( hBOOL @ ( c_in @ B @ ( c_Wellfounded_Oacc @ D @ E ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[657]) ).
thf(329,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ C @ ( tc_prod @ B @ B ) ) )
| ~ ( c_Nitpick_Orefl_H @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nitpick_Orefl_H__def_0) ).
thf(1406,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ C @ ( tc_prod @ B @ B ) ) )
| ~ ( c_Nitpick_Orefl_H @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(11,axiom,
! [B: $i,A: $i] :
( ( c_Relation_Osym @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ B )
| ~ ( c_Relation_Osym @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__trancl_0) ).
thf(730,plain,
! [B: $i,A: $i] :
( ( c_Relation_Osym @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ B )
| ~ ( c_Relation_Osym @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(272,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ B @ tc_bool ) ) @ C )
!= C )
| ( c_lessequals @ A @ C @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__Un__eq_1) ).
thf(1290,plain,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ B @ tc_bool ) ) @ C )
!= C )
| ( c_lessequals @ A @ C @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(16,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Obot @ A )
| ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ A ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot__least_0) ).
thf(741,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Obot @ A )
| ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ A ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(174,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Ototal__on @ A @ ( c_Relation_Oconverse @ B @ C @ C ) @ C )
| ~ ( c_Relation_Ototal__on @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_total__on__converse_1) ).
thf(1073,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Ototal__on @ A @ ( c_Relation_Oconverse @ B @ C @ C ) @ C )
| ~ ( c_Relation_Ototal__on @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(392,axiom,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ A @ ( tc_fun @ B @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__subset_0) ).
thf(1544,plain,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ A @ ( tc_fun @ B @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(609,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Product__Type_OSigma @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( c_COMBK @ D @ ( tc_fun @ E @ tc_bool ) @ B ) @ B @ E )
= ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( c_Product__Type_OSigma @ A @ ( c_COMBK @ D @ ( tc_fun @ E @ tc_bool ) @ B ) @ B @ E ) @ ( tc_fun @ ( tc_prod @ B @ E ) @ tc_bool ) ) @ ( c_Product__Type_OSigma @ C @ ( c_COMBK @ D @ ( tc_fun @ E @ tc_bool ) @ B ) @ B @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Times__Diff__distrib1_0) ).
thf(2014,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Product__Type_OSigma @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( c_COMBK @ D @ ( tc_fun @ E @ tc_bool ) @ B ) @ B @ E )
= ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( c_Product__Type_OSigma @ A @ ( c_COMBK @ D @ ( tc_fun @ E @ tc_bool ) @ B ) @ B @ E ) @ ( tc_fun @ ( tc_prod @ B @ E ) @ tc_bool ) ) @ ( c_Product__Type_OSigma @ C @ ( c_COMBK @ D @ ( tc_fun @ E @ tc_bool ) @ B ) @ B @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[609]) ).
thf(159,axiom,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ A ) @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__idem_0) ).
thf(1041,plain,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ A ) @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(77,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( hAPP @ B @ C ) @ D ) )
| ~ ( hBOOL @ ( c_in @ C @ E @ F ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ B @ F @ ( tc_fun @ D @ tc_bool ) ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__D_0) ).
thf(861,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( hAPP @ B @ C ) @ D ) )
| ~ ( hBOOL @ ( c_in @ C @ E @ F ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ B @ F @ ( tc_fun @ D @ tc_bool ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(443,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oimage @ A @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ C @ E )
= ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ A @ B @ C @ E ) @ ( tc_fun @ E @ tc_bool ) ) @ ( c_Set_Oimage @ A @ D @ C @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__Un_0) ).
thf(1655,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oimage @ A @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ C @ E )
= ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ A @ B @ C @ E ) @ ( tc_fun @ E @ tc_bool ) ) @ ( c_Set_Oimage @ A @ D @ C @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(203,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) )
= ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__left__absorb_0) ).
thf(1137,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) )
= ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(282,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_split @ A @ B @ C @ D ) @ ( c_Pair @ E @ F @ B @ C ) )
= ( hAPP @ ( hAPP @ A @ E ) @ F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_split__case__cert_0) ).
thf(1310,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_split @ A @ B @ C @ D ) @ ( c_Pair @ E @ F @ B @ C ) )
= ( hAPP @ ( hAPP @ A @ E ) @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(9,negated_conjecture,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( v_F @ C ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ C @ v_i ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
| ( A = B )
| ~ ( c_Relation_Ototal__on @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ tc_bool ) ) @ ( hAPP @ C @ ( v_Pa @ C ) ) @ tc_Arrow__Order__Mirabelle_Oalt )
| ~ ( c_Relation_Oirrefl @ ( hAPP @ C @ ( v_Pa @ C ) ) @ tc_Arrow__Order__Mirabelle_Oalt )
| ~ ( c_Relation_Otrans @ ( hAPP @ C @ ( v_Pa @ C ) ) @ tc_Arrow__Order__Mirabelle_Oalt ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_8) ).
thf(715,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( v_F @ C ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ C @ v_i ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
| ( A = B )
| ~ ( c_Relation_Ototal__on @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ tc_bool ) ) @ ( hAPP @ C @ ( v_Pa @ C ) ) @ tc_Arrow__Order__Mirabelle_Oalt )
| ~ ( c_Relation_Oirrefl @ ( hAPP @ C @ ( v_Pa @ C ) ) @ tc_Arrow__Order__Mirabelle_Oalt )
| ~ ( c_Relation_Otrans @ ( hAPP @ C @ ( v_Pa @ C ) ) @ tc_Arrow__Order__Mirabelle_Oalt ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(667,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ ( tc_fun @ D @ tc_bool ) ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1E_1) ).
thf(2141,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ ( tc_fun @ D @ tc_bool ) ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[667]) ).
thf(545,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_Orel__comp @ A @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_bool ) ) @ E ) @ F @ C @ D )
= ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ A @ B @ F @ C @ D ) @ ( tc_fun @ ( tc_prod @ F @ D ) @ tc_bool ) ) @ ( c_Relation_Orel__comp @ A @ E @ F @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__comp__distrib_0) ).
thf(1872,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_Orel__comp @ A @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_bool ) ) @ E ) @ F @ C @ D )
= ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ A @ B @ F @ C @ D ) @ ( tc_fun @ ( tc_prod @ F @ D ) @ tc_bool ) ) @ ( c_Relation_Orel__comp @ A @ E @ F @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).
thf(245,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( c_Relation_ORange @ A @ B @ C ) @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Relation_ORange @ D @ B @ C ) ) @ ( c_Relation_ORange @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A @ ( tc_fun @ ( tc_prod @ B @ C ) @ tc_bool ) ) @ D ) @ B @ C ) @ ( tc_fun @ C @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__Diff__subset_0) ).
thf(1233,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( c_Relation_ORange @ A @ B @ C ) @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Relation_ORange @ D @ B @ C ) ) @ ( c_Relation_ORange @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A @ ( tc_fun @ ( tc_prod @ B @ C ) @ tc_bool ) ) @ D ) @ B @ C ) @ ( tc_fun @ C @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(292,axiom,
! [B: $i,A: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ ( tc_fun @ A @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__subsetI_0) ).
thf(1327,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)],[292]) ).
thf(437,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ C @ ( tc_fun @ B @ tc_bool ) ) @ D ) )
= ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( tc_fun @ B @ tc_bool ) ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Int__distrib_0) ).
thf(1640,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ C @ ( tc_fun @ B @ tc_bool ) ) @ D ) )
= ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( tc_fun @ B @ tc_bool ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(169,axiom,
! [B: $i,A: $i] : ( hBOOL @ ( c_in @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UNIV__I_0) ).
thf(1063,plain,
! [B: $i,A: $i] : ( hBOOL @ ( c_in @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(353,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Otrans @ A @ B )
| ~ ( c_Equiv__Relations_Oequiv @ C @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv_Otrans_0) ).
thf(1458,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Otrans @ A @ B )
| ~ ( c_Equiv__Relations_Oequiv @ C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(214,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ A ) @ C )
= ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I1_J_0) ).
thf(1164,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ A ) @ C )
= ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(44,axiom,
! [B: $i,A: $i] : ( c_Relation_Osingle__valued @ ( c_Relation_OId__on @ A @ B ) @ B @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_single__valued__Id__on_0) ).
thf(797,plain,
! [B: $i,A: $i] : ( c_Relation_Osingle__valued @ ( c_Relation_OId__on @ A @ B ) @ B @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(678,axiom,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ A @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( tc_fun @ C @ tc_bool ) ) @ A ) @ ( tc_fun @ C @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__upper2_0) ).
thf(2168,plain,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ A @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( tc_fun @ C @ tc_bool ) ) @ A ) @ ( tc_fun @ C @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[678]) ).
thf(259,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl_Or__into__trancl_0) ).
thf(1260,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(493,axiom,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A @ B ) @ C ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_1) ).
thf(1761,plain,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A @ B ) @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).
thf(100,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_Set_Oinsert @ C @ B ) @ D ) )
= ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_Set_Oinsert @ C @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) ) @ ( tc_fun @ B @ tc_bool ) ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__insert2_0) ).
thf(913,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_Set_Oinsert @ C @ B ) @ D ) )
= ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_Set_Oinsert @ C @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) ) @ ( tc_fun @ B @ tc_bool ) ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(305,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Wellfounded_Oacc @ B @ C ) @ C ) )
| ~ ( c_Wellfounded_Owf @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__wfD_0) ).
thf(1354,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Wellfounded_Oacc @ B @ C ) @ C ) )
| ~ ( c_Wellfounded_Owf @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(669,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Product__Type_OSigma @ A @ ( c_COMBK @ B @ ( tc_fun @ C @ tc_bool ) @ D ) @ D @ C )
!= ( c_Product__Type_OSigma @ E @ ( c_COMBK @ B @ ( tc_fun @ C @ tc_bool ) @ D ) @ D @ C ) )
| ~ ( hBOOL @ ( c_in @ F @ B @ C ) )
| ( A = E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Times__eq__cancel2_0) ).
thf(2146,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Product__Type_OSigma @ A @ ( c_COMBK @ B @ ( tc_fun @ C @ tc_bool ) @ D ) @ D @ C )
!= ( c_Product__Type_OSigma @ E @ ( c_COMBK @ B @ ( tc_fun @ C @ tc_bool ) @ D ) @ D @ C ) )
| ~ ( hBOOL @ ( c_in @ F @ B @ C ) )
| ( A = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[669]) ).
thf(374,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ A @ B ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_split @ A @ E @ F @ ( tc_fun @ G @ tc_bool ) ) @ ( c_Pair @ B @ C @ E @ F ) ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_splitD_H_0) ).
thf(1507,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ A @ B ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_split @ A @ E @ F @ ( tc_fun @ G @ tc_bool ) ) @ ( c_Pair @ B @ C @ E @ F ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(108,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( hAPP @ ( c_Relation_OImage @ A @ B @ C ) @ D ) @ E @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ ( c_Product__Type_OSigma @ F @ ( c_COMBK @ E @ ( tc_fun @ C @ tc_bool ) @ B ) @ B @ C ) @ ( tc_fun @ ( tc_prod @ B @ C ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__subset_0) ).
thf(930,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( hAPP @ ( c_Relation_OImage @ A @ B @ C ) @ D ) @ E @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ ( c_Product__Type_OSigma @ F @ ( c_COMBK @ E @ ( tc_fun @ C @ tc_bool ) @ B ) @ B @ C ) @ ( tc_fun @ ( tc_prod @ B @ C ) @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(184,axiom,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ A @ ( hAPP @ ( c_Set_Oinsert @ B @ C ) @ A ) @ ( tc_fun @ C @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insertI_0) ).
thf(1095,plain,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ A @ ( hAPP @ ( c_Set_Oinsert @ B @ C ) @ A ) @ ( tc_fun @ C @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(228,axiom,
! [B: $i,A: $i] :
( ( ( c_Transitive__Closure_Otrancl @ A @ B )
= A )
| ~ ( c_Relation_Otrans @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__id_0) ).
thf(1196,plain,
! [B: $i,A: $i] :
( ( ( c_Transitive__Closure_Otrancl @ A @ B )
= A )
| ~ ( c_Relation_Otrans @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(527,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ B @ A @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) )
| ~ ( c_Relation_Oantisym @ D @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisymD_0) ).
thf(1835,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ B @ A @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) )
| ~ ( c_Relation_Oantisym @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).
thf(625,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Relation_OImage @ A @ B @ C ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ E @ F @ ( tc_fun @ B @ tc_bool ) ) )
= ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( c_COMBB @ ( c_Relation_OImage @ A @ B @ C ) @ E @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ C @ tc_bool ) @ F ) @ F @ ( tc_fun @ C @ tc_bool ) ) )
| ( D
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ F @ tc_bool ) ) )
| ~ ( c_Relation_Osingle__valued @ ( c_Relation_Oconverse @ A @ B @ C ) @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__INT__eq_0) ).
thf(2046,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Relation_OImage @ A @ B @ C ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ E @ F @ ( tc_fun @ B @ tc_bool ) ) )
= ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( c_COMBB @ ( c_Relation_OImage @ A @ B @ C ) @ E @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ C @ tc_bool ) @ F ) @ F @ ( tc_fun @ C @ tc_bool ) ) )
| ( D
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ F @ tc_bool ) ) )
| ~ ( c_Relation_Osingle__valued @ ( c_Relation_Oconverse @ A @ B @ C ) @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[625]) ).
thf(37,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Orefl__on @ A @ ( c_Relation_Oconverse @ B @ C @ C ) @ C )
| ~ ( c_Relation_Orefl__on @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__converse_1) ).
thf(782,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Orefl__on @ A @ ( c_Relation_Oconverse @ B @ C @ C ) @ C )
| ~ ( c_Relation_Orefl__on @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(426,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( tc_fun @ B @ tc_bool ) ) @ D )
= ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ B @ tc_bool ) ) @ D ) @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ ( tc_fun @ B @ tc_bool ) ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__distrib2_0) ).
thf(1613,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( tc_fun @ B @ tc_bool ) ) @ D )
= ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ B @ tc_bool ) ) @ D ) @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ ( tc_fun @ B @ tc_bool ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(251,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ B @ tc_bool ) ) @ C )
= ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ ( tc_fun @ B @ tc_bool ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__commute_0) ).
thf(1243,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ B @ tc_bool ) ) @ C )
= ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ ( tc_fun @ B @ tc_bool ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(502,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Wellfounded_Owf @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ A @ A @ B @ B @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ ( c_Relation_Orel__comp @ C @ A @ B @ B @ B ) ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ C ) @ B )
| ~ ( c_Wellfounded_Owf @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__union__merge_0) ).
thf(1782,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Wellfounded_Owf @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ A @ A @ B @ B @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ ( c_Relation_Orel__comp @ C @ A @ B @ B @ B ) ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ C ) @ B )
| ~ ( c_Wellfounded_Owf @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).
thf(88,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( c_lessequals @ C @ A @ ( tc_fun @ D @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__predicate1D_0) ).
thf(885,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( c_lessequals @ C @ A @ ( tc_fun @ D @ tc_bool ) )
| ~ ( hBOOL @ ( hAPP @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(161,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( c_in @ C @ ( c_Wellfounded_Oacc @ D @ t_a ) @ t_a ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ C @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ A @ D ) @ t_a @ t_a ) @ D @ ( tc_prod @ t_a @ t_a ) ) )
| ~ ( hBOOL @ ( c_in @ B @ ( c_Wellfounded_Oacc @ D @ t_a ) @ t_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_Oinducts_0) ).
thf(1046,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( c_in @ C @ ( c_Wellfounded_Oacc @ D @ t_a ) @ t_a ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ C @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ A @ D ) @ t_a @ t_a ) @ D @ ( tc_prod @ t_a @ t_a ) ) )
| ~ ( hBOOL @ ( c_in @ B @ ( c_Wellfounded_Oacc @ D @ t_a ) @ t_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(441,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( c_lessequals @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ A ) @ C ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I1_J_0) ).
thf(1650,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( c_lessequals @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ A ) @ C ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).
thf(439,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ C @ ( tc_fun @ B @ tc_bool ) ) @ D ) )
= D )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_lessequals @ D @ A @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__diff_0) ).
thf(1645,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ C @ ( tc_fun @ B @ tc_bool ) ) @ D ) )
= D )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_lessequals @ D @ A @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(475,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Wellfounded_Owf @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ C ) @ B )
| ~ ( c_lessequals @ ( c_Relation_Orel__comp @ A @ C @ B @ B @ B ) @ A @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) )
| ~ ( c_Wellfounded_Owf @ C @ B )
| ~ ( c_Wellfounded_Owf @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__union__compatible_0) ).
thf(1724,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Wellfounded_Owf @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ C ) @ B )
| ~ ( c_lessequals @ ( c_Relation_Orel__comp @ A @ C @ B @ B @ B ) @ A @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) )
| ~ ( c_Wellfounded_Owf @ C @ B )
| ~ ( c_Wellfounded_Owf @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).
thf(361,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__2 @ A @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bex__UNIV_2) ).
thf(1475,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__2 @ A @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(634,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1 @ A @ B @ C @ D ) @ B @ D @ D ) @ C @ ( tc_prod @ D @ D ) ) )
| ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ D @ D ) @ C @ ( tc_prod @ D @ D ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ D @ D ) @ ( c_Transitive__Closure_Otrancl @ C @ D ) @ ( tc_prod @ D @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tranclE_1) ).
thf(2067,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1 @ A @ B @ C @ D ) @ B @ D @ D ) @ C @ ( tc_prod @ D @ D ) ) )
| ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ D @ D ) @ C @ ( tc_prod @ D @ D ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ D @ D ) @ ( c_Transitive__Closure_Otrancl @ C @ D ) @ ( tc_prod @ D @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[634]) ).
thf(386,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Recdef_Ocut @ A @ B @ C @ D @ E )
= ( c_Recdef_Ocut @ F @ B @ C @ D @ E ) )
| ( hBOOL @ ( c_in @ ( c_Pair @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ A @ F @ B @ C @ D @ E ) @ C @ D @ D ) @ B @ ( tc_prod @ D @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cuts__eq_1) ).
thf(1529,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Recdef_Ocut @ A @ B @ C @ D @ E )
= ( c_Recdef_Ocut @ F @ B @ C @ D @ E ) )
| ( hBOOL @ ( c_in @ ( c_Pair @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ A @ F @ B @ C @ D @ E ) @ C @ D @ D ) @ B @ ( tc_prod @ D @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(243,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Transitive__Closure_Ortrancl @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) ) @ D ) @ C ) @ ( tc_prod @ C @ C ) ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__rtrancl__UnI_1) ).
thf(1228,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Transitive__Closure_Ortrancl @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) ) @ D ) @ C ) @ ( tc_prod @ C @ C ) ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(257,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ ( c_COMBK @ A @ B @ C ) @ D @ C @ B )
= ( hAPP @ ( c_Set_Oinsert @ A @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( c_in @ E @ D @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__constant_0) ).
thf(1254,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ ( c_COMBK @ A @ B @ C ) @ D @ C @ B )
= ( hAPP @ ( c_Set_Oinsert @ A @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( c_in @ E @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(271,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( c_ATP__Linkup_Osko__Complete__Lattice__XINTER__UNIV__conv__1__1 @ B @ A @ C @ D ) )
!= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_bool ) ) )
| ( ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_bool ) )
= ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ B @ A @ C @ ( tc_fun @ D @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INTER__UNIV__conv_I1_J_2) ).
thf(1287,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( c_ATP__Linkup_Osko__Complete__Lattice__XINTER__UNIV__conv__1__1 @ B @ A @ C @ D ) )
!= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_bool ) ) )
| ( ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_bool ) )
= ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ B @ A @ C @ ( tc_fun @ D @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(468,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ C @ ( tc_prod @ B @ B ) ) )
| ~ ( hBOOL @ ( c_in @ A @ D @ B ) )
| ~ ( c_Relation_Orefl__on @ D @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__def_1) ).
thf(1709,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ C @ ( tc_prod @ B @ B ) ) )
| ~ ( hBOOL @ ( c_in @ A @ D @ B ) )
| ~ ( c_Relation_Orefl__on @ D @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
thf(596,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ D @ C @ C ) @ ( c_Relation_OId__on @ B @ C ) @ ( tc_prod @ C @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Id__on__iff_1) ).
thf(1985,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ D @ C @ C ) @ ( c_Relation_OId__on @ B @ C ) @ ( tc_prod @ C @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[596]) ).
thf(276,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ E @ ( tc_prod @ C @ D ) ) )
| ~ ( hBOOL @ ( c_in @ B @ ( hAPP @ ( c_Relation_OImage @ E @ C @ D ) @ ( hAPP @ ( c_Set_Oinsert @ A @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__singleton__iff_0) ).
thf(1298,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ E @ ( tc_prod @ C @ D ) ) )
| ~ ( hBOOL @ ( c_in @ B @ ( hAPP @ ( c_Relation_OImage @ E @ C @ D ) @ ( hAPP @ ( c_Set_Oinsert @ A @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(8,negated_conjecture,
! [A: $i] :
( ( c_Relation_Ototal__on @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ tc_bool ) ) @ ( v_F @ A ) @ tc_Arrow__Order__Mirabelle_Oalt )
| ~ ( c_Relation_Ototal__on @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ tc_bool ) ) @ ( hAPP @ A @ ( hAPP @ v_x @ A ) ) @ tc_Arrow__Order__Mirabelle_Oalt )
| ~ ( c_Relation_Oirrefl @ ( hAPP @ A @ ( hAPP @ v_x @ A ) ) @ tc_Arrow__Order__Mirabelle_Oalt )
| ~ ( c_Relation_Otrans @ ( hAPP @ A @ ( hAPP @ v_x @ A ) ) @ tc_Arrow__Order__Mirabelle_Oalt ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_7) ).
thf(719,plain,
! [A: $i] :
( ( c_Relation_Ototal__on @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ tc_bool ) ) @ ( v_F @ A ) @ tc_Arrow__Order__Mirabelle_Oalt )
| ~ ( c_Relation_Ototal__on @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ tc_bool ) ) @ ( hAPP @ A @ ( hAPP @ v_x @ A ) ) @ tc_Arrow__Order__Mirabelle_Oalt )
| ~ ( c_Relation_Oirrefl @ ( hAPP @ A @ ( hAPP @ v_x @ A ) ) @ tc_Arrow__Order__Mirabelle_Oalt )
| ~ ( c_Relation_Otrans @ ( hAPP @ A @ ( hAPP @ v_x @ A ) ) @ tc_Arrow__Order__Mirabelle_Oalt ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(289,axiom,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ A @ ( hAPP @ ( c_Set_Oinsert @ A @ B ) @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__iff_1) ).
thf(1323,plain,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ A @ ( hAPP @ ( c_Set_Oinsert @ A @ B ) @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(102,axiom,
! [A: $i] :
( ~ ( class_Orderings_Otop @ A )
| ( ( hAPP @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ t_a @ A ) ) @ v_x )
= ( c_Orderings_Otop__class_Otop @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_top__fun__eq_0) ).
thf(917,plain,
! [A: $i] :
( ~ ( class_Orderings_Otop @ A )
| ( ( hAPP @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ t_a @ A ) ) @ v_x )
= ( c_Orderings_Otop__class_Otop @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(47,axiom,
( ( c_Relation_ORange @ v_r @ t_a @ t_b )
= ( c_Relation_ODomain @ ( c_Relation_Oconverse @ v_r @ t_a @ t_b ) @ t_b @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__def__raw_0) ).
thf(802,plain,
( ( c_Relation_ORange @ v_r @ t_a @ t_b )
= ( c_Relation_ODomain @ ( c_Relation_Oconverse @ v_r @ t_a @ t_b ) @ t_b @ t_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(522,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ ( c_Set_Oinsert @ A @ B ) @ C ) @ ( tc_fun @ B @ tc_bool ) ) @ D )
= ( hAPP @ ( c_Set_Oinsert @ A @ B ) @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ ( tc_fun @ B @ tc_bool ) ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__insert__left_0) ).
thf(1826,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ ( c_Set_Oinsert @ A @ B ) @ C ) @ ( tc_fun @ B @ tc_bool ) ) @ D )
= ( hAPP @ ( c_Set_Oinsert @ A @ B ) @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ ( tc_fun @ B @ tc_bool ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).
thf(268,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Pair @ A @ B @ C @ D )
!= ( c_Pair @ E @ F @ C @ D ) )
| ( A = E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Pair__eq_0) ).
thf(1279,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Pair @ A @ B @ C @ D )
!= ( c_Pair @ E @ F @ C @ D ) )
| ( A = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(599,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( c_lessequals @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ A ) @ C ) @ A ) @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ A ) @ D ) ) @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ A ) @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ A ) @ D ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distrib__inf__le_0) ).
thf(1992,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( c_lessequals @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ A ) @ C ) @ A ) @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ A ) @ D ) ) @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ A ) @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ A ) @ D ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[599]) ).
thf(167,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Product__Type_OSigma @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D @ B @ E )
= ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Product__Type_OSigma @ A @ D @ B @ E ) @ ( tc_fun @ ( tc_prod @ B @ E ) @ tc_bool ) ) @ ( c_Product__Type_OSigma @ C @ D @ B @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sigma__Un__distrib1_0) ).
thf(1059,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Product__Type_OSigma @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D @ B @ E )
= ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Product__Type_OSigma @ A @ D @ B @ E ) @ ( tc_fun @ ( tc_prod @ B @ E ) @ tc_bool ) ) @ ( c_Product__Type_OSigma @ C @ D @ B @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(294,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ A ) @ B ) @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supE_1) ).
thf(1330,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ A ) @ B ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(539,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ D @ C @ C ) @ E @ ( tc_prod @ C @ C ) ) )
| ~ ( c_Equiv__Relations_Oequiv @ B @ E @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__class__eq__iff_1) ).
thf(1860,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ D @ C @ C ) @ E @ ( tc_prod @ C @ C ) ) )
| ~ ( c_Equiv__Relations_Oequiv @ B @ E @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).
thf(261,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Transitive__Closure_Otrancl @ B @ C ) @ ( tc_prod @ C @ C ) ) )
| ~ ( hBOOL @ ( c_in @ A @ B @ ( tc_prod @ C @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_r__into__trancl_H_0) ).
thf(1264,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Transitive__Closure_Otrancl @ B @ C ) @ ( tc_prod @ C @ C ) ) )
| ~ ( hBOOL @ ( c_in @ A @ B @ ( tc_prod @ C @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(701,axiom,
! [B: $i,A: $i] :
( ( c_Wellfounded_Owf @ A @ B )
| ~ ( hBOOL @ ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__acc__iff__1__1 @ A @ B ) @ ( c_Wellfounded_Oacc @ A @ B ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__acc__iff_1) ).
thf(2217,plain,
! [B: $i,A: $i] :
( ( c_Wellfounded_Owf @ A @ B )
| ~ ( hBOOL @ ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__acc__iff__1__1 @ A @ B ) @ ( c_Wellfounded_Oacc @ A @ B ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[701]) ).
thf(687,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Transitive__Closure_Otrancl @ B @ C ) @ ( tc_prod @ C @ C ) ) )
| ~ ( c_lessequals @ D @ B @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__mono_0) ).
thf(2185,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Transitive__Closure_Otrancl @ B @ C ) @ ( tc_prod @ C @ C ) ) )
| ~ ( c_lessequals @ D @ B @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[687]) ).
thf(409,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__UNIV__right_0) ).
thf(1577,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(525,axiom,
! [B: $i,A: $i] : ( c_Relation_Otrans @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__rtrancl_0) ).
thf(1832,plain,
! [B: $i,A: $i] : ( c_Relation_Otrans @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).
thf(110,axiom,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Otrancl @ A @ B )
= ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ ( c_Relation_Orel__comp @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ A @ B @ B @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__unfold_0) ).
thf(934,plain,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Otrancl @ A @ B )
= ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ ( c_Relation_Orel__comp @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ A @ B @ B @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(393,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( hAPP @ ( c_Set_Oinsert @ B @ C ) @ D ) @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ D @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertCI_0) ).
thf(1545,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( hAPP @ ( c_Set_Oinsert @ B @ C ) @ D ) @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(510,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( hAPP @ B @ C ) @ D ) )
| ~ ( hBOOL @ ( c_in @ C @ E @ F ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ B @ F @ ( tc_fun @ D @ tc_bool ) ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__iff_0) ).
thf(1800,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( hAPP @ B @ C ) @ D ) )
| ~ ( hBOOL @ ( c_in @ C @ E @ F ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ E @ B @ F @ ( tc_fun @ D @ tc_bool ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).
thf(679,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( tc_fun @ B @ tc_bool ) ) @ C )
= C )
| ~ ( c_lessequals @ C @ A @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__absorb1_0) ).
thf(2169,plain,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( tc_fun @ B @ tc_bool ) ) @ C )
= C )
| ~ ( c_lessequals @ C @ A @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[679]) ).
thf(207,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ( B = A )
| ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ C @ A ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mkbot_4) ).
thf(1147,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ( B = A )
| ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ C @ A ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(626,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( c_COMBB @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) @ ( tc_fun @ C @ tc_bool ) @ A ) @ A @ ( tc_fun @ C @ tc_bool ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__simps_I2_J_0) ).
thf(2049,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( c_COMBB @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) @ ( tc_fun @ C @ tc_bool ) @ A ) @ A @ ( tc_fun @ C @ tc_bool ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[626]) ).
thf(32,axiom,
! [B: $i,A: $i] :
( ( ( c_Relation_Oconverse @ A @ B @ B )
!= A )
| ( c_Relation_Osym @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__conv__converse__eq_1) ).
thf(770,plain,
! [B: $i,A: $i] :
( ( ( c_Relation_Oconverse @ A @ B @ B )
!= A )
| ( c_Relation_Osym @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(325,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( c_lessequals @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ B @ C @ D @ A ) @ ( hAPP @ C @ E ) @ A )
| ~ ( hBOOL @ ( c_in @ E @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INF__leI_0) ).
thf(1398,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( c_lessequals @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ B @ C @ D @ A ) @ ( hAPP @ C @ E ) @ A )
| ~ ( hBOOL @ ( c_in @ E @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(193,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ A @ ( c_ATP__Linkup_Osko__Relation__XDomainE__1__1 @ A @ B @ C @ D ) @ C @ D ) @ B @ ( tc_prod @ C @ D ) ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_Relation_ODomain @ B @ C @ D ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DomainE_0) ).
thf(1115,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ A @ ( c_ATP__Linkup_Osko__Relation__XDomainE__1__1 @ A @ B @ C @ D ) @ C @ D ) @ B @ ( tc_prod @ C @ D ) ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_Relation_ODomain @ B @ C @ D ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(405,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ A @ ( c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1 @ A @ B @ C @ D ) @ C @ D ) @ B @ ( tc_prod @ C @ D ) ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_Relation_ODomain @ B @ C @ D ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__iff_0) ).
thf(1568,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ A @ ( c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1 @ A @ B @ C @ D ) @ C @ D ) @ B @ ( tc_prod @ C @ D ) ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_Relation_ODomain @ B @ C @ D ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(674,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ D @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnCI_0) ).
thf(2158,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[674]) ).
thf(309,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Wellfounded_Oacc @ B @ C ) @ C ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ D @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ B @ C ) @ ( tc_prod @ C @ C ) ) )
| ~ ( hBOOL @ ( c_in @ D @ ( c_Wellfounded_Oacc @ B @ C ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__downwards_0) ).
thf(1362,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Wellfounded_Oacc @ B @ C ) @ C ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ D @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ B @ C ) @ ( tc_prod @ C @ C ) ) )
| ~ ( hBOOL @ ( c_in @ D @ ( c_Wellfounded_Oacc @ B @ C ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(567,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_Otrans @ ( c_Relation_Oinv__image @ A @ B @ C @ D ) @ D )
| ~ ( c_Relation_Otrans @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__inv__image_0) ).
thf(1922,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_Otrans @ ( c_Relation_Oinv__image @ A @ B @ C @ D ) @ D )
| ~ ( c_Relation_Otrans @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).
thf(55,axiom,
! [B: $i,A: $i] : ( c_Relation_Oantisym @ ( c_Relation_OId__on @ A @ B ) @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__Id__on_0) ).
thf(817,plain,
! [B: $i,A: $i] : ( c_Relation_Oantisym @ ( c_Relation_OId__on @ A @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(553,axiom,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ A @ ( hAPP @ ( c_Set_Oinsert @ A @ B ) @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertI1_0) ).
thf(1892,plain,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ A @ ( hAPP @ ( c_Set_Oinsert @ A @ B ) @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).
thf(317,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Relation_OImage @ A @ B @ B ) @ ( hAPP @ ( c_Set_Oinsert @ C @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) )
= ( hAPP @ ( c_Relation_OImage @ A @ B @ B ) @ ( hAPP @ ( c_Set_Oinsert @ D @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ C @ D @ B @ B ) @ A @ ( tc_prod @ B @ B ) ) )
| ~ ( hBOOL @ ( c_in @ D @ E @ B ) )
| ~ ( hBOOL @ ( c_in @ C @ E @ B ) )
| ~ ( c_Equiv__Relations_Oequiv @ E @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__equiv__class__iff_1) ).
thf(1379,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Relation_OImage @ A @ B @ B ) @ ( hAPP @ ( c_Set_Oinsert @ C @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) )
= ( hAPP @ ( c_Relation_OImage @ A @ B @ B ) @ ( hAPP @ ( c_Set_Oinsert @ D @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ C @ D @ B @ B ) @ A @ ( tc_prod @ B @ B ) ) )
| ~ ( hBOOL @ ( c_in @ D @ E @ B ) )
| ~ ( hBOOL @ ( c_in @ C @ E @ B ) )
| ~ ( c_Equiv__Relations_Oequiv @ E @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(287,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( hAPP @ ( c_Set_Oinsert @ B @ C ) @ D ) @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( hAPP @ ( c_Set_Oinsert @ B @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ) @ D @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_4) ).
thf(1319,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( hAPP @ ( c_Set_Oinsert @ B @ C ) @ D ) @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( hAPP @ ( c_Set_Oinsert @ B @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ) @ D @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(466,axiom,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ A ) @ ( c_Orderings_Otop__class_Otop @ A ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__top__right_0) ).
thf(1704,plain,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ A ) @ ( c_Orderings_Otop__class_Otop @ A ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).
thf(81,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( c_in @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Set__Xball__UNIV__1__2 @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ball__UNIV_2) ).
thf(870,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( c_in @ B @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Set__Xball__UNIV__1__2 @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(363,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( c_lessequals @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A ) @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ A ) @ D ) ) @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A ) @ C ) @ A ) @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A ) @ D ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distrib__sup__le_0) ).
thf(1479,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( c_lessequals @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A ) @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ A ) @ D ) ) @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A ) @ C ) @ A ) @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A ) @ D ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(424,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_Set_Oinsert @ C @ B ) @ D ) )
= ( hAPP @ ( c_Set_Oinsert @ C @ B ) @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ B @ tc_bool ) ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__insert__right_0) ).
thf(1609,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_Set_Oinsert @ C @ B ) @ D ) )
= ( hAPP @ ( c_Set_Oinsert @ C @ B ) @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ B @ tc_bool ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(126,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_FunDef_Oin__rel @ A @ B @ C @ D @ E )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ B @ C @ D @ E ) @ A @ ( tc_prod @ D @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__rel__def_1) ).
thf(969,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_FunDef_Oin__rel @ A @ B @ C @ D @ E )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ B @ C @ D @ E ) @ A @ ( tc_prod @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(301,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Wellfounded_Oacyclic @ A @ B )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) )
| ~ ( c_Wellfounded_Oacyclic @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acyclic__subset_0) ).
thf(1347,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Wellfounded_Oacyclic @ A @ B )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) )
| ~ ( c_Wellfounded_Oacyclic @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(407,axiom,
( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_bool ) ) @ v_x )
= ( c_in @ v_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_bool ) ) @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot__empty__eq_0) ).
thf(1572,plain,
( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_bool ) ) @ v_x )
= ( c_in @ v_x @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ tc_bool ) ) @ t_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(517,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( tc_fun @ B @ tc_bool ) ) @ D )
= ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ C @ ( tc_fun @ B @ tc_bool ) ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Diff_0) ).
thf(1815,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( tc_fun @ B @ tc_bool ) ) @ D )
= ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ C @ ( tc_fun @ B @ tc_bool ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).
thf(369,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Oirrefl @ A @ B )
| ~ ( c_Order__Relation_Ostrict__linear__order__on @ C @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_strict__linear__order__on__def_1) ).
thf(1494,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Oirrefl @ A @ B )
| ~ ( c_Order__Relation_Ostrict__linear__order__on @ C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(105,axiom,
! [B: $i,A: $i] :
( ( class_Lattices_Obounded__lattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Obounded__lattice @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Obounded__lattice) ).
thf(924,plain,
! [B: $i,A: $i] :
( ( class_Lattices_Obounded__lattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Obounded__lattice @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(356,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_Orel__comp @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ ( tc_prod @ B @ C ) @ tc_bool ) ) @ D ) @ E @ B @ C @ F )
= ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ A @ E @ B @ C @ F ) @ ( tc_fun @ ( tc_prod @ B @ F ) @ tc_bool ) ) @ ( c_Relation_Orel__comp @ D @ E @ B @ C @ F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__comp__distrib2_0) ).
thf(1465,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_Orel__comp @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ ( tc_prod @ B @ C ) @ tc_bool ) ) @ D ) @ E @ B @ C @ F )
= ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ A @ E @ B @ C @ F ) @ ( tc_fun @ ( tc_prod @ B @ F ) @ tc_bool ) ) @ ( c_Relation_Orel__comp @ D @ E @ B @ C @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(616,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Set_Oinsert @ A @ B ) @ ( hAPP @ ( c_Set_Oinsert @ C @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) )
= ( hAPP @ ( c_Set_Oinsert @ C @ B ) @ ( hAPP @ ( c_Set_Oinsert @ A @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_4) ).
thf(2027,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Set_Oinsert @ A @ B ) @ ( hAPP @ ( c_Set_Oinsert @ C @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) )
= ( hAPP @ ( c_Set_Oinsert @ C @ B ) @ ( hAPP @ ( c_Set_Oinsert @ A @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[616]) ).
thf(40,axiom,
! [B: $i,A: $i] :
( ( c_Relation_Oantisym @ ( c_Relation_Oconverse @ A @ B @ B ) @ B )
| ~ ( c_Relation_Oantisym @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__converse_1) ).
thf(789,plain,
! [B: $i,A: $i] :
( ( c_Relation_Oantisym @ ( c_Relation_Oconverse @ A @ B @ B ) @ B )
| ~ ( c_Relation_Oantisym @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(644,axiom,
! [B: $i,A: $i] :
( ( c_Relation_Otrans @ A @ B )
| ( hBOOL @ ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XtransI__1__2 @ A @ B ) @ ( c_ATP__Linkup_Osko__Relation__XtransI__1__3 @ A @ B ) @ B @ B ) @ A @ ( tc_prod @ B @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_transI_1) ).
thf(2090,plain,
! [B: $i,A: $i] :
( ( c_Relation_Otrans @ A @ B )
| ( hBOOL @ ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XtransI__1__2 @ A @ B ) @ ( c_ATP__Linkup_Osko__Relation__XtransI__1__3 @ A @ B ) @ B @ B ) @ A @ ( tc_prod @ B @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[644]) ).
thf(434,axiom,
! [B: $i,A: $i] :
( ( ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) )
= B )
| ~ ( hBOOL @ ( c_in @ ( c_ATP__Linkup_Osko__Set__XUNIV__eq__I__1__1 @ B @ A ) @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UNIV__eq__I_0) ).
thf(1632,plain,
! [B: $i,A: $i] :
( ( ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) )
= B )
| ~ ( hBOOL @ ( c_in @ ( c_ATP__Linkup_Osko__Set__XUNIV__eq__I__1__1 @ B @ A ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(523,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ B @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ A ) @ D ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infE_0) ).
thf(1828,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ B @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ A ) @ D ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).
thf(208,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) @ D )
= D ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__extend__simps_I1_J_0) ).
thf(1151,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) @ D )
= D ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(149,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( c_COMBB @ ( c_Set_Oinsert @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) @ ( tc_fun @ C @ tc_bool ) @ E ) @ E @ ( tc_fun @ C @ tc_bool ) )
= ( hAPP @ ( c_Set_Oinsert @ B @ C ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ D @ E @ ( tc_fun @ C @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__simps_I5_J_0) ).
thf(1020,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( c_COMBB @ ( c_Set_Oinsert @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) @ ( tc_fun @ C @ tc_bool ) @ E ) @ E @ ( tc_fun @ C @ tc_bool ) )
= ( hAPP @ ( c_Set_Oinsert @ B @ C ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ D @ E @ ( tc_fun @ C @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(454,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ A @ C @ D ) ) )
| ~ ( hBOOL @ ( c_in @ B @ ( c_Wellfounded_Oacc @ C @ D ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__induct__rule_2) ).
thf(1677,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ A @ C @ D ) ) )
| ~ ( hBOOL @ ( c_in @ B @ ( c_Wellfounded_Oacc @ C @ D ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).
thf(585,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Set_Oinsert @ A @ B ) @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ C @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_Set_Oinsert @ A @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) ) )
= ( hAPP @ ( c_Set_Oinsert @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff__single_0) ).
thf(1960,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Set_Oinsert @ A @ B ) @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ C @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_Set_Oinsert @ A @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) ) )
= ( hAPP @ ( c_Set_Oinsert @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).
thf(124,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ D @ C ) )
| ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__mp_0) ).
thf(966,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ D @ C ) )
| ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(367,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ A )
| ( ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A ) @ C ) @ A ) @ D )
= ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ A ) @ D ) @ A ) @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__distrib2_0) ).
thf(1489,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ A )
| ( ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A ) @ C ) @ A ) @ D )
= ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ A ) @ D ) @ A ) @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(711,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Wellfounded_Oacc @ A @ B ) @ ( c_Wellfounded_Oacc @ C @ B ) @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_lessequals @ C @ A @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__subset_0) ).
thf(2237,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Wellfounded_Oacc @ A @ B ) @ ( c_Wellfounded_Oacc @ C @ B ) @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_lessequals @ C @ A @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[711]) ).
thf(333,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_Oconverse @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ ( tc_prod @ B @ C ) @ tc_bool ) ) @ D ) @ B @ C )
= ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Oconverse @ A @ B @ C ) @ ( tc_fun @ ( tc_prod @ C @ B ) @ tc_bool ) ) @ ( c_Relation_Oconverse @ D @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__Un_0) ).
thf(1415,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_Oconverse @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ ( tc_prod @ B @ C ) @ tc_bool ) ) @ D ) @ B @ C )
= ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Oconverse @ A @ B @ C ) @ ( tc_fun @ ( tc_prod @ C @ B ) @ tc_bool ) ) @ ( c_Relation_Oconverse @ D @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(278,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D @ B @ ( tc_fun @ E @ tc_bool ) )
= ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ D @ B @ ( tc_fun @ E @ tc_bool ) ) @ ( tc_fun @ E @ tc_bool ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ D @ B @ ( tc_fun @ E @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__Un_0) ).
thf(1302,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D @ B @ ( tc_fun @ E @ tc_bool ) )
= ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ D @ B @ ( tc_fun @ E @ tc_bool ) ) @ ( tc_fun @ E @ tc_bool ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ D @ B @ ( tc_fun @ E @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(24,axiom,
! [B: $i,A: $i] : ( c_Relation_Orefl__on @ A @ ( c_Relation_OId__on @ A @ B ) @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__Id__on_0) ).
thf(756,plain,
! [B: $i,A: $i] : ( c_Relation_Orefl__on @ A @ ( c_Relation_OId__on @ A @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(448,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) )
= ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ B @ C @ D @ ( tc_fun @ A @ tc_bool ) ) )
| ( hBOOL @ ( c_in @ ( c_ATP__Linkup_Osko__Complete__Lattice__XINTER__UNIV__conv__1__1 @ B @ C @ D @ A ) @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INTER__UNIV__conv_I1_J_1) ).
thf(1664,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) )
= ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ B @ C @ D @ ( tc_fun @ A @ tc_bool ) ) )
| ( hBOOL @ ( c_in @ ( c_ATP__Linkup_Osko__Complete__Lattice__XINTER__UNIV__conv__1__1 @ B @ C @ D @ A ) @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).
thf(651,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Wellfounded_Oacc @ B @ C ) @ C ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ D @ C @ C ) @ B @ ( tc_prod @ C @ C ) ) )
| ~ ( hBOOL @ ( c_in @ D @ ( c_Wellfounded_Oacc @ B @ C ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__downward_0) ).
thf(2105,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Wellfounded_Oacc @ B @ C ) @ C ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ D @ C @ C ) @ B @ ( tc_prod @ C @ C ) ) )
| ~ ( hBOOL @ ( c_in @ D @ ( c_Wellfounded_Oacc @ B @ C ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[651]) ).
thf(515,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Relation_OImage @ ( c_Relation_OId__on @ A @ B ) @ B @ B ) @ C )
= ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__Id__on_0) ).
thf(1811,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Relation_OImage @ ( c_Relation_OId__on @ A @ B ) @ B @ B ) @ C )
= ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).
thf(456,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( c_in @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bex__empty_0) ).
thf(1682,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( c_in @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).
thf(64,axiom,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Otrancl @ A @ B )
= ( c_Relation_Orel__comp @ A @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ B @ B @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__unfold__left_0) ).
thf(834,plain,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Otrancl @ A @ B )
= ( c_Relation_Orel__comp @ A @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ B @ B @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(538,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( tc_fun @ B @ tc_bool ) ) @ D )
= ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( tc_fun @ B @ tc_bool ) ) @ D ) @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ ( tc_fun @ B @ tc_bool ) ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Un__distrib2_0) ).
thf(1858,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( tc_fun @ B @ tc_bool ) ) @ D )
= ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( tc_fun @ B @ tc_bool ) ) @ D ) @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ ( tc_fun @ B @ tc_bool ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).
thf(541,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ B @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ A ) @ C ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__inf__iff_1) ).
thf(1864,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ B @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ A ) @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).
thf(659,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
!= ( c_Set_Oimage @ B @ C @ D @ A ) )
| ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__is__image_0) ).
thf(2122,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)],[659]) ).
thf(269,axiom,
! [C: $i,B: $i,A: $i] :
~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ C @ A ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mktop_0) ).
thf(1283,plain,
! [C: $i,B: $i,A: $i] :
~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ C @ A ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(637,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Pair @ A @ B @ C @ D )
!= ( c_Pair @ E @ F @ C @ D ) )
| ( B = F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Pair__eq_1) ).
thf(2073,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Pair @ A @ B @ C @ D )
!= ( c_Pair @ E @ F @ C @ D ) )
| ( B = F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[637]) ).
thf(216,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
| ( hBOOL @ ( c_in @ A @ ( c_Relation_ODomain @ D @ C @ C ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Not__Domain__rtrancl_0) ).
thf(1169,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
| ( hBOOL @ ( c_in @ A @ ( c_Relation_ODomain @ D @ C @ C ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(316,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ ( c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 @ B @ D @ C ) @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) )
| ~ ( hBOOL @ ( c_in @ E @ B @ C ) )
| ~ ( c_Wellfounded_Owf @ D @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wfE__min_1) ).
thf(1377,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ ( c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 @ B @ D @ C ) @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) )
| ~ ( hBOOL @ ( c_in @ E @ B @ C ) )
| ~ ( c_Wellfounded_Owf @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(689,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A ) @ C ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__ge1_0) ).
thf(2190,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A ) @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[689]) ).
thf(13,axiom,
! [B: $i,A: $i] :
( ( c_Wellfounded_Owf @ ( c_Relation_Oconverse @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ B @ B ) @ B )
| ~ ( c_Wellfounded_Owf @ ( c_Relation_Oconverse @ A @ B @ B ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__converse__trancl_0) ).
thf(734,plain,
! [B: $i,A: $i] :
( ( c_Wellfounded_Owf @ ( c_Relation_Oconverse @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ B @ B ) @ B )
| ~ ( c_Wellfounded_Owf @ ( c_Relation_Oconverse @ A @ B @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(551,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Ominus @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ B @ ( tc_fun @ t_a @ A ) ) @ C ) @ v_x )
= ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( hAPP @ B @ v_x ) @ A ) @ ( hAPP @ C @ v_x ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__diff__def_0) ).
thf(1886,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Ominus @ A )
| ( ( hAPP @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ B @ ( tc_fun @ t_a @ A ) ) @ C ) @ v_x )
= ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( hAPP @ B @ v_x ) @ A ) @ ( hAPP @ C @ v_x ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).
thf(195,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ ( c_Relation_Orel__comp @ E @ F @ C @ G @ D ) @ ( tc_prod @ C @ D ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ H @ B @ G @ D ) @ F @ ( tc_prod @ G @ D ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ H @ C @ G ) @ E @ ( tc_prod @ C @ G ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__compI_0) ).
thf(1119,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ ( c_Relation_Orel__comp @ E @ F @ C @ G @ D ) @ ( tc_prod @ C @ D ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ H @ B @ G @ D ) @ F @ ( tc_prod @ G @ D ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ H @ C @ G ) @ E @ ( tc_prod @ C @ G ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(323,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Relation_Oinv__image @ D @ E @ F @ C ) @ ( tc_prod @ C @ C ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ ( hAPP @ E @ A ) @ ( hAPP @ E @ B ) @ F @ F ) @ D @ ( tc_prod @ F @ F ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__inv__image_1) ).
thf(1394,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Relation_Oinv__image @ D @ E @ F @ C ) @ ( tc_prod @ C @ C ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ ( hAPP @ E @ A ) @ ( hAPP @ E @ B ) @ F @ F ) @ D @ ( tc_prod @ F @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(665,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Diff__Int_0) ).
thf(2137,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[665]) ).
thf(303,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ A @ tc_bool ) ) @ B )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty__left_0) ).
thf(1351,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ A @ tc_bool ) ) @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(300,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Product__Type_OSigma @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( c_COMBK @ D @ ( tc_fun @ E @ tc_bool ) @ B ) @ B @ E )
= ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Product__Type_OSigma @ A @ ( c_COMBK @ D @ ( tc_fun @ E @ tc_bool ) @ B ) @ B @ E ) @ ( tc_fun @ ( tc_prod @ B @ E ) @ tc_bool ) ) @ ( c_Product__Type_OSigma @ C @ ( c_COMBK @ D @ ( tc_fun @ E @ tc_bool ) @ B ) @ B @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Times__Un__distrib1_0) ).
thf(1345,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Product__Type_OSigma @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( c_COMBK @ D @ ( tc_fun @ E @ tc_bool ) @ B ) @ B @ E )
= ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Product__Type_OSigma @ A @ ( c_COMBK @ D @ ( tc_fun @ E @ tc_bool ) @ B ) @ B @ E ) @ ( tc_fun @ ( tc_prod @ B @ E ) @ tc_bool ) ) @ ( c_Product__Type_OSigma @ C @ ( c_COMBK @ D @ ( tc_fun @ E @ tc_bool ) @ B ) @ B @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(328,axiom,
class_Orderings_Opreorder @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Opreorder) ).
thf(1405,plain,
class_Orderings_Opreorder @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(230,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1 @ A @ B @ C @ D ) @ C @ D @ D ) @ ( c_Transitive__Closure_Ortrancl @ A @ D ) @ ( tc_prod @ D @ D ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ B @ C @ D @ D ) @ ( c_Transitive__Closure_Otrancl @ A @ D ) @ ( tc_prod @ D @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tranclD_1) ).
thf(1201,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1 @ A @ B @ C @ D ) @ C @ D @ D ) @ ( c_Transitive__Closure_Ortrancl @ A @ D ) @ ( tc_prod @ D @ D ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ B @ C @ D @ D ) @ ( c_Transitive__Closure_Otrancl @ A @ D ) @ ( tc_prod @ D @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(382,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ A @ tc_bool ) ) @ B )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__Diff_0) ).
thf(1521,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ A @ tc_bool ) ) @ B )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(696,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ( A = D )
| ~ ( c_lessequals @ E @ ( c_Product__Type_OSigma @ B @ ( c_COMBK @ B @ ( tc_fun @ C @ tc_bool ) @ C ) @ C @ C ) @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ D @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ E @ C ) @ ( tc_prod @ C @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__subset__Sigma__aux_0) ).
thf(2205,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ( A = D )
| ~ ( c_lessequals @ E @ ( c_Product__Type_OSigma @ B @ ( c_COMBK @ B @ ( tc_fun @ C @ tc_bool ) @ C ) @ C @ C ) @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ D @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ E @ C ) @ ( tc_prod @ C @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[696]) ).
thf(462,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ A @ ( v_sko__Transitive__Closure__Xtrancl__Xcases__1 @ A @ B @ C ) @ t_a @ t_a ) @ ( c_Transitive__Closure_Otrancl @ C @ t_a ) @ ( tc_prod @ t_a @ t_a ) ) )
| ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ t_a @ t_a ) @ C @ ( tc_prod @ t_a @ t_a ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ t_a @ t_a ) @ ( c_Transitive__Closure_Otrancl @ C @ t_a ) @ ( tc_prod @ t_a @ t_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl_Ocases_0) ).
thf(1696,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ A @ ( v_sko__Transitive__Closure__Xtrancl__Xcases__1 @ A @ B @ C ) @ t_a @ t_a ) @ ( c_Transitive__Closure_Otrancl @ C @ t_a ) @ ( tc_prod @ t_a @ t_a ) ) )
| ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ t_a @ t_a ) @ C @ ( tc_prod @ t_a @ t_a ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ t_a @ t_a ) @ ( c_Transitive__Closure_Otrancl @ C @ t_a ) @ ( tc_prod @ t_a @ t_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).
thf(592,axiom,
! [B: $i,A: $i] :
( ( c_Relation_Otrans @ A @ B )
| ( hBOOL @ ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XtransI__1__1 @ A @ B ) @ ( c_ATP__Linkup_Osko__Relation__XtransI__1__2 @ A @ B ) @ B @ B ) @ A @ ( tc_prod @ B @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_transI_0) ).
thf(1975,plain,
! [B: $i,A: $i] :
( ( c_Relation_Otrans @ A @ B )
| ( hBOOL @ ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XtransI__1__1 @ A @ B ) @ ( c_ATP__Linkup_Osko__Relation__XtransI__1__2 @ A @ B ) @ B @ B ) @ A @ ( tc_prod @ B @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).
thf(131,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ D @ A @ C @ C ) @ E @ ( tc_prod @ C @ C ) ) )
| ~ ( c_Equiv__Relations_Oequiv @ B @ E @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__class__eq__iff_2) ).
thf(981,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ D @ A @ C @ C ) @ E @ ( tc_prod @ C @ C ) ) )
| ~ ( c_Equiv__Relations_Oequiv @ B @ E @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(30,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( c_lessequals @ D @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I6_J_0) ).
thf(766,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)],[30]) ).
thf(530,axiom,
! [B: $i,A: $i] : ( c_Relation_Ototal__on @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_total__on__empty_0) ).
thf(1843,plain,
! [B: $i,A: $i] : ( c_Relation_Ototal__on @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).
thf(630,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ ( tc_fun @ B @ tc_bool ) ) @ D ) ) @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ ( tc_fun @ B @ tc_bool ) ) @ A ) )
= ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ ( tc_fun @ B @ tc_bool ) ) @ D ) ) @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ ( tc_fun @ B @ tc_bool ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__crazy_0) ).
thf(2058,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ ( tc_fun @ B @ tc_bool ) ) @ D ) ) @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ ( tc_fun @ B @ tc_bool ) ) @ A ) )
= ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ ( tc_fun @ B @ tc_bool ) ) @ D ) ) @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ ( tc_fun @ B @ tc_bool ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[630]) ).
thf(604,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ D @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__iff_2) ).
thf(2002,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ D @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[604]) ).
thf(139,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ ( c_Transitive__Closure_Otrancl @ C @ B ) @ ( tc_prod @ B @ B ) ) )
| ~ ( c_Wellfounded_Oacyclic @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acyclic__def_0) ).
thf(998,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ ( c_Transitive__Closure_Otrancl @ C @ B ) @ ( tc_prod @ B @ B ) ) )
| ~ ( c_Wellfounded_Oacyclic @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(422,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ E @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ E @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__trancl__trancl_0) ).
thf(1604,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ E @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ E @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(608,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
| ( A = D )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ C @ D ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mkbot_2) ).
thf(2011,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
| ( A = D )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ C @ D ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[608]) ).
thf(103,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ B @ A @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) )
| ~ ( c_Relation_Osym @ D @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__def_0) ).
thf(920,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ B @ A @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) )
| ~ ( c_Relation_Osym @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(114,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Ototal__on @ A @ B @ C )
| ~ ( c_Order__Relation_Ostrict__linear__order__on @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_strict__linear__order__on__def_2) ).
thf(942,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Ototal__on @ A @ B @ C )
| ~ ( c_Order__Relation_Ostrict__linear__order__on @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(460,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ A ) @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A ) @ C ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__absorb_0) ).
thf(1691,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ A ) @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A ) @ C ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).
thf(344,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ C ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ C @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ A @ D @ E ) @ E @ E ) @ D @ ( tc_prod @ E @ E ) ) )
| ~ ( hBOOL @ ( c_in @ B @ ( c_Wellfounded_Oacc @ D @ E ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__induct__rule_1) ).
thf(1438,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ C ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ C @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 @ A @ D @ E ) @ E @ E ) @ D @ ( tc_prod @ E @ E ) ) )
| ~ ( hBOOL @ ( c_in @ B @ ( c_Wellfounded_Oacc @ D @ E ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(42,axiom,
! [B: $i,A: $i] :
( ( c_Wellfounded_Owf @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ B )
| ~ ( c_Wellfounded_Owf @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__trancl_0) ).
thf(793,plain,
! [B: $i,A: $i] :
( ( c_Wellfounded_Owf @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ B )
| ~ ( c_Wellfounded_Owf @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(280,axiom,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Ortrancl @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ ( c_Relation_OId @ B ) ) @ B )
= ( c_Transitive__Closure_Ortrancl @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__r__diff__Id_0) ).
thf(1306,plain,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Ortrancl @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ ( c_Relation_OId @ B ) ) @ B )
= ( c_Transitive__Closure_Ortrancl @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(229,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Relation_ODomain @ B @ C @ C ) @ C ) )
| ( hBOOL @ ( c_in @ ( c_Pair @ A @ A @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ B @ C ) @ ( tc_prod @ C @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Not__Domain__rtrancl_1) ).
thf(1199,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Relation_ODomain @ B @ C @ C ) @ C ) )
| ( hBOOL @ ( c_in @ ( c_Pair @ A @ A @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ B @ C ) @ ( tc_prod @ C @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(209,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( ( hAPP @ ( c_HOL_Ominus__class_Ominus @ B @ A ) @ C )
!= ( hAPP @ ( c_HOL_Ominus__class_Ominus @ D @ A ) @ E ) )
| ( c_lessequals @ E @ D @ A )
| ~ ( c_lessequals @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__eqI_0) ).
thf(1153,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( ( hAPP @ ( c_HOL_Ominus__class_Ominus @ B @ A ) @ C )
!= ( hAPP @ ( c_HOL_Ominus__class_Ominus @ D @ A ) @ E ) )
| ( c_lessequals @ E @ D @ A )
| ~ ( c_lessequals @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(297,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ ( hAPP @ ( c_Set_Oinsert @ D @ C ) @ B ) @ ( tc_fun @ C @ tc_bool ) )
| ( hBOOL @ ( c_in @ D @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert_0) ).
thf(1338,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ ( hAPP @ ( c_Set_Oinsert @ D @ C ) @ B ) @ ( tc_fun @ C @ tc_bool ) )
| ( hBOOL @ ( c_in @ D @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(564,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ C )
= ( hAPP @ ( hAPP @ A @ D ) @ E ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ C @ E @ F @ F ) @ G @ ( tc_prod @ F @ F ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ B @ D @ H @ H ) @ I @ ( tc_prod @ H @ H ) ) )
| ~ ( c_Equiv__Relations_Ocongruent2 @ I @ G @ A @ H @ F @ J ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_congruent2_Ocongruent2_0) ).
thf(1915,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ A @ B ) @ C )
= ( hAPP @ ( hAPP @ A @ D ) @ E ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ C @ E @ F @ F ) @ G @ ( tc_prod @ F @ F ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ B @ D @ H @ H ) @ I @ ( tc_prod @ H @ H ) ) )
| ~ ( c_Equiv__Relations_Ocongruent2 @ I @ G @ A @ H @ F @ J ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).
thf(603,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ C @ ( tc_fun @ B @ tc_bool ) ) @ A ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__disjoint_0) ).
thf(2000,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ C @ ( tc_fun @ B @ tc_bool ) ) @ A ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[603]) ).
thf(641,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Wellfounded_Oacc @ B @ C ) @ C ) )
| ~ ( hBOOL @ ( c_in @ D @ ( c_Wellfounded_Oacc @ B @ C ) @ C ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ D @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ B @ C ) @ ( tc_prod @ C @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__downwards__aux_0) ).
thf(2083,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Wellfounded_Oacc @ B @ C ) @ C ) )
| ~ ( hBOOL @ ( c_in @ D @ ( c_Wellfounded_Oacc @ B @ C ) @ C ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ D @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ B @ C ) @ ( tc_prod @ C @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[641]) ).
thf(480,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Wellfounded_Oacc @ B @ C ) @ C ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ D @ C @ C ) @ B @ ( tc_prod @ C @ C ) ) )
| ~ ( hBOOL @ ( c_in @ D @ ( c_Wellfounded_Oacc @ B @ C ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_Ocases_0) ).
thf(1736,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Wellfounded_Oacc @ B @ C ) @ C ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ D @ C @ C ) @ B @ ( tc_prod @ C @ C ) ) )
| ~ ( hBOOL @ ( c_in @ D @ ( c_Wellfounded_Oacc @ B @ C ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).
thf(6,negated_conjecture,
! [A: $i] :
( ( c_Relation_Otrans @ ( v_F @ A ) @ tc_Arrow__Order__Mirabelle_Oalt )
| ~ ( c_Relation_Ototal__on @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ tc_bool ) ) @ ( hAPP @ A @ ( hAPP @ v_x @ A ) ) @ tc_Arrow__Order__Mirabelle_Oalt )
| ~ ( c_Relation_Oirrefl @ ( hAPP @ A @ ( hAPP @ v_x @ A ) ) @ tc_Arrow__Order__Mirabelle_Oalt )
| ~ ( c_Relation_Otrans @ ( hAPP @ A @ ( hAPP @ v_x @ A ) ) @ tc_Arrow__Order__Mirabelle_Oalt ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_5) ).
thf(714,plain,
! [A: $i] :
( ( c_Relation_Otrans @ ( v_F @ A ) @ tc_Arrow__Order__Mirabelle_Oalt )
| ~ ( c_Relation_Ototal__on @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ tc_bool ) ) @ ( hAPP @ A @ ( hAPP @ v_x @ A ) ) @ tc_Arrow__Order__Mirabelle_Oalt )
| ~ ( c_Relation_Oirrefl @ ( hAPP @ A @ ( hAPP @ v_x @ A ) ) @ tc_Arrow__Order__Mirabelle_Oalt )
| ~ ( c_Relation_Otrans @ ( hAPP @ A @ ( hAPP @ v_x @ A ) ) @ tc_Arrow__Order__Mirabelle_Oalt ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(543,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1E_0) ).
thf(1868,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).
thf(45,axiom,
! [B: $i,A: $i] :
( ( c_Relation_Osym @ A @ B )
| ~ ( c_Relation_Osym @ ( c_Relation_Oconverse @ A @ B @ B ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__converse_0) ).
thf(798,plain,
! [B: $i,A: $i] :
( ( c_Relation_Osym @ A @ B )
| ~ ( c_Relation_Osym @ ( c_Relation_Oconverse @ A @ B @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(213,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( c_Relation_ODomain @ A @ B @ C ) @ ( tc_fun @ B @ tc_bool ) ) @ ( c_Relation_ODomain @ D @ B @ C ) ) @ ( c_Relation_ODomain @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A @ ( tc_fun @ ( tc_prod @ B @ C ) @ tc_bool ) ) @ D ) @ B @ C ) @ ( tc_fun @ B @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__Diff__subset_0) ).
thf(1163,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( c_Relation_ODomain @ A @ B @ C ) @ ( tc_fun @ B @ tc_bool ) ) @ ( c_Relation_ODomain @ D @ B @ C ) ) @ ( c_Relation_ODomain @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A @ ( tc_fun @ ( tc_prod @ B @ C ) @ tc_bool ) ) @ D ) @ B @ C ) @ ( tc_fun @ B @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(266,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ B @ A @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) )
| ~ ( c_Relation_Osym @ D @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_symD_0) ).
thf(1274,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ B @ A @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) )
| ~ ( c_Relation_Osym @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(240,axiom,
class_Lattices_Odistrib__lattice @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Odistrib__lattice) ).
thf(1223,plain,
class_Lattices_Odistrib__lattice @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(19,axiom,
! [A: $i] :
( ( c_Relation_Oconverse @ ( c_Relation_OId @ A ) @ A @ A )
= ( c_Relation_OId @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__Id_0) ).
thf(746,plain,
! [A: $i] :
( ( c_Relation_Oconverse @ ( c_Relation_OId @ A ) @ A @ A )
= ( c_Relation_OId @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(299,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_ODomain @ ( hAPP @ ( c_Set_Oinsert @ ( c_Pair @ A @ B @ C @ D ) @ ( tc_prod @ C @ D ) ) @ E ) @ C @ D )
= ( hAPP @ ( c_Set_Oinsert @ A @ C ) @ ( c_Relation_ODomain @ E @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__insert_0) ).
thf(1343,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_ODomain @ ( hAPP @ ( c_Set_Oinsert @ ( c_Pair @ A @ B @ C @ D ) @ ( tc_prod @ C @ D ) ) @ E ) @ C @ D )
= ( hAPP @ ( c_Set_Oinsert @ A @ C ) @ ( c_Relation_ODomain @ E @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(35,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Orefl__on @ A @ B @ C )
| ~ ( c_Equiv__Relations_Oequiv @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv_Orefl__on_0) ).
thf(778,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Orefl__on @ A @ B @ C )
| ~ ( c_Equiv__Relations_Oequiv @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(381,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Ototal__on @ A @ B @ C )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__Xtotal__on__def__1__1 @ A @ B @ C ) @ ( c_ATP__Linkup_Osko__Relation__Xtotal__on__def__1__2 @ A @ B @ C ) @ C @ C ) @ B @ ( tc_prod @ C @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_total__on__def_4) ).
thf(1519,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Ototal__on @ A @ B @ C )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__Xtotal__on__def__1__1 @ A @ B @ C ) @ ( c_ATP__Linkup_Osko__Relation__Xtotal__on__def__1__2 @ A @ B @ C ) @ C @ C ) @ B @ ( tc_prod @ C @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(197,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
= ( hAPP @ ( c_Set_Oinsert @ B @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) )
| ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
| ~ ( c_lessequals @ A @ ( hAPP @ ( c_Set_Oinsert @ B @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__singletonD_0) ).
thf(1123,plain,
! [C: $i,B: $i,A: $i] :
( ( A
= ( hAPP @ ( c_Set_Oinsert @ B @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) )
| ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) )
| ~ ( c_lessequals @ A @ ( hAPP @ ( c_Set_Oinsert @ B @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(521,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ E @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ E @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__rtrancl__trancl_0) ).
thf(1824,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ E @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ E @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).
thf(54,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_lessequals @ B @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).
thf(815,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( c_lessequals @ B @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(663,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Wellfounded_Oacc @ B @ C ) @ C ) )
| ~ ( hBOOL @ ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1 @ B @ A @ C ) @ ( c_Wellfounded_Oacc @ B @ C ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_OaccI_1) ).
thf(2132,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Wellfounded_Oacc @ B @ C ) @ C ) )
| ~ ( hBOOL @ ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1 @ B @ A @ C ) @ ( c_Wellfounded_Oacc @ B @ C ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[663]) ).
thf(406,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Product__Type_OSigma @ A @ ( c_COMBK @ B @ ( tc_fun @ C @ tc_bool ) @ D ) @ D @ C ) @ ( c_Product__Type_OSigma @ E @ ( c_COMBK @ B @ ( tc_fun @ C @ tc_bool ) @ D ) @ D @ C ) @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_bool ) )
| ~ ( c_lessequals @ A @ E @ ( tc_fun @ D @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ F @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Times__subset__cancel2_1) ).
thf(1570,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Product__Type_OSigma @ A @ ( c_COMBK @ B @ ( tc_fun @ C @ tc_bool ) @ D ) @ D @ C ) @ ( c_Product__Type_OSigma @ E @ ( c_COMBK @ B @ ( tc_fun @ C @ tc_bool ) @ D ) @ D @ C ) @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_bool ) )
| ~ ( c_lessequals @ A @ E @ ( tc_fun @ D @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ F @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(218,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ A @ ( c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1 @ A @ B @ C @ D ) @ D @ D ) @ ( c_Transitive__Closure_Ortrancl @ C @ D ) @ ( tc_prod @ D @ D ) ) )
| ( A = B )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ D @ D ) @ ( c_Transitive__Closure_Ortrancl @ C @ D ) @ ( tc_prod @ D @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtranclE_0) ).
thf(1174,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ A @ ( c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1 @ A @ B @ C @ D ) @ D @ D ) @ ( c_Transitive__Closure_Ortrancl @ C @ D ) @ ( tc_prod @ D @ D ) ) )
| ( A = B )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ D @ D ) @ ( c_Transitive__Closure_Ortrancl @ C @ D ) @ ( tc_prod @ D @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(372,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ B @ tc_bool ) ) @ C )
= A )
| ~ ( c_lessequals @ C @ A @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__absorb2_0) ).
thf(1502,plain,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ B @ tc_bool ) ) @ C )
= A )
| ~ ( c_lessequals @ C @ A @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(487,axiom,
! [B: $i,A: $i] : ( c_lessequals @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__UNIV_0) ).
thf(1751,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)],[487]) ).
thf(57,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Olinorder @ A )
| ( c_lessequals @ B @ C @ A )
| ( c_lessequals @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__linear_0) ).
thf(820,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)],[57]) ).
thf(550,axiom,
! [A: $i] :
( ~ ( class_Orderings_Obot @ A )
| ( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ A ) ) @ v_x )
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot__fun__eq_0) ).
thf(1883,plain,
! [A: $i] :
( ~ ( class_Orderings_Obot @ A )
| ( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ t_a @ A ) ) @ v_x )
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).
thf(401,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ A ) @ B ) @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__sup__iff_1) ).
thf(1560,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ A ) @ B ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(337,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( c_lessequals @ B @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ A ) @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I4_J_0) ).
thf(1423,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( c_lessequals @ B @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ A ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(575,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/sandbox/benchmark/theBenchmark.p',cls_COMBB__def_0) ).
thf(1938,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)],[575]) ).
thf(311,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ E @ ( tc_prod @ C @ D ) ) )
| ~ ( c_FunDef_Oin__rel @ E @ A @ B @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__rel__def_0) ).
thf(1365,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ E @ ( tc_prod @ C @ D ) ) )
| ~ ( c_FunDef_Oin__rel @ E @ A @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(566,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ B @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ A ) @ D ) @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infI_0) ).
thf(1920,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ B @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ A ) @ D ) @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).
thf(589,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A ) @ C )
= C )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__sup_0) ).
thf(1968,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A ) @ C )
= C )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).
thf(73,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( B = C )
| ~ ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__antisym__conv_0) ).
thf(852,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)],[73]) ).
thf(275,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A ) @ C ) @ D @ A )
| ~ ( c_lessequals @ C @ D @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supI_0) ).
thf(1296,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A ) @ C ) @ D @ A )
| ~ ( c_lessequals @ C @ D @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(458,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A ) @ D ) @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supE_0) ).
thf(1687,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A ) @ D ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).
thf(699,axiom,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) @ ( tc_prod @ B @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl_Ortrancl__refl_0) ).
thf(2213,plain,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) @ ( tc_prod @ B @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[699]) ).
thf(25,axiom,
! [B: $i,A: $i] :
( ( c_Relation_ORange @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ B @ B )
= ( c_Relation_ORange @ A @ B @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__range_0) ).
thf(757,plain,
! [B: $i,A: $i] :
( ( c_Relation_ORange @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ B @ B )
= ( c_Relation_ORange @ A @ B @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(698,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ A @ C @ D ) ) )
| ~ ( hBOOL @ ( c_in @ B @ ( c_Wellfounded_Oacc @ C @ D ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__induct_2) ).
thf(2211,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 @ A @ C @ D ) ) )
| ~ ( hBOOL @ ( c_in @ B @ ( c_Wellfounded_Oacc @ C @ D ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[698]) ).
thf(199,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Relation_OId__on @ D @ C ) @ ( tc_prod @ C @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Id__on__iff_0) ).
thf(1128,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Relation_OId__on @ D @ C ) @ ( tc_prod @ C @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(322,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A ) @ D ) @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__sup__iff_0) ).
thf(1392,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A ) @ D ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(128,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ ( c_COMBK @ A @ B @ C ) @ D @ C @ B )
= ( hAPP @ ( c_Set_Oinsert @ A @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) )
| ( D
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__constant__conv_1) ).
thf(974,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ ( c_COMBK @ A @ B @ C ) @ D @ C @ B )
= ( hAPP @ ( c_Set_Oinsert @ A @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) )
| ( D
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(145,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_Set_Oinsert @ C @ B ) @ D ) )
= ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A @ ( tc_fun @ B @ tc_bool ) ) @ D ) @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_Set_Oinsert @ C @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__insert_0) ).
thf(1012,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_Set_Oinsert @ C @ B ) @ D ) )
= ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A @ ( tc_fun @ B @ tc_bool ) ) @ D ) @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_Set_Oinsert @ C @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(155,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Product__Type_OSigma @ A @ ( c_COMBK @ D @ ( tc_fun @ E @ tc_bool ) @ C ) @ C @ E ) @ ( c_Product__Type_OSigma @ B @ ( c_COMBK @ D @ ( tc_fun @ E @ tc_bool ) @ C ) @ C @ E ) @ ( tc_fun @ ( tc_prod @ C @ E ) @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ F @ D @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Times__subset__cancel2_0) ).
thf(1032,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Product__Type_OSigma @ A @ ( c_COMBK @ D @ ( tc_fun @ E @ tc_bool ) @ C ) @ C @ E ) @ ( c_Product__Type_OSigma @ B @ ( c_COMBK @ D @ ( tc_fun @ E @ tc_bool ) @ C ) @ C @ E ) @ ( tc_fun @ ( tc_prod @ C @ E ) @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ F @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(421,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ D @ C ) )
| ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__iff_0) ).
thf(1602,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ D @ C ) )
| ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(519,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_ORange @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ ( tc_prod @ B @ C ) @ tc_bool ) ) @ D ) @ B @ C )
= ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_ORange @ A @ B @ C ) @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Relation_ORange @ D @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__Un__eq_0) ).
thf(1819,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_ORange @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ ( tc_prod @ B @ C ) @ tc_bool ) ) @ D ) @ B @ C )
= ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_ORange @ A @ B @ C ) @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Relation_ORange @ D @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).
thf(431,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( c_lessequals @ B @ A @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equalityI_0) ).
thf(1624,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)],[431]) ).
thf(694,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Recdef_Ocut @ A @ B @ C @ D @ E )
!= ( c_Recdef_Ocut @ F @ B @ C @ D @ E ) )
| ( ( hAPP @ A @ G )
= ( hAPP @ F @ G ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ G @ C @ D @ D ) @ B @ ( tc_prod @ D @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cuts__eq_0) ).
thf(2200,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Recdef_Ocut @ A @ B @ C @ D @ E )
!= ( c_Recdef_Ocut @ F @ B @ C @ D @ E ) )
| ( ( hAPP @ A @ G )
= ( hAPP @ F @ G ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ G @ C @ D @ D ) @ B @ ( tc_prod @ D @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[694]) ).
thf(62,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_Oconverse @ ( c_Relation_Oinv__image @ A @ B @ C @ D ) @ D @ D )
= ( c_Relation_Oinv__image @ ( c_Relation_Oconverse @ A @ C @ C ) @ B @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__inv__image_0) ).
thf(830,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_Oconverse @ ( c_Relation_Oinv__image @ A @ B @ C @ D ) @ D @ D )
= ( c_Relation_Oinv__image @ ( c_Relation_Oconverse @ A @ C @ C ) @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(90,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ A @ C ) ) )
| ~ ( hBOOL @ ( c_in @ B @ ( c_Wellfounded_Oacc @ C @ t_a ) @ t_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_Oinducts_2) ).
thf(889,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ A @ C ) ) )
| ~ ( hBOOL @ ( c_in @ B @ ( c_Wellfounded_Oacc @ C @ t_a ) @ t_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(684,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
| ( hBOOL @ ( c_in @ ( c_Pair @ B @ A @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ E @ A @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ E @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
| ~ ( c_Relation_Osingle__valued @ D @ C @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_single__valued__confluent_0) ).
thf(2179,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
| ( hBOOL @ ( c_in @ ( c_Pair @ B @ A @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ E @ A @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ E @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
| ~ ( c_Relation_Osingle__valued @ D @ C @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[684]) ).
thf(505,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A ) @ C ) @ D @ A )
| ~ ( c_lessequals @ C @ D @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__least_0) ).
thf(1787,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A ) @ C ) @ D @ A )
| ~ ( c_lessequals @ C @ D @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).
thf(685,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Relation_OImage @ A @ B @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__empty_0) ).
thf(2181,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Relation_OImage @ A @ B @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[685]) ).
thf(482,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( c_Relation_OImage @ ( c_Relation_OId @ A ) @ A @ A ) @ B )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__Id_0) ).
thf(1740,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( c_Relation_OImage @ ( c_Relation_OId @ A ) @ A @ A ) @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).
thf(562,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ A ) @ C )
= ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__commute_0) ).
thf(1910,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ A ) @ C )
= ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).
thf(68,axiom,
! [B: $i,A: $i] :
( ( c_Relation_Oantisym @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ B )
| ~ ( c_Wellfounded_Oacyclic @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acyclic__impl__antisym__rtrancl_0) ).
thf(842,plain,
! [B: $i,A: $i] :
( ( c_Relation_Oantisym @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ B )
| ~ ( c_Wellfounded_Oacyclic @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(327,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ( A = B )
| ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ C @ B ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mktop_4) ).
thf(1402,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ C @ B ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(417,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ C @ D ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
| ( A = B )
| ( B = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mkbot_5) ).
thf(1592,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ C @ D ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
| ( A = B )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(512,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XImageE__1__1 @ A @ B @ C @ D @ E ) @ B @ D @ E ) @ C @ ( tc_prod @ D @ E ) ) )
| ~ ( hBOOL @ ( c_in @ B @ ( hAPP @ ( c_Relation_OImage @ C @ D @ E ) @ A ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ImageE_0) ).
thf(1804,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XImageE__1__1 @ A @ B @ C @ D @ E ) @ B @ D @ E ) @ C @ ( tc_prod @ D @ E ) ) )
| ~ ( hBOOL @ ( c_in @ B @ ( hAPP @ ( c_Relation_OImage @ C @ D @ E ) @ A ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).
thf(293,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ ( tc_fun @ C @ tc_bool ) ) @ B ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__subset__iff_1) ).
thf(1328,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ ( tc_fun @ C @ tc_bool ) ) @ B ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(196,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_ODomain @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ ( tc_prod @ B @ C ) @ tc_bool ) ) @ D ) @ B @ C )
= ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_ODomain @ A @ B @ C ) @ ( tc_fun @ B @ tc_bool ) ) @ ( c_Relation_ODomain @ D @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__Un__eq_0) ).
thf(1121,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_ODomain @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ ( tc_prod @ B @ C ) @ tc_bool ) ) @ D ) @ B @ C )
= ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_ODomain @ A @ B @ C ) @ ( tc_fun @ B @ tc_bool ) ) @ ( c_Relation_ODomain @ D @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(170,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__empty_0) ).
thf(1064,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(537,axiom,
! [B: $i,A: $i] :
( ( c_lessequals @ ( c_Relation_Orel__comp @ A @ A @ B @ B @ B ) @ A @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) )
| ~ ( c_Relation_Otrans @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__O__subset_0) ).
thf(1856,plain,
! [B: $i,A: $i] :
( ( c_lessequals @ ( c_Relation_Orel__comp @ A @ A @ B @ B @ B ) @ A @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) )
| ~ ( c_Relation_Otrans @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).
thf(338,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ A @ B ) @ C ) @ ( c_Set_Oimage @ ( c_split @ A @ D @ E @ F ) @ G @ ( tc_prod @ D @ E ) @ F ) @ F ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ B @ C @ D @ E ) @ G @ ( tc_prod @ D @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pair__imageI_0) ).
thf(1425,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( hAPP @ ( hAPP @ A @ B ) @ C ) @ ( c_Set_Oimage @ ( c_split @ A @ D @ E @ F ) @ G @ ( tc_prod @ D @ E ) @ F ) @ F ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ B @ C @ D @ E ) @ G @ ( tc_prod @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(142,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ E @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ E @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__rtrancl__into__rtrancl_0) ).
thf(1006,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ E @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ E @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(548,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_ATP__Linkup_Osko__Relation__Xtotal__on__def__1__1 @ A @ B @ C )
!= ( c_ATP__Linkup_Osko__Relation__Xtotal__on__def__1__2 @ A @ B @ C ) )
| ( c_Relation_Ototal__on @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_total__on__def_3) ).
thf(1878,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_ATP__Linkup_Osko__Relation__Xtotal__on__def__1__1 @ A @ B @ C )
!= ( c_ATP__Linkup_Osko__Relation__Xtotal__on__def__1__2 @ A @ B @ C ) )
| ( c_Relation_Ototal__on @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).
thf(490,axiom,
! [A: $i] :
( ( c_Relation_ORange @ ( c_Relation_OId @ A ) @ A @ A )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__Id_0) ).
thf(1755,plain,
! [A: $i] :
( ( c_Relation_ORange @ ( c_Relation_OId @ A ) @ A @ A )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).
thf(135,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( hAPP @ ( c_Set_Oinsert @ B @ C ) @ D ) @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ D @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__iff_2) ).
thf(989,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( hAPP @ ( c_Set_Oinsert @ B @ C ) @ D ) @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(75,axiom,
! [B: $i,A: $i] :
( ( c_Relation_ORange @ ( c_Relation_OId__on @ A @ B ) @ B @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__Id__on_0) ).
thf(857,plain,
! [B: $i,A: $i] :
( ( c_Relation_ORange @ ( c_Relation_OId__on @ A @ B ) @ B @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(308,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1 @ A @ B @ C @ D ) @ C @ D @ D ) @ ( c_Transitive__Closure_Otrancl @ A @ D ) @ ( tc_prod @ D @ D ) ) )
| ( hBOOL @ ( c_in @ ( c_Pair @ B @ C @ D @ D ) @ A @ ( tc_prod @ D @ D ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ B @ C @ D @ D ) @ ( c_Transitive__Closure_Otrancl @ A @ D ) @ ( tc_prod @ D @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__tranclE_1) ).
thf(1360,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1 @ A @ B @ C @ D ) @ C @ D @ D ) @ ( c_Transitive__Closure_Otrancl @ A @ D ) @ ( tc_prod @ D @ D ) ) )
| ( hBOOL @ ( c_in @ ( c_Pair @ B @ C @ D @ D ) @ A @ ( tc_prod @ D @ D ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ B @ C @ D @ D ) @ ( c_Transitive__Closure_Otrancl @ A @ D ) @ ( tc_prod @ D @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(574,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ C ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ C @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ A @ D ) @ t_a @ t_a ) @ D @ ( tc_prod @ t_a @ t_a ) ) )
| ~ ( hBOOL @ ( c_in @ B @ ( c_Wellfounded_Oacc @ D @ t_a ) @ t_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_Oinduct_1) ).
thf(1936,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ C ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ C @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ A @ D ) @ t_a @ t_a ) @ D @ ( tc_prod @ t_a @ t_a ) ) )
| ~ ( hBOOL @ ( c_in @ B @ ( c_Wellfounded_Oacc @ D @ t_a ) @ t_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).
thf(246,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ B @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ C ) )
| ( hBOOL @ ( c_in @ A @ D @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DiffI_0) ).
thf(1234,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ B @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ C ) )
| ( hBOOL @ ( c_in @ A @ D @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(391,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( tc_fun @ B @ tc_bool ) ) @ C )
= A )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__absorb2_0) ).
thf(1541,plain,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( tc_fun @ B @ tc_bool ) ) @ C )
= A )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(83,axiom,
! [B: $i,A: $i] :
( ( class_Lattices_Oupper__semilattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Olattice @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Oupper__semilattice) ).
thf(874,plain,
! [B: $i,A: $i] :
( ( class_Lattices_Oupper__semilattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Olattice @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(656,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ A @ C ) ) )
| ~ ( hBOOL @ ( c_in @ B @ ( c_Wellfounded_Oacc @ C @ t_a ) @ t_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_Oinduct_2) ).
thf(2115,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ A @ C ) ) )
| ~ ( hBOOL @ ( c_in @ B @ ( c_Wellfounded_Oacc @ C @ t_a ) @ t_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[656]) ).
thf(494,axiom,
! [B: $i,A: $i] :
( ( class_Lattices_Olower__semilattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Olattice @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olower__semilattice) ).
thf(1762,plain,
! [B: $i,A: $i] :
( ( class_Lattices_Olower__semilattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Olattice @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).
thf(649,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XRangeE__1__1 @ A @ B @ C @ D ) @ A @ D @ C ) @ B @ ( tc_prod @ D @ C ) ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_Relation_ORange @ B @ D @ C ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_RangeE_0) ).
thf(2100,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XRangeE__1__1 @ A @ B @ C @ D ) @ A @ D @ C ) @ B @ ( tc_prod @ D @ C ) ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_Relation_ORange @ B @ D @ C ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[649]) ).
thf(264,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( c_in @ A @ B @ C ) )
| ( hBOOL @ ( c_in @ ( hAPP @ D @ A ) @ ( c_Set_Oimage @ D @ B @ C @ E ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__image__eqI_0) ).
thf(1270,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( c_in @ A @ B @ C ) )
| ( hBOOL @ ( c_in @ ( hAPP @ D @ A ) @ ( c_Set_Oimage @ D @ B @ C @ E ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(498,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_Set_Oinsert @ C @ B ) @ D ) )
= ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( tc_fun @ B @ tc_bool ) ) @ D ) )
| ( hBOOL @ ( c_in @ C @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__right_1) ).
thf(1772,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_Set_Oinsert @ C @ B ) @ D ) )
= ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( tc_fun @ B @ tc_bool ) ) @ D ) )
| ( hBOOL @ ( c_in @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).
thf(508,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Transitive__Closure_Ortrancl @ A @ B )
= ( c_Transitive__Closure_Ortrancl @ C @ B ) )
| ~ ( c_lessequals @ A @ ( c_Transitive__Closure_Ortrancl @ C @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) )
| ~ ( c_lessequals @ C @ A @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__subset_0) ).
thf(1794,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Transitive__Closure_Ortrancl @ A @ B )
= ( c_Transitive__Closure_Ortrancl @ C @ B ) )
| ~ ( c_lessequals @ A @ ( c_Transitive__Closure_Ortrancl @ C @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) )
| ~ ( c_lessequals @ C @ A @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).
thf(582,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_lessequals @ C @ D @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__least_0) ).
thf(1953,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_lessequals @ C @ D @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).
thf(185,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ ( c_Relation_Oconverse @ E @ D @ C ) @ ( tc_prod @ C @ D ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ B @ A @ D @ C ) @ E @ ( tc_prod @ D @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__iff_1) ).
thf(1096,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ ( c_Relation_Oconverse @ E @ D @ C ) @ ( tc_prod @ C @ D ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ B @ A @ D @ C ) @ E @ ( tc_prod @ D @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(451,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Relation_OImage @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ ( tc_prod @ B @ C ) @ tc_bool ) ) @ D ) @ B @ C ) @ E )
= ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ ( c_Relation_OImage @ A @ B @ C ) @ E ) @ ( tc_fun @ C @ tc_bool ) ) @ ( hAPP @ ( c_Relation_OImage @ D @ B @ C ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Image_0) ).
thf(1672,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Relation_OImage @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ ( tc_prod @ B @ C ) @ tc_bool ) ) @ D ) @ B @ C ) @ E )
= ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ ( c_Relation_OImage @ A @ B @ C ) @ E ) @ ( tc_fun @ C @ tc_bool ) ) @ ( hAPP @ ( c_Relation_OImage @ D @ B @ C ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).
thf(640,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) )
| ( hBOOL @ ( c_in @ ( c_Pair @ B @ A @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) )
| ( B = A )
| ~ ( hBOOL @ ( c_in @ A @ E @ C ) )
| ~ ( hBOOL @ ( c_in @ B @ E @ C ) )
| ~ ( c_Relation_Ototal__on @ E @ D @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_total__on__def_0) ).
thf(2080,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) )
| ( hBOOL @ ( c_in @ ( c_Pair @ B @ A @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) )
| ( B = A )
| ~ ( hBOOL @ ( c_in @ A @ E @ C ) )
| ~ ( hBOOL @ ( c_in @ B @ E @ C ) )
| ~ ( c_Relation_Ototal__on @ E @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[640]) ).
thf(413,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( hAPP @ ( c_Set_Oinsert @ B @ C ) @ D ) @ ( tc_fun @ C @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ B @ A @ C ) )
| ~ ( c_lessequals @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( hAPP @ ( c_Set_Oinsert @ B @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ) @ D @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__single__insert_0) ).
thf(1584,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( hAPP @ ( c_Set_Oinsert @ B @ C ) @ D ) @ ( tc_fun @ C @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ B @ A @ C ) )
| ~ ( c_lessequals @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( hAPP @ ( c_Set_Oinsert @ B @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ) @ D @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(464,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__subset__iff_0) ).
thf(1700,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(236,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__UNIV__right_0) ).
thf(1214,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(552,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Relation_OId @ C ) @ ( tc_prod @ C @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pair__in__Id__conv_0) ).
thf(1889,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Relation_OId @ C ) @ ( tc_prod @ C @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).
thf(335,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ B @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ C ) )
| ( hBOOL @ ( c_in @ A @ D @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__iff_2) ).
thf(1419,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ B @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ C ) )
| ( hBOOL @ ( c_in @ A @ D @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(153,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oimage @ ( c_COMBK @ A @ B @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C @ B )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__constant__conv_0) ).
thf(1028,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oimage @ ( c_COMBK @ A @ B @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C @ B )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(178,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A ) @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ A ) @ D ) )
= ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ A ) @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I7_J_0) ).
thf(1082,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A ) @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ A ) @ D ) )
= ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ A ) @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(614,axiom,
! [B: $i,A: $i] :
( ( c_lessequals @ ( c_Relation_Orel__comp @ ( c_Relation_Oconverse @ A @ B @ B ) @ A @ B @ B @ B ) @ A @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) )
| ~ ( c_Relation_Otrans @ A @ B )
| ~ ( c_Relation_Osym @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__trans__comp__subset_0) ).
thf(2023,plain,
! [B: $i,A: $i] :
( ( c_lessequals @ ( c_Relation_Orel__comp @ ( c_Relation_Oconverse @ A @ B @ B ) @ A @ B @ B @ B ) @ A @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) )
| ~ ( c_Relation_Otrans @ A @ B )
| ~ ( c_Relation_Osym @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[614]) ).
thf(587,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Osym @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ C ) @ B )
| ~ ( c_Relation_Osym @ C @ B )
| ~ ( c_Relation_Osym @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__Un_0) ).
thf(1964,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Osym @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ C ) @ B )
| ~ ( c_Relation_Osym @ C @ B )
| ~ ( c_Relation_Osym @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).
thf(577,axiom,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Otrancl @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ ( c_Relation_OId @ B ) ) @ B )
= ( c_Transitive__Closure_Ortrancl @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__reflcl_0) ).
thf(1942,plain,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Otrancl @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ ( c_Relation_OId @ B ) ) @ B )
= ( c_Transitive__Closure_Ortrancl @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).
thf(446,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ A ) @ C ) @ A ) @ D )
= ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ A ) @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I2_J_0) ).
thf(1659,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ A ) @ C ) @ A ) @ D )
= ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ A ) @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(95,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
| ( A = B )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtranclD_0) ).
thf(901,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
| ( A = B )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(175,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ ( hAPP @ A @ B ) @ ( hAPP @ A @ C ) @ D @ D ) @ E @ ( tc_prod @ D @ D ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ B @ C @ F @ F ) @ ( c_Relation_Oinv__image @ E @ A @ D @ F ) @ ( tc_prod @ F @ F ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__inv__image_0) ).
thf(1075,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ ( hAPP @ A @ B ) @ ( hAPP @ A @ C ) @ D @ D ) @ E @ ( tc_prod @ D @ D ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ B @ C @ F @ F ) @ ( c_Relation_Oinv__image @ E @ A @ D @ F ) @ ( tc_prod @ F @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(628,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Recdef_Ocut @ A @ B @ C @ D @ E ) @ F )
= ( hAPP @ A @ F ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ F @ C @ D @ D ) @ B @ ( tc_prod @ D @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tfl__cut__apply_0) ).
thf(2053,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Recdef_Ocut @ A @ B @ C @ D @ E ) @ F )
= ( hAPP @ A @ F ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ F @ C @ D @ D ) @ B @ ( tc_prod @ D @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[628]) ).
thf(692,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ D @ A @ C @ C ) @ E @ ( tc_prod @ C @ C ) ) )
| ~ ( c_Relation_Orefl__on @ B @ E @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__onD2_0) ).
thf(2196,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ D @ A @ C @ C ) @ E @ ( tc_prod @ C @ C ) ) )
| ~ ( c_Relation_Orefl__on @ B @ E @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[692]) ).
thf(507,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ A ) @ C )
!= ( c_Orderings_Otop__class_Otop @ A ) )
| ( B
= ( c_Orderings_Otop__class_Otop @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__eq__top__eq1_0) ).
thf(1791,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ A ) @ C )
!= ( c_Orderings_Otop__class_Otop @ A ) )
| ( B
= ( c_Orderings_Otop__class_Otop @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).
thf(680,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ ( tc_fun @ B @ tc_bool ) ) @ D ) )
= ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A @ ( tc_fun @ B @ tc_bool ) ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Int_0) ).
thf(2172,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ ( tc_fun @ B @ tc_bool ) ) @ D ) )
= ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A @ ( tc_fun @ B @ tc_bool ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[680]) ).
thf(621,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Relation_OImage @ A @ B @ B ) @ ( hAPP @ ( c_Set_Oinsert @ C @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) )
= ( hAPP @ ( c_Relation_OImage @ A @ B @ B ) @ ( hAPP @ ( c_Set_Oinsert @ D @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ C @ D @ B @ B ) @ A @ ( tc_prod @ B @ B ) ) )
| ~ ( c_Equiv__Relations_Oequiv @ E @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__class__eq__iff_0) ).
thf(2038,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Relation_OImage @ A @ B @ B ) @ ( hAPP @ ( c_Set_Oinsert @ C @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) )
= ( hAPP @ ( c_Relation_OImage @ A @ B @ B ) @ ( hAPP @ ( c_Set_Oinsert @ D @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ C @ D @ B @ B ) @ A @ ( tc_prod @ B @ B ) ) )
| ~ ( c_Equiv__Relations_Oequiv @ E @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[621]) ).
thf(348,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ ( c_Relation_OId @ B ) )
= ( c_Transitive__Closure_Ortrancl @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__reflcl__absorb_0) ).
thf(1446,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ ( c_Relation_OId @ B ) )
= ( c_Transitive__Closure_Ortrancl @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(147,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Wellfounded_Oacyclic @ A @ B )
| ~ ( c_Wellfounded_Oacyclic @ ( hAPP @ ( c_Set_Oinsert @ ( c_Pair @ C @ D @ B @ B ) @ ( tc_prod @ B @ B ) ) @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acyclic__insert_0) ).
thf(1016,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Wellfounded_Oacyclic @ A @ B )
| ~ ( c_Wellfounded_Oacyclic @ ( hAPP @ ( c_Set_Oinsert @ ( c_Pair @ C @ D @ B @ B ) @ ( tc_prod @ B @ B ) ) @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(233,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( hAPP @ ( c_Set_Oinsert @ A @ B ) @ C ) @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_Set_Oinsert @ A @ B ) @ D ) )
= ( hAPP @ ( c_Set_Oinsert @ A @ B ) @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ ( tc_fun @ B @ tc_bool ) ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__inter__insert_0) ).
thf(1207,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( hAPP @ ( c_Set_Oinsert @ A @ B ) @ C ) @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_Set_Oinsert @ A @ B ) @ D ) )
= ( hAPP @ ( c_Set_Oinsert @ A @ B ) @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ ( tc_fun @ B @ tc_bool ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(642,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Product__Type_OSigma @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D @ B @ E )
= ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( c_Product__Type_OSigma @ A @ D @ B @ E ) @ ( tc_fun @ ( tc_prod @ B @ E ) @ tc_bool ) ) @ ( c_Product__Type_OSigma @ C @ D @ B @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sigma__Diff__distrib1_0) ).
thf(2085,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Product__Type_OSigma @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D @ B @ E )
= ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( c_Product__Type_OSigma @ A @ D @ B @ E ) @ ( tc_fun @ ( tc_prod @ B @ E ) @ tc_bool ) ) @ ( c_Product__Type_OSigma @ C @ D @ B @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[642]) ).
thf(66,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Relation_Orel__comp @ ( c_Relation_Oconverse @ A @ B @ B ) @ A @ B @ B @ B )
= A )
| ~ ( c_Equiv__Relations_Oequiv @ C @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__comp__eq_0) ).
thf(837,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Relation_Orel__comp @ ( c_Relation_Oconverse @ A @ B @ B ) @ A @ B @ B @ B )
= A )
| ~ ( c_Equiv__Relations_Oequiv @ C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(290,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ C @ ( tc_prod @ B @ B ) ) )
| ( hBOOL @ ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1 @ C @ B ) @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1 @ C @ B ) @ B @ B ) @ ( c_Transitive__Closure_Otrancl @ C @ B ) @ ( tc_prod @ B @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_irrefl__trancl__rD_0) ).
thf(1324,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ C @ ( tc_prod @ B @ B ) ) )
| ( hBOOL @ ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1 @ C @ B ) @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1 @ C @ B ) @ B @ B ) @ ( c_Transitive__Closure_Otrancl @ C @ B ) @ ( tc_prod @ B @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(254,axiom,
class_Orderings_Obot @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Obot) ).
thf(1249,plain,
class_Orderings_Obot @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(200,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ C @ ( tc_prod @ B @ B ) ) )
| ~ ( hBOOL @ ( c_in @ A @ D @ B ) )
| ~ ( c_Relation_Orefl__on @ D @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__onD_0) ).
thf(1131,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ C @ ( tc_prod @ B @ B ) ) )
| ~ ( hBOOL @ ( c_in @ A @ D @ B ) )
| ~ ( c_Relation_Orefl__on @ D @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(397,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( hAPP @ ( c_Relation_OImage @ A @ B @ B ) @ ( hAPP @ ( c_Set_Oinsert @ C @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) ) @ ( hAPP @ ( c_Relation_OImage @ A @ B @ B ) @ ( hAPP @ ( c_Set_Oinsert @ D @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) ) @ ( tc_fun @ B @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ C @ D @ B @ B ) @ A @ ( tc_prod @ B @ B ) ) )
| ~ ( c_Equiv__Relations_Oequiv @ E @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__class__subset_0) ).
thf(1552,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( hAPP @ ( c_Relation_OImage @ A @ B @ B ) @ ( hAPP @ ( c_Set_Oinsert @ C @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) ) @ ( hAPP @ ( c_Relation_OImage @ A @ B @ B ) @ ( hAPP @ ( c_Set_Oinsert @ D @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) ) @ ( tc_fun @ B @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ C @ D @ B @ B ) @ A @ ( tc_prod @ B @ B ) ) )
| ~ ( c_Equiv__Relations_Oequiv @ E @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(163,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( tc_fun @ B @ tc_bool ) ) @ D )
= ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( tc_fun @ B @ tc_bool ) ) @ D ) @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ ( tc_fun @ B @ tc_bool ) ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Int__distrib2_0) ).
thf(1050,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( tc_fun @ B @ tc_bool ) ) @ D )
= ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( tc_fun @ B @ tc_bool ) ) @ D ) @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ ( tc_fun @ B @ tc_bool ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(99,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ~ ( hBOOL @ ( c_in @ B @ D @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ A @ E @ ( tc_fun @ F @ tc_bool ) ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INF1__iff_0) ).
thf(911,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ~ ( hBOOL @ ( c_in @ B @ D @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ A @ E @ ( tc_fun @ F @ tc_bool ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(606,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Set_Oinsert @ A @ B ) @ C )
!= ( hAPP @ ( c_Set_Oinsert @ A @ B ) @ D ) )
| ( hBOOL @ ( c_in @ A @ D @ B ) )
| ( hBOOL @ ( c_in @ A @ C @ B ) )
| ( C = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__ident_0) ).
thf(2006,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Set_Oinsert @ A @ B ) @ C )
!= ( hAPP @ ( c_Set_Oinsert @ A @ B ) @ D ) )
| ( hBOOL @ ( c_in @ A @ D @ B ) )
| ( hBOOL @ ( c_in @ A @ C @ B ) )
| ( C = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[606]) ).
thf(579,axiom,
! [B: $i,A: $i] :
( ( c_Relation_ORange @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ B @ B )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__rtrancl_0) ).
thf(1947,plain,
! [B: $i,A: $i] :
( ( c_Relation_ORange @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ B @ B )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).
thf(535,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ ( tc_fun @ B @ tc_bool ) ) @ D ) )
= ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ B @ tc_bool ) ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__distrib_0) ).
thf(1852,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ ( tc_fun @ B @ tc_bool ) ) @ D ) )
= ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ B @ tc_bool ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).
thf(546,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1 @ A @ B @ C @ D @ E @ F @ G ) @ B @ G @ F ) @ D @ ( tc_prod @ G @ F ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ E @ F ) @ ( c_Relation_Orel__comp @ C @ D @ E @ G @ F ) @ ( tc_prod @ E @ F ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__compEpair_1) ).
thf(1874,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1 @ A @ B @ C @ D @ E @ F @ G ) @ B @ G @ F ) @ D @ ( tc_prod @ G @ F ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ E @ F ) @ ( c_Relation_Orel__comp @ C @ D @ E @ G @ F ) @ ( tc_prod @ E @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).
thf(340,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A ) @ C )
= ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__commute_0) ).
thf(1429,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A ) @ C )
= ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(420,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( tc_fun @ B @ tc_bool ) ) @ D )
!= ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ ( tc_fun @ B @ tc_bool ) ) @ D ) ) )
| ( c_lessequals @ D @ A @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__assoc__eq_0) ).
thf(1599,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( tc_fun @ B @ tc_bool ) ) @ D )
!= ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ ( tc_fun @ B @ tc_bool ) ) @ D ) ) )
| ( c_lessequals @ D @ A @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(471,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Set_Oinsert @ A @ B ) @ ( hAPP @ ( c_Set_Oinsert @ A @ B ) @ C ) )
= ( hAPP @ ( c_Set_Oinsert @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__absorb2_0) ).
thf(1715,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Set_Oinsert @ A @ B ) @ ( hAPP @ ( c_Set_Oinsert @ A @ B ) @ C ) )
= ( hAPP @ ( c_Set_Oinsert @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
thf(473,axiom,
class_HOL_Ominus @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__HOL_Ominus) ).
thf(1720,plain,
class_HOL_Ominus @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).
thf(594,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
= ( hAPP @ A @ C ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ B @ C @ D @ D ) @ E @ ( tc_prod @ D @ D ) ) )
| ~ ( c_Equiv__Relations_Ocongruent @ E @ A @ D @ F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_congruent_Ocongruent_0) ).
thf(1979,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
= ( hAPP @ A @ C ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ B @ C @ D @ D ) @ E @ ( tc_prod @ D @ D ) ) )
| ~ ( c_Equiv__Relations_Ocongruent @ E @ A @ D @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[594]) ).
thf(492,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ A @ tc_bool ) ) @ B )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__empty__left_0) ).
thf(1759,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ A @ tc_bool ) ) @ B )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).
thf(660,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ A ) @ D ) @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supI2_0) ).
thf(2125,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ A ) @ D ) @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[660]) ).
thf(415,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Set__Xball__UNIV__1__1 @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ball__UNIV_1) ).
thf(1588,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Set__Xball__UNIV__1__1 @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(133,axiom,
! [A: $i] : ( c_Relation_Otrans @ ( c_Relation_OId @ A ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__Id_0) ).
thf(985,plain,
! [A: $i] : ( c_Relation_Otrans @ ( c_Relation_OId @ A ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(350,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ B @ tc_bool ) ) @ C )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
| ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty_0) ).
thf(1451,plain,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ B @ tc_bool ) ) @ C )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
| ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(15,axiom,
! [B: $i,A: $i] :
( ( ( c_Relation_Oconverse @ A @ B @ B )
= A )
| ~ ( c_Relation_Osym @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__conv__converse__eq_0) ).
thf(738,plain,
! [B: $i,A: $i] :
( ( ( c_Relation_Oconverse @ A @ B @ B )
= A )
| ~ ( c_Relation_Osym @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(390,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__UNIV_0) ).
thf(1539,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(352,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ D @ ( tc_fun @ C @ tc_bool ) ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DiffE_1) ).
thf(1456,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ D @ ( tc_fun @ C @ tc_bool ) ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(318,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Set_Oinsert @ A @ B ) @ C )
= C )
| ~ ( hBOOL @ ( c_in @ A @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__absorb_0) ).
thf(1382,plain,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Set_Oinsert @ A @ B ) @ C )
= C )
| ~ ( hBOOL @ ( c_in @ A @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(262,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Ototal__on @ A @ B @ C )
| ( hBOOL @ ( c_in @ ( c_ATP__Linkup_Osko__Relation__Xtotal__on__def__1__2 @ A @ B @ C ) @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_total__on__def_2) ).
thf(1266,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Ototal__on @ A @ B @ C )
| ( hBOOL @ ( c_in @ ( c_ATP__Linkup_Osko__Relation__Xtotal__on__def__1__2 @ A @ B @ C ) @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(672,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 @ A @ B @ C ) @ A @ C ) )
| ~ ( hBOOL @ ( c_in @ D @ A @ C ) )
| ~ ( c_Wellfounded_Owf @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__eq__minimal_0) ).
thf(2153,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 @ A @ B @ C ) @ A @ C ) )
| ~ ( hBOOL @ ( c_in @ D @ A @ C ) )
| ~ ( c_Wellfounded_Owf @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[672]) ).
thf(226,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Otop @ A )
| ( c_lessequals @ B @ ( c_Orderings_Otop__class_Otop @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_top__greatest_0) ).
thf(1192,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Otop @ A )
| ( c_lessequals @ B @ ( c_Orderings_Otop__class_Otop @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(572,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ B @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ A ) @ D ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__inf__iff_0) ).
thf(1932,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ B @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ A ) @ D ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).
thf(432,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Product__Type_OSigma @ B @ ( c_COMBK @ B @ ( tc_fun @ C @ tc_bool ) @ C ) @ C @ C ) @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) )
| ~ ( c_Equiv__Relations_Oequiv @ B @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__type_0) ).
thf(1627,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Product__Type_OSigma @ B @ ( c_COMBK @ B @ ( tc_fun @ C @ tc_bool ) @ C ) @ C @ C ) @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) )
| ~ ( c_Equiv__Relations_Oequiv @ B @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(384,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Osko__Recdef__Xtfl__wf__induct__1__1 @ A @ C @ D ) ) )
| ~ ( c_Wellfounded_Owf @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tfl__wf__induct_1) ).
thf(1525,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_List_Osko__Recdef__Xtfl__wf__induct__1__1 @ A @ C @ D ) ) )
| ~ ( c_Wellfounded_Owf @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(342,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_lessequals @ A @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ ( tc_fun @ B @ tc_bool ) ) @ D ) @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__subset__conv_1) ).
thf(1434,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_lessequals @ A @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ ( tc_fun @ B @ tc_bool ) ) @ D ) @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(695,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( hAPP @ ( c_Set_Oinsert @ A @ B ) @ C ) @ D @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_lessequals @ C @ D @ ( tc_fun @ B @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ A @ D @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_2) ).
thf(2203,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( hAPP @ ( c_Set_Oinsert @ A @ B ) @ C ) @ D @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_lessequals @ C @ D @ ( tc_fun @ B @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ A @ D @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[695]) ).
thf(112,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oimage @ A @ B @ C @ D )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) )
| ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__is__empty_0) ).
thf(938,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)],[112]) ).
thf(250,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ A @ tc_bool ) ) @ B )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__UNIV__left_0) ).
thf(1241,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ A @ tc_bool ) ) @ B )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(623,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Ototal__on @ A @ B @ C )
| ~ ( c_Relation_Ototal__on @ A @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ B @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) ) @ ( c_Relation_OId @ C ) ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_total__on__diff__Id_0) ).
thf(2043,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Ototal__on @ A @ B @ C )
| ~ ( c_Relation_Ototal__on @ A @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ B @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) ) @ ( c_Relation_OId @ C ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[623]) ).
thf(173,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( hAPP @ ( c_Set_Oinsert @ A @ B ) @ C ) @ ( hAPP @ ( c_Set_Oinsert @ A @ B ) @ D ) @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_lessequals @ C @ D @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__mono_0) ).
thf(1071,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( hAPP @ ( c_Set_Oinsert @ A @ B ) @ C ) @ ( hAPP @ ( c_Set_Oinsert @ A @ B ) @ D ) @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_lessequals @ C @ D @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(119,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oimage @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B @ C )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__empty_0) ).
thf(953,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)],[119]) ).
thf(3,negated_conjecture,
! [A: $i] : ( c_Relation_Ototal__on @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ tc_bool ) ) @ ( hAPP @ v_P @ A ) @ tc_Arrow__Order__Mirabelle_Oalt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(718,plain,
! [A: $i] : ( c_Relation_Ototal__on @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ tc_bool ) ) @ ( hAPP @ v_P @ A ) @ tc_Arrow__Order__Mirabelle_Oalt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(478,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ A @ tc_bool ) ) @ B )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__UNIV__left_0) ).
thf(1732,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ A @ tc_bool ) ) @ B )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).
thf(106,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Transitive__Closure_Ortrancl @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) ) @ B )
= ( c_Transitive__Closure_Ortrancl @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__Un__rtrancl_0) ).
thf(926,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Transitive__Closure_Ortrancl @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) ) @ B )
= ( c_Transitive__Closure_Ortrancl @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(697,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( tc_fun @ B @ tc_bool ) ) @ C )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
| ( ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A @ ( tc_fun @ B @ tc_bool ) ) @ C )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__triv_0) ).
thf(2208,plain,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( tc_fun @ B @ tc_bool ) ) @ C )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
| ( ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A @ ( tc_fun @ B @ tc_bool ) ) @ C )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[697]) ).
thf(49,axiom,
! [B: $i,A: $i] :
( ( c_Relation_Orel__comp @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ B @ B @ B )
= ( c_Transitive__Closure_Ortrancl @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__idemp__self__comp_0) ).
thf(805,plain,
! [B: $i,A: $i] :
( ( c_Relation_Orel__comp @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ B @ B @ B )
= ( c_Transitive__Closure_Ortrancl @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(532,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( c_in @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ball__empty_0) ).
thf(1846,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( c_in @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).
thf(165,axiom,
! [B: $i,A: $i] :
( ( c_Relation_Otrans @ A @ B )
| ( hBOOL @ ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__Xtrans__def__1__2 @ A @ B ) @ ( c_ATP__Linkup_Osko__Relation__Xtrans__def__1__3 @ A @ B ) @ B @ B ) @ A @ ( tc_prod @ B @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__def_2) ).
thf(1054,plain,
! [B: $i,A: $i] :
( ( c_Relation_Otrans @ A @ B )
| ( hBOOL @ ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__Xtrans__def__1__2 @ A @ B ) @ ( c_ATP__Linkup_Osko__Relation__Xtrans__def__1__3 @ A @ B ) @ B @ B ) @ A @ ( tc_prod @ B @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(379,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Wellfounded_Owf @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ C ) @ B )
| ~ ( c_Wellfounded_Owf @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ A @ A @ B @ B @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ ( c_Relation_Orel__comp @ C @ A @ B @ B @ B ) ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__union__merge_1) ).
thf(1515,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Wellfounded_Owf @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ C ) @ B )
| ~ ( c_Wellfounded_Owf @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ A @ A @ B @ B @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ ( c_Relation_Orel__comp @ C @ A @ B @ B @ B ) ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(703,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Product__Type_OSigma @ B @ ( c_COMBK @ B @ ( tc_fun @ C @ tc_bool ) @ C ) @ C @ C ) @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) )
| ~ ( c_Relation_Orefl__on @ B @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__def_0) ).
thf(2221,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Product__Type_OSigma @ B @ ( c_COMBK @ B @ ( tc_fun @ C @ tc_bool ) @ C ) @ C @ C ) @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) )
| ~ ( c_Relation_Orefl__on @ B @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[703]) ).
thf(152,axiom,
! [B: $i,A: $i] :
( ( class_HOL_Ominus @ ( tc_fun @ A @ B ) )
| ~ ( class_HOL_Ominus @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__HOL_Ominus) ).
thf(1026,plain,
! [B: $i,A: $i] :
( ( class_HOL_Ominus @ ( tc_fun @ A @ B ) )
| ~ ( class_HOL_Ominus @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(555,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A ) @ C )
= ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I5_J_0) ).
thf(1895,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A ) @ C )
= ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).
thf(215,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E ) )
| ~ ( hBOOL @ ( c_in @ B @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__eqI_0) ).
thf(1167,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E ) )
| ~ ( hBOOL @ ( c_in @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(33,axiom,
! [B: $i,A: $i] :
( ( c_Wellfounded_Oacyclic @ A @ B )
| ~ ( c_Wellfounded_Oacyclic @ ( c_Relation_Oconverse @ A @ B @ B ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acyclic__converse_0) ).
thf(773,plain,
! [B: $i,A: $i] :
( ( c_Wellfounded_Oacyclic @ A @ B )
| ~ ( c_Wellfounded_Oacyclic @ ( c_Relation_Oconverse @ A @ B @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(601,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ C @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ ( tc_fun @ D @ tc_bool ) ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup1E_0) ).
thf(1996,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ C @ B ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ ( tc_fun @ D @ tc_bool ) ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[601]) ).
thf(495,axiom,
! [B: $i,A: $i] :
( ( class_Orderings_Oorder @ ( tc_fun @ A @ B ) )
| ~ ( class_Orderings_Oorder @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Oorder) ).
thf(1764,plain,
! [B: $i,A: $i] :
( ( class_Orderings_Oorder @ ( tc_fun @ A @ B ) )
| ~ ( class_Orderings_Oorder @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).
thf(489,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rangeI_0) ).
thf(1754,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) @ C @ D ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).
thf(418,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( c_in @ C @ ( c_Wellfounded_Oacc @ D @ t_a ) @ t_a ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ C @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ A @ D ) @ t_a @ t_a ) @ D @ ( tc_prod @ t_a @ t_a ) ) )
| ~ ( hBOOL @ ( c_in @ B @ ( c_Wellfounded_Oacc @ D @ t_a ) @ t_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_Oinduct_0) ).
thf(1595,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( c_in @ C @ ( c_Wellfounded_Oacc @ D @ t_a ) @ t_a ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ C @ ( v_sko__Wellfounded__Xacc__Xinduct__1 @ A @ D ) @ t_a @ t_a ) @ D @ ( tc_prod @ t_a @ t_a ) ) )
| ~ ( hBOOL @ ( c_in @ B @ ( c_Wellfounded_Oacc @ D @ t_a ) @ t_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(315,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Set_Oinsert @ A @ B ) @ C )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
| ( hBOOL @ ( c_in @ A @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Ononempty__iff_2) ).
thf(1374,plain,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Set_Oinsert @ A @ B ) @ C )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
| ( hBOOL @ ( c_in @ A @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(710,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A ) @ C ) @ D @ A )
| ~ ( c_lessequals @ C @ D @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__sup__iff_2) ).
thf(2235,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A ) @ C ) @ D @ A )
| ~ ( c_lessequals @ C @ D @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[710]) ).
thf(97,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ E @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ E @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl_Ortrancl__into__rtrancl_0) ).
thf(906,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ E @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ E @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(202,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntE_0) ).
thf(1135,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(440,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ ( tc_fun @ B @ tc_bool ) ) @ D ) )
= ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( tc_fun @ B @ tc_bool ) ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__left__commute_0) ).
thf(1648,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ ( tc_fun @ B @ tc_bool ) ) @ D ) )
= ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( tc_fun @ B @ tc_bool ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).
thf(21,axiom,
! [B: $i,A: $i] :
( ( c_Wellfounded_Owf @ A @ B )
| ~ ( c_Wellfounded_Owf @ ( c_Relation_Orel__comp @ A @ A @ B @ B @ B ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__comp__self_1) ).
thf(750,plain,
! [B: $i,A: $i] :
( ( c_Wellfounded_Owf @ A @ B )
| ~ ( c_Wellfounded_Owf @ ( c_Relation_Orel__comp @ A @ A @ B @ B @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(376,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) )
| ~ ( hBOOL @ ( c_in @ E @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( hAPP @ ( c_Relation_OImage @ D @ C @ C ) @ ( hAPP @ ( c_Set_Oinsert @ A @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ) @ ( tc_fun @ C @ tc_bool ) ) @ ( hAPP @ ( c_Relation_OImage @ D @ C @ C ) @ ( hAPP @ ( c_Set_Oinsert @ B @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ) ) @ C ) )
| ~ ( c_Equiv__Relations_Oequiv @ F @ D @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__class__nondisjoint_0) ).
thf(1510,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) )
| ~ ( hBOOL @ ( c_in @ E @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( hAPP @ ( c_Relation_OImage @ D @ C @ C ) @ ( hAPP @ ( c_Set_Oinsert @ A @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ) @ ( tc_fun @ C @ tc_bool ) ) @ ( hAPP @ ( c_Relation_OImage @ D @ C @ C ) @ ( hAPP @ ( c_Set_Oinsert @ B @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ) ) @ C ) )
| ~ ( c_Equiv__Relations_Oequiv @ F @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(463,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) )
| ~ ( hBOOL @ ( c_in @ B @ E @ C ) )
| ~ ( c_lessequals @ ( hAPP @ ( c_Relation_OImage @ D @ C @ C ) @ ( hAPP @ ( c_Set_Oinsert @ B @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ) @ ( hAPP @ ( c_Relation_OImage @ D @ C @ C ) @ ( hAPP @ ( c_Set_Oinsert @ A @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ) @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_Equiv__Relations_Oequiv @ E @ D @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__equiv__class_0) ).
thf(1698,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) )
| ~ ( hBOOL @ ( c_in @ B @ E @ C ) )
| ~ ( c_lessequals @ ( hAPP @ ( c_Relation_OImage @ D @ C @ C ) @ ( hAPP @ ( c_Set_Oinsert @ B @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ) @ ( hAPP @ ( c_Relation_OImage @ D @ C @ C ) @ ( hAPP @ ( c_Set_Oinsert @ A @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ) @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_Equiv__Relations_Oequiv @ E @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(188,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ ( c_Set_Oimage @ A @ B @ C @ D ) @ E @ D @ ( tc_fun @ F @ tc_bool ) )
= ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ B @ ( c_COMBB @ E @ A @ D @ ( tc_fun @ F @ tc_bool ) @ C ) @ C @ ( tc_fun @ F @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__simps_I10_J_0) ).
thf(1103,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ ( c_Set_Oimage @ A @ B @ C @ D ) @ E @ D @ ( tc_fun @ F @ tc_bool ) )
= ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ B @ ( c_COMBB @ E @ A @ D @ ( tc_fun @ F @ tc_bool ) @ C ) @ C @ ( tc_fun @ F @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(619,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1 @ A @ B @ C @ D ) @ B @ D @ D ) @ C @ ( tc_prod @ D @ D ) ) )
| ( A = B )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ D @ D ) @ ( c_Transitive__Closure_Ortrancl @ C @ D ) @ ( tc_prod @ D @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtranclE_1) ).
thf(2033,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XrtranclE__1__1 @ A @ B @ C @ D ) @ B @ D @ D ) @ C @ ( tc_prod @ D @ D ) ) )
| ( A = B )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ D @ D ) @ ( c_Transitive__Closure_Ortrancl @ C @ D ) @ ( tc_prod @ D @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[619]) ).
thf(670,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( hAPP @ ( c_Set_Oinsert @ B @ C ) @ D ) @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) )
| ( hBOOL @ ( c_in @ B @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert_1) ).
thf(2149,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( hAPP @ ( c_Set_Oinsert @ B @ C ) @ D ) @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) )
| ( hBOOL @ ( c_in @ B @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[670]) ).
thf(238,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( c_in @ A @ B @ C ) )
| ( hBOOL @ ( c_in @ ( hAPP @ D @ A ) @ ( c_Set_Oimage @ D @ B @ C @ E ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__iff_2) ).
thf(1219,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( c_in @ A @ B @ C ) )
| ( hBOOL @ ( c_in @ ( hAPP @ D @ A ) @ ( c_Set_Oimage @ D @ B @ C @ E ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(59,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_ODomain @ ( c_Relation_Oconverse @ A @ B @ C ) @ C @ B )
= ( c_Relation_ORange @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__converse_0) ).
thf(824,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_ODomain @ ( c_Relation_Oconverse @ A @ B @ C ) @ C @ B )
= ( c_Relation_ORange @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(96,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ E @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ E @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__into__trancl2_0) ).
thf(904,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ E @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ E @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(526,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ C ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ C @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1 @ A @ D @ E ) @ E @ E ) @ D @ ( tc_prod @ E @ E ) ) )
| ~ ( c_Wellfounded_Owf @ D @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__induct__rule_0) ).
thf(1833,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ C ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ C @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__rule__1__1 @ A @ D @ E ) @ E @ E ) @ D @ ( tc_prod @ E @ E ) ) )
| ~ ( c_Wellfounded_Owf @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).
thf(12,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Orel__comp @ A @ ( c_Relation_OId @ B ) @ C @ B @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_R__O__Id_0) ).
thf(732,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Orel__comp @ A @ ( c_Relation_OId @ B ) @ C @ B @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(429,axiom,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) @ ( tc_prod @ B @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__eq__or__trancl_1) ).
thf(1620,plain,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) @ ( tc_prod @ B @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(488,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( tc_fun @ B @ tc_bool ) ) @ D )
= ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ ( tc_fun @ B @ tc_bool ) ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__assoc_0) ).
thf(1752,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( tc_fun @ B @ tc_bool ) ) @ D )
= ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ ( tc_fun @ B @ tc_bool ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).
thf(610,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ E @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ E @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_r__r__into__trancl_0) ).
thf(2016,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ E @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ E @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[610]) ).
thf(320,axiom,
! [C: $i,B: $i,A: $i] :
~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ C @ B ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mkbot_0) ).
thf(1388,plain,
! [C: $i,B: $i,A: $i] :
~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ C @ B ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(17,axiom,
! [A: $i] : ( c_Relation_Oantisym @ ( c_Relation_OId @ A ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__Id_0) ).
thf(743,plain,
! [A: $i] : ( c_Relation_Oantisym @ ( c_Relation_OId @ A ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(60,axiom,
! [B: $i,A: $i] :
( ( c_Wellfounded_Owf @ ( c_Relation_Orel__comp @ A @ A @ B @ B @ B ) @ B )
| ~ ( c_Wellfounded_Owf @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__comp__self_0) ).
thf(826,plain,
! [B: $i,A: $i] :
( ( c_Wellfounded_Owf @ ( c_Relation_Orel__comp @ A @ A @ B @ B @ B ) @ B )
| ~ ( c_Wellfounded_Owf @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(388,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ A @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1 @ B @ A @ C @ D ) @ D @ D ) @ B @ ( tc_prod @ D @ D ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ C @ D @ D ) @ ( c_Transitive__Closure_Otrancl @ B @ D ) @ ( tc_prod @ D @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tranclD_0) ).
thf(1535,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ A @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1 @ B @ A @ C @ D ) @ D @ D ) @ B @ ( tc_prod @ D @ D ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ C @ D @ D ) @ ( c_Transitive__Closure_Otrancl @ B @ D ) @ ( tc_prod @ D @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(121,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ( c_lessequals @ ( c_Set_Oimage @ D @ A @ C @ E ) @ ( c_Set_Oimage @ D @ B @ C @ E ) @ ( tc_fun @ E @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__image__iff_2) ).
thf(958,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)],[121]) ).
thf(242,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Wellfounded_Oacc @ B @ C ) @ C ) )
| ( hBOOL @ ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1 @ B @ A @ C ) @ A @ C @ C ) @ B @ ( tc_prod @ C @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_OaccI_0) ).
thf(1226,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Wellfounded_Oacc @ B @ C ) @ C ) )
| ( hBOOL @ ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1 @ B @ A @ C ) @ A @ C @ C ) @ B @ ( tc_prod @ C @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(664,axiom,
! [B: $i,A: $i] :
( ( A
= ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XIdE__1__1 @ A @ B ) @ ( c_ATP__Linkup_Osko__Relation__XIdE__1__1 @ A @ B ) @ B @ B ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_Relation_OId @ B ) @ ( tc_prod @ B @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IdE_0) ).
thf(2134,plain,
! [B: $i,A: $i] :
( ( A
= ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XIdE__1__1 @ A @ B ) @ ( c_ATP__Linkup_Osko__Relation__XIdE__1__1 @ A @ B ) @ B @ B ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_Relation_OId @ B ) @ ( tc_prod @ B @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[664]) ).
thf(427,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ C ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ C @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ A @ D ) @ t_a @ t_a ) @ D @ ( tc_prod @ t_a @ t_a ) ) )
| ~ ( hBOOL @ ( c_in @ B @ ( c_Wellfounded_Oacc @ D @ t_a ) @ t_a ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_Oinducts_1) ).
thf(1615,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ C ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ C @ ( v_sko__Wellfounded__Xacc__Xinducts__1 @ A @ D ) @ t_a @ t_a ) @ D @ ( tc_prod @ t_a @ t_a ) ) )
| ~ ( hBOOL @ ( c_in @ B @ ( c_Wellfounded_Oacc @ D @ t_a ) @ t_a ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(503,axiom,
! [B: $i,A: $i] : ( c_lessequals @ A @ A @ ( tc_fun @ B @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equalityE_0) ).
thf(1784,plain,
! [B: $i,A: $i] : ( c_lessequals @ A @ A @ ( tc_fun @ B @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).
thf(442,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( c_COMBB @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) @ ( tc_fun @ C @ tc_bool ) @ E ) @ E @ ( tc_fun @ C @ tc_bool ) )
= ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ D @ E @ ( tc_fun @ C @ tc_bool ) ) ) )
| ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__simps_I2_J_1) ).
thf(1652,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( c_COMBB @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) @ ( tc_fun @ C @ tc_bool ) @ E ) @ E @ ( tc_fun @ C @ tc_bool ) )
= ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ D @ E @ ( tc_fun @ C @ tc_bool ) ) ) )
| ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).
thf(570,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Set_Oimage @ A @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ C @ E ) @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oimage @ A @ B @ C @ E ) @ ( tc_fun @ E @ tc_bool ) ) @ ( c_Set_Oimage @ A @ D @ C @ E ) ) @ ( tc_fun @ E @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__Int__subset_0) ).
thf(1929,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Set_Oimage @ A @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ C @ E ) @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oimage @ A @ B @ C @ E ) @ ( tc_fun @ E @ tc_bool ) ) @ ( c_Set_Oimage @ A @ D @ C @ E ) ) @ ( tc_fun @ E @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).
thf(204,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Set_Oinsert @ A @ B ) @ C )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__not__empty_0) ).
thf(1139,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Set_Oinsert @ A @ B ) @ C )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(450,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ A @ B @ C @ D @ E @ F ) )
!= ( hAPP @ B @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ A @ B @ C @ D @ E @ F ) ) )
| ( ( c_Recdef_Ocut @ A @ C @ D @ E @ F )
= ( c_Recdef_Ocut @ B @ C @ D @ E @ F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cuts__eq_2) ).
thf(1669,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ A @ B @ C @ D @ E @ F ) )
!= ( hAPP @ B @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ A @ B @ C @ D @ E @ F ) ) )
| ( ( c_Recdef_Ocut @ A @ C @ D @ E @ F )
= ( c_Recdef_Ocut @ B @ C @ D @ E @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(111,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Wellfounded_Owf @ ( hAPP @ ( c_Set_Oinsert @ ( c_Pair @ A @ B @ C @ C ) @ ( tc_prod @ C @ C ) ) @ D ) @ C )
| ( hBOOL @ ( c_in @ ( c_Pair @ B @ A @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
| ~ ( c_Wellfounded_Owf @ D @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__insert_2) ).
thf(936,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Wellfounded_Owf @ ( hAPP @ ( c_Set_Oinsert @ ( c_Pair @ A @ B @ C @ C ) @ ( tc_prod @ C @ C ) ) @ D ) @ C )
| ( hBOOL @ ( c_in @ ( c_Pair @ B @ A @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
| ~ ( c_Wellfounded_Owf @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(617,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ D @ E @ ( tc_fun @ B @ tc_bool ) ) )
= ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( c_COMBB @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ B @ tc_bool ) ) @ D @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) @ E ) @ E @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__extend__simps_I7_J_0) ).
thf(2029,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ D @ E @ ( tc_fun @ B @ tc_bool ) ) )
= ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( c_COMBB @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ B @ tc_bool ) ) @ D @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) @ E ) @ E @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[617]) ).
thf(467,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A @ ( tc_fun @ C @ tc_bool ) ) @ B ) @ D @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__subset__conv_0) ).
thf(1707,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A @ ( tc_fun @ C @ tc_bool ) ) @ B ) @ D @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).
thf(283,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__into__rtrancl_0) ).
thf(1312,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(39,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_Orel__comp @ ( c_Relation_Orel__comp @ A @ B @ C @ D @ E ) @ F @ C @ E @ G )
= ( c_Relation_Orel__comp @ A @ ( c_Relation_Orel__comp @ B @ F @ D @ E @ G ) @ C @ D @ G ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_O__assoc_0) ).
thf(787,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_Orel__comp @ ( c_Relation_Orel__comp @ A @ B @ C @ D @ E ) @ F @ C @ E @ G )
= ( c_Relation_Orel__comp @ A @ ( c_Relation_Orel__comp @ B @ F @ D @ E @ G ) @ C @ D @ G ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(1,negated_conjecture,
! [A: $i] : ( c_Relation_Otrans @ ( hAPP @ v_P @ A ) @ tc_Arrow__Order__Mirabelle_Oalt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(713,plain,
! [A: $i] : ( c_Relation_Otrans @ ( hAPP @ v_P @ A ) @ tc_Arrow__Order__Mirabelle_Oalt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(435,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_ATP__Linkup_Osko__Relation__XId__onE__1__1 @ A @ B @ C ) @ A @ C ) )
| ~ ( hBOOL @ ( c_in @ B @ ( c_Relation_OId__on @ A @ C ) @ ( tc_prod @ C @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Id__onE_0) ).
thf(1635,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_ATP__Linkup_Osko__Relation__XId__onE__1__1 @ A @ B @ C ) @ A @ C ) )
| ~ ( hBOOL @ ( c_in @ B @ ( c_Relation_OId__on @ A @ C ) @ ( tc_prod @ C @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(249,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ ( v_sko__Transitive__Closure__Xtrancl__Xcases__1 @ A @ B @ C ) @ B @ t_a @ t_a ) @ C @ ( tc_prod @ t_a @ t_a ) ) )
| ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ t_a @ t_a ) @ C @ ( tc_prod @ t_a @ t_a ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ t_a @ t_a ) @ ( c_Transitive__Closure_Otrancl @ C @ t_a ) @ ( tc_prod @ t_a @ t_a ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl_Ocases_1) ).
thf(1239,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ ( v_sko__Transitive__Closure__Xtrancl__Xcases__1 @ A @ B @ C ) @ B @ t_a @ t_a ) @ C @ ( tc_prod @ t_a @ t_a ) ) )
| ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ t_a @ t_a ) @ C @ ( tc_prod @ t_a @ t_a ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ t_a @ t_a ) @ ( c_Transitive__Closure_Otrancl @ C @ t_a ) @ ( tc_prod @ t_a @ t_a ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(295,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ D @ E @ ( tc_fun @ B @ tc_bool ) ) )
= ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( c_COMBB @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( tc_fun @ B @ tc_bool ) ) @ D @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) @ E ) @ E @ ( tc_fun @ B @ tc_bool ) ) )
| ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__extend__simps_I2_J_1) ).
thf(1332,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ D @ E @ ( tc_fun @ B @ tc_bool ) ) )
= ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( c_COMBB @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( tc_fun @ B @ tc_bool ) ) @ D @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) @ E ) @ E @ ( tc_fun @ B @ tc_bool ) ) )
| ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(182,axiom,
class_Lattices_Obounded__lattice @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Obounded__lattice) ).
thf(1092,plain,
class_Lattices_Obounded__lattice @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(48,axiom,
! [A: $i] : ( c_Relation_Osym @ ( c_Relation_OId @ A ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__Id_0) ).
thf(804,plain,
! [A: $i] : ( c_Relation_Osym @ ( c_Relation_OId @ A ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(117,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ A )
| ( ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ A ) @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ A ) @ D ) )
= ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ A ) @ C ) @ A ) @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__distrib1_0) ).
thf(947,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ A )
| ( ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ A ) @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ A ) @ D ) )
= ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ A ) @ C ) @ A ) @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(241,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( hAPP @ B @ C ) @ D ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ C @ A @ E @ D ) @ ( c_Product__Type_OSigma @ F @ B @ E @ D ) @ ( tc_prod @ E @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SigmaD2_0) ).
thf(1224,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( hAPP @ B @ C ) @ D ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ C @ A @ E @ D ) @ ( c_Product__Type_OSigma @ F @ B @ E @ D ) @ ( tc_prod @ E @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(306,axiom,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Ortrancl @ A @ B )
= ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ ( c_Relation_OId @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nitpick_Ortrancl__def_0) ).
thf(1356,plain,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Ortrancl @ A @ B )
= ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ ( c_Relation_OId @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(453,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_ATP__Linkup_Osko__Relation__XImageE__1__1 @ A @ B @ C @ D @ E ) @ A @ D ) )
| ~ ( hBOOL @ ( c_in @ B @ ( hAPP @ ( c_Relation_OImage @ C @ D @ E ) @ A ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ImageE_1) ).
thf(1675,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_ATP__Linkup_Osko__Relation__XImageE__1__1 @ A @ B @ C @ D @ E ) @ A @ D ) )
| ~ ( hBOOL @ ( c_in @ B @ ( hAPP @ ( c_Relation_OImage @ C @ D @ E ) @ A ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(677,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_Set_Oinsert @ C @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) ) @ D @ ( tc_fun @ B @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ C @ A @ B ) )
| ~ ( c_lessequals @ A @ ( hAPP @ ( c_Set_Oinsert @ C @ B ) @ D ) @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_0) ).
thf(2166,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_Set_Oinsert @ C @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) ) @ D @ ( tc_fun @ B @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ C @ A @ B ) )
| ~ ( c_lessequals @ A @ ( hAPP @ ( c_Set_Oinsert @ C @ B ) @ D ) @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[677]) ).
thf(181,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XImage__iff__1__1 @ A @ B @ C @ D @ E ) @ B @ D @ E ) @ C @ ( tc_prod @ D @ E ) ) )
| ~ ( hBOOL @ ( c_in @ B @ ( hAPP @ ( c_Relation_OImage @ C @ D @ E ) @ A ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__iff_1) ).
thf(1090,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XImage__iff__1__1 @ A @ B @ C @ D @ E ) @ B @ D @ E ) @ C @ ( tc_prod @ D @ E ) ) )
| ~ ( hBOOL @ ( c_in @ B @ ( hAPP @ ( c_Relation_OImage @ C @ D @ E ) @ A ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(227,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Relation_ODomain @ A @ B @ C ) @ ( c_Relation_ODomain @ D @ B @ C ) @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ ( tc_prod @ B @ C ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__mono_0) ).
thf(1194,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Relation_ODomain @ A @ B @ C ) @ ( c_Relation_ODomain @ D @ B @ C ) @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ ( tc_prod @ B @ C ) @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(639,axiom,
! [B: $i,A: $i] : ( c_lessequals @ ( c_Relation_OId__on @ A @ B ) @ ( c_Product__Type_OSigma @ A @ ( c_COMBK @ A @ ( tc_fun @ B @ tc_bool ) @ B ) @ B @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Id__on__subset__Times_0) ).
thf(2079,plain,
! [B: $i,A: $i] : ( c_lessequals @ ( c_Relation_OId__on @ A @ B ) @ ( c_Product__Type_OSigma @ A @ ( c_COMBK @ A @ ( tc_fun @ B @ tc_bool ) @ B ) @ B @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[639]) ).
thf(330,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_COMBK @ A @ B @ C ) @ D )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBK__def_0) ).
thf(1408,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_COMBK @ A @ B @ C ) @ D )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(700,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( c_Set_Oinsert @ A @ B ) @ C ) @ ( tc_fun @ B @ tc_bool ) ) @ D )
= ( hAPP @ ( c_Set_Oinsert @ A @ B ) @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ C @ ( tc_fun @ B @ tc_bool ) ) @ D ) ) )
| ( hBOOL @ ( c_in @ A @ D @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff__if_1) ).
thf(2214,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( c_Set_Oinsert @ A @ B ) @ C ) @ ( tc_fun @ B @ tc_bool ) ) @ D )
= ( hAPP @ ( c_Set_Oinsert @ A @ B ) @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ C @ ( tc_fun @ B @ tc_bool ) ) @ D ) ) )
| ( hBOOL @ ( c_in @ A @ D @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[700]) ).
thf(302,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E ) )
| ~ ( hBOOL @ ( c_in @ B @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_imageI_0) ).
thf(1349,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E ) )
| ~ ( hBOOL @ ( c_in @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(138,axiom,
! [B: $i,A: $i] :
( ( class_Orderings_Opreorder @ ( tc_fun @ A @ B ) )
| ~ ( class_Orderings_Opreorder @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Opreorder) ).
thf(996,plain,
! [B: $i,A: $i] :
( ( class_Orderings_Opreorder @ ( tc_fun @ A @ B ) )
| ~ ( class_Orderings_Opreorder @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(368,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A @ ( tc_fun @ B @ tc_bool ) ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__cancel_0) ).
thf(1492,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A @ ( tc_fun @ B @ tc_bool ) ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(206,axiom,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A ) @ ( c_Orderings_Obot__class_Obot @ A ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__bot__right_0) ).
thf(1144,plain,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A ) @ ( c_Orderings_Obot__class_Obot @ A ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(86,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
| ~ ( c_Wellfounded_Owf @ ( hAPP @ ( c_Set_Oinsert @ ( c_Pair @ B @ A @ C @ C ) @ ( tc_prod @ C @ C ) ) @ D ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__insert_1) ).
thf(880,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
| ~ ( c_Wellfounded_Owf @ ( hAPP @ ( c_Set_Oinsert @ ( c_Pair @ B @ A @ C @ C ) @ ( tc_prod @ C @ C ) ) @ D ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(29,axiom,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Otrancl @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ B )
= ( c_Transitive__Closure_Ortrancl @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__trancl__absorb_0) ).
thf(764,plain,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Otrancl @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ B )
= ( c_Transitive__Closure_Ortrancl @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(130,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ ( c_Product__Type_OSigma @ C @ ( c_COMBK @ C @ ( tc_fun @ B @ tc_bool ) @ B ) @ B @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) )
| ~ ( c_lessequals @ A @ ( c_Product__Type_OSigma @ C @ ( c_COMBK @ C @ ( tc_fun @ B @ tc_bool ) @ B ) @ B @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__subset__Sigma_0) ).
thf(979,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ ( c_Product__Type_OSigma @ C @ ( c_COMBK @ C @ ( tc_fun @ B @ tc_bool ) @ B ) @ B @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) )
| ~ ( c_lessequals @ A @ ( c_Product__Type_OSigma @ C @ ( c_COMBK @ C @ ( tc_fun @ B @ tc_bool ) @ B ) @ B @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(234,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( c_in @ A @ ( hAPP @ ( c_Set_Oinsert @ B @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singletonE_0) ).
thf(1209,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( c_in @ A @ ( hAPP @ ( c_Set_Oinsert @ B @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(658,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_ODomain @ A @ B @ B ) @ ( tc_fun @ B @ tc_bool ) ) @ ( c_Relation_ORange @ C @ B @ B ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
| ~ ( c_Wellfounded_Owf @ C @ B )
| ~ ( c_Wellfounded_Owf @ A @ B )
| ( c_Wellfounded_Owf @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__Un_0) ).
thf(2119,plain,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_ODomain @ A @ B @ B ) @ ( tc_fun @ B @ tc_bool ) ) @ ( c_Relation_ORange @ C @ B @ B ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
| ~ ( c_Wellfounded_Owf @ C @ B )
| ~ ( c_Wellfounded_Owf @ A @ B )
| ( c_Wellfounded_Owf @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[658]) ).
thf(671,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( tc_fun @ B @ tc_bool ) ) @ D )
= ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A @ ( tc_fun @ B @ tc_bool ) ) @ D ) @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ C @ ( tc_fun @ B @ tc_bool ) ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Diff_0) ).
thf(2151,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( tc_fun @ B @ tc_bool ) ) @ D )
= ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A @ ( tc_fun @ B @ tc_bool ) ) @ D ) @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ C @ ( tc_fun @ B @ tc_bool ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[671]) ).
thf(707,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Ototal__on @ A @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ B @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) ) @ ( c_Relation_OId @ C ) ) @ C )
| ~ ( c_Relation_Ototal__on @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_total__on__diff__Id_1) ).
thf(2229,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Ototal__on @ A @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ B @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) ) @ ( c_Relation_OId @ C ) ) @ C )
| ~ ( c_Relation_Ototal__on @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[707]) ).
thf(38,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( B = C )
| ~ ( c_lessequals @ C @ B @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__antisym_0) ).
thf(784,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)],[38]) ).
thf(194,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ A ) @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__ge2_0) ).
thf(1117,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ A ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(408,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ B @ A @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) )
| ~ ( c_Relation_Oantisym @ D @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__def_0) ).
thf(1574,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ B @ A @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) )
| ~ ( c_Relation_Oantisym @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(513,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ ( c_Relation_OId__on @ C @ B ) @ ( tc_prod @ B @ B ) ) )
| ~ ( hBOOL @ ( c_in @ A @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Id__on__eqI_0) ).
thf(1806,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ ( c_Relation_OId__on @ C @ B ) @ ( tc_prod @ B @ B ) ) )
| ~ ( hBOOL @ ( c_in @ A @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).
thf(162,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ ( tc_fun @ B @ tc_bool ) ) @ E ) @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_lessequals @ C @ E @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__mono_0) ).
thf(1048,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ ( tc_fun @ B @ tc_bool ) ) @ E ) @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_lessequals @ C @ E @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(14,axiom,
! [B: $i,A: $i] :
( ( c_Wellfounded_Oacyclic @ A @ B )
| ~ ( c_Wellfounded_Owf @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__acyclic_0) ).
thf(736,plain,
! [B: $i,A: $i] :
( ( c_Wellfounded_Oacyclic @ A @ B )
| ~ ( c_Wellfounded_Owf @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(78,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( hAPP @ ( c_Relation_OImage @ B @ C @ C ) @ ( hAPP @ ( c_Set_Oinsert @ A @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ) @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ D @ C ) )
| ~ ( c_Equiv__Relations_Oequiv @ D @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__class__self_0) ).
thf(863,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( hAPP @ ( c_Relation_OImage @ B @ C @ C ) @ ( hAPP @ ( c_Set_Oinsert @ A @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ) @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ D @ C ) )
| ~ ( c_Equiv__Relations_Oequiv @ D @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(633,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Wellfounded_Owf @ A @ B )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) )
| ~ ( c_Wellfounded_Owf @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__subset_0) ).
thf(2065,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Wellfounded_Owf @ A @ B )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) )
| ~ ( c_Wellfounded_Owf @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[633]) ).
thf(449,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Relation_OImage @ A @ B @ C ) @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ ( tc_fun @ B @ tc_bool ) ) @ E ) )
= ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ ( c_Relation_OImage @ A @ B @ C ) @ D ) @ ( tc_fun @ C @ tc_bool ) ) @ ( hAPP @ ( c_Relation_OImage @ A @ B @ C ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__Un_0) ).
thf(1667,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Relation_OImage @ A @ B @ C ) @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ ( tc_fun @ B @ tc_bool ) ) @ E ) )
= ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ ( c_Relation_OImage @ A @ B @ C ) @ D ) @ ( tc_fun @ C @ tc_bool ) ) @ ( hAPP @ ( c_Relation_OImage @ A @ B @ C ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).
thf(52,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ D @ C @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__trans_0) ).
thf(811,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ D @ C @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(359,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( c_in @ A @ B @ C ) )
| ( hBOOL @ ( c_in @ D @ ( hAPP @ E @ A ) @ F ) )
| ~ ( hBOOL @ ( c_in @ D @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ B @ E @ C @ ( tc_fun @ F @ tc_bool ) ) @ F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__E_0) ).
thf(1471,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( c_in @ A @ B @ C ) )
| ( hBOOL @ ( c_in @ D @ ( hAPP @ E @ A ) @ F ) )
| ~ ( hBOOL @ ( c_in @ D @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ B @ E @ C @ ( tc_fun @ F @ tc_bool ) ) @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(654,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Equiv__Relations_Ocongruent @ A @ ( hAPP @ B @ C ) @ D @ E )
| ~ ( hBOOL @ ( c_in @ C @ F @ G ) )
| ~ ( c_Equiv__Relations_Ocongruent2 @ H @ A @ B @ G @ D @ E )
| ~ ( c_Equiv__Relations_Oequiv @ F @ H @ G ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_congruent2__implies__congruent_0) ).
thf(2111,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Equiv__Relations_Ocongruent @ A @ ( hAPP @ B @ C ) @ D @ E )
| ~ ( hBOOL @ ( c_in @ C @ F @ G ) )
| ~ ( c_Equiv__Relations_Ocongruent2 @ H @ A @ B @ G @ D @ E )
| ~ ( c_Equiv__Relations_Oequiv @ F @ H @ G ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[654]) ).
thf(520,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ C @ D ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
| ( B = D )
| ( A = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mktop_3) ).
thf(1821,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ C @ D ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
| ( B = D )
| ( A = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).
thf(540,axiom,
! [B: $i,A: $i] :
~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ A @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ B @ A ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mktop_1) ).
thf(1862,plain,
! [B: $i,A: $i] :
~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ A @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ B @ A ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).
thf(71,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_ORange @ A @ B @ C )
= ( c_Relation_ODomain @ ( c_Relation_Oconverse @ A @ B @ C ) @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__def_0) ).
thf(848,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_ORange @ A @ B @ C )
= ( c_Relation_ODomain @ ( c_Relation_Oconverse @ A @ B @ C ) @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(528,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A ) @ C )
!= C )
| ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__sup_1) ).
thf(1838,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A ) @ C )
!= C )
| ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).
thf(101,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ E @ ( tc_prod @ C @ D ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ B @ A @ D @ C ) @ ( c_Relation_Oconverse @ E @ C @ D ) @ ( tc_prod @ D @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converseD_0) ).
thf(915,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ E @ ( tc_prod @ C @ D ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ B @ A @ D @ C ) @ ( c_Relation_Oconverse @ E @ C @ D ) @ ( tc_prod @ D @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(150,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ E @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ E @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__into__trancl2_0) ).
thf(1022,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ E @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ E @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(273,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ E @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ E @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) )
| ~ ( c_Relation_Otrans @ D @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__def_0) ).
thf(1293,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ E @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ E @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) )
| ~ ( c_Relation_Otrans @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(219,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( hAPP @ ( c_Set_Oinsert @ B @ C ) @ D ) @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) )
| ( hBOOL @ ( c_in @ B @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_2) ).
thf(1177,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( hAPP @ ( c_Set_Oinsert @ B @ C ) @ D ) @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) )
| ( hBOOL @ ( c_in @ B @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(615,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ C ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ C @ ( c_List_Osko__Recdef__Xtfl__wf__induct__1__1 @ A @ D @ E ) @ E @ E ) @ D @ ( tc_prod @ E @ E ) ) )
| ~ ( c_Wellfounded_Owf @ D @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tfl__wf__induct_0) ).
thf(2025,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ C ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ C @ ( c_List_Osko__Recdef__Xtfl__wf__induct__1__1 @ A @ D @ E ) @ E @ E ) @ D @ ( tc_prod @ E @ E ) ) )
| ~ ( c_Wellfounded_Owf @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[615]) ).
thf(177,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1 @ A @ B @ C ) @ ( c_Wellfounded_Oacc @ A @ C ) @ C ) )
| ( hBOOL @ ( c_in @ B @ ( c_Wellfounded_Oacc @ A @ C ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__acc__down_1) ).
thf(1080,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1 @ A @ B @ C ) @ ( c_Wellfounded_Oacc @ A @ C ) @ C ) )
| ( hBOOL @ ( c_in @ B @ ( c_Wellfounded_Oacc @ A @ C ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(399,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ A ) @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ A ) @ D ) )
= ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ A ) @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__left__commute_0) ).
thf(1556,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ A ) @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ A ) @ D ) )
= ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ A ) @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(354,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( c_Set_Oinsert @ A @ B ) @ C ) @ ( tc_fun @ B @ tc_bool ) ) @ D )
= ( hAPP @ ( c_HOL_Ominus__class_Ominus @ C @ ( tc_fun @ B @ tc_bool ) ) @ D ) )
| ~ ( hBOOL @ ( c_in @ A @ D @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff1_0) ).
thf(1460,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( c_Set_Oinsert @ A @ B ) @ C ) @ ( tc_fun @ B @ tc_bool ) ) @ D )
= ( hAPP @ ( c_HOL_Ominus__class_Ominus @ C @ ( tc_fun @ B @ tc_bool ) ) @ D ) )
| ~ ( hBOOL @ ( c_in @ A @ D @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(109,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ ( tc_fun @ B @ tc_bool ) ) @ C ) )
= ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( tc_fun @ B @ tc_bool ) ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Int2_0) ).
thf(932,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ ( tc_fun @ B @ tc_bool ) ) @ C ) )
= ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( tc_fun @ B @ tc_bool ) ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(168,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oimage @ A @ ( hAPP @ ( c_Set_Oinsert @ B @ C ) @ D ) @ C @ E )
= ( hAPP @ ( c_Set_Oinsert @ ( hAPP @ A @ B ) @ E ) @ ( c_Set_Oimage @ A @ D @ C @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__insert_0) ).
thf(1061,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oimage @ A @ ( hAPP @ ( c_Set_Oinsert @ B @ C ) @ D ) @ C @ E )
= ( hAPP @ ( c_Set_Oinsert @ ( hAPP @ A @ B ) @ E ) @ ( c_Set_Oimage @ A @ D @ C @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(132,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( hAPP @ ( c_Relation_OImage @ B @ C @ D ) @ E ) @ D ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ F @ A @ C @ D ) @ B @ ( tc_prod @ C @ D ) ) )
| ~ ( hBOOL @ ( c_in @ F @ E @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__iff_2) ).
thf(983,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( hAPP @ ( c_Relation_OImage @ B @ C @ D ) @ E ) @ D ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ F @ A @ C @ D ) @ B @ ( tc_prod @ C @ D ) ) )
| ~ ( hBOOL @ ( c_in @ F @ E @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(569,axiom,
! [B: $i,A: $i] :
( ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
| ~ ( c_lessequals @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__empty_0) ).
thf(1926,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)],[569]) ).
thf(31,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_Osym @ ( c_Relation_Oinv__image @ A @ B @ C @ D ) @ D )
| ~ ( c_Relation_Osym @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__inv__image_0) ).
thf(768,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_Osym @ ( c_Relation_Oinv__image @ A @ B @ C @ D ) @ D )
| ~ ( c_Relation_Osym @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(36,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_Osingle__valued @ ( c_Relation_Orel__comp @ A @ B @ C @ D @ E ) @ C @ E )
| ~ ( c_Relation_Osingle__valued @ B @ D @ E )
| ~ ( c_Relation_Osingle__valued @ A @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_single__valued__rel__comp_0) ).
thf(780,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_Osingle__valued @ ( c_Relation_Orel__comp @ A @ B @ C @ D @ E ) @ C @ E )
| ~ ( c_Relation_Osingle__valued @ B @ D @ E )
| ~ ( c_Relation_Osingle__valued @ A @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(666,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) )
| ~ ( c_lessequals @ A @ ( c_Transitive__Closure_Ortrancl @ C @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__subset__rtrancl_0) ).
thf(2139,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) )
| ~ ( c_lessequals @ A @ ( c_Transitive__Closure_Ortrancl @ C @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[666]) ).
thf(134,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) )
!= ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ B @ C @ D @ ( tc_fun @ A @ tc_bool ) ) )
| ( ( hAPP @ C @ E )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( hBOOL @ ( c_in @ E @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INTER__UNIV__conv_I1_J_0) ).
thf(986,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) )
!= ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ B @ C @ D @ ( tc_fun @ A @ tc_bool ) ) )
| ( ( hAPP @ C @ E )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) )
| ~ ( hBOOL @ ( c_in @ E @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(192,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ E @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ E @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) )
| ~ ( c_Relation_Otrans @ D @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_transD_0) ).
thf(1113,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ E @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ E @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) )
| ~ ( c_Relation_Otrans @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(362,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Set_Oimage @ A @ B @ C @ D ) @ ( c_Set_Oimage @ A @ E @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ B @ E @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__mono_0) ).
thf(1477,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)],[362]) ).
thf(370,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ C @ D ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
| ( A = D )
| ( B = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mkbot_3) ).
thf(1496,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ C @ D ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
| ( A = D )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(591,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XRange__iff__1__1 @ A @ B @ C @ D ) @ A @ D @ C ) @ B @ ( tc_prod @ D @ C ) ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_Relation_ORange @ B @ D @ C ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__iff_0) ).
thf(1973,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XRange__iff__1__1 @ A @ B @ C @ D ) @ A @ D @ C ) @ B @ ( tc_prod @ D @ C ) ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_Relation_ORange @ B @ D @ C ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).
thf(635,axiom,
! [B: $i,A: $i] : ( c_lessequals @ A @ A @ ( tc_fun @ B @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__refl_0) ).
thf(2069,plain,
! [B: $i,A: $i] : ( c_lessequals @ A @ A @ ( tc_fun @ B @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[635]) ).
thf(402,axiom,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Otop__class_Otop @ A ) @ A ) @ B )
= ( c_Orderings_Otop__class_Otop @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__top__left_0) ).
thf(1562,plain,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Otop__class_Otop @ A ) @ A ) @ B )
= ( c_Orderings_Otop__class_Otop @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(529,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ A ) @ C ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__le1_0) ).
thf(1841,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ A ) @ C ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).
thf(324,axiom,
! [B: $i,A: $i] :
( ( c_Relation_Oantisym @ A @ B )
| ~ ( c_Relation_Oantisym @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ ( c_Relation_OId @ B ) ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__reflcl_0) ).
thf(1396,plain,
! [B: $i,A: $i] :
( ( c_Relation_Oantisym @ A @ B )
| ~ ( c_Relation_Oantisym @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ ( c_Relation_OId @ B ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(627,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ ( hAPP @ ( c_Set_Oinsert @ A @ B ) @ C ) @ D @ B @ ( tc_fun @ E @ tc_bool ) )
= ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( hAPP @ D @ A ) @ ( tc_fun @ E @ tc_bool ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ D @ B @ ( tc_fun @ E @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__insert_0) ).
thf(2051,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ ( hAPP @ ( c_Set_Oinsert @ A @ B ) @ C ) @ D @ B @ ( tc_fun @ E @ tc_bool ) )
= ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( hAPP @ D @ A ) @ ( tc_fun @ E @ tc_bool ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ D @ B @ ( tc_fun @ E @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[627]) ).
thf(160,axiom,
! [B: $i,A: $i] :
( ( c_Wellfounded_Owf @ A @ B )
| ~ ( hBOOL @ ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1 @ A @ B ) @ ( c_Wellfounded_Oacc @ A @ B ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__wfI_0) ).
thf(1044,plain,
! [B: $i,A: $i] :
( ( c_Wellfounded_Owf @ A @ B )
| ~ ( hBOOL @ ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1 @ A @ B ) @ ( c_Wellfounded_Oacc @ A @ B ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(252,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ A ) @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ A ) @ C ) )
= ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I4_J_0) ).
thf(1245,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ A ) @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ A ) @ C ) )
= ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(171,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( hAPP @ ( c_HOL_Ominus__class_Ominus @ B @ A ) @ B )
!= ( hAPP @ ( c_HOL_Ominus__class_Ominus @ C @ A ) @ D ) )
| ( C = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__eqI_0) ).
thf(1066,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Oab__group__add @ A )
| ( ( hAPP @ ( c_HOL_Ominus__class_Ominus @ B @ A ) @ B )
!= ( hAPP @ ( c_HOL_Ominus__class_Ominus @ C @ A ) @ D ) )
| ( C = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(80,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( tc_fun @ B @ tc_bool ) ) @ C )
= ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Diff__cancel2_0) ).
thf(868,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( tc_fun @ B @ tc_bool ) ) @ C )
= ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(499,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Ototal__on @ A @ B @ C )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__Xtotal__on__def__1__2 @ A @ B @ C ) @ ( c_ATP__Linkup_Osko__Relation__Xtotal__on__def__1__1 @ A @ B @ C ) @ C @ C ) @ B @ ( tc_prod @ C @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_total__on__def_5) ).
thf(1775,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Ototal__on @ A @ B @ C )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__Xtotal__on__def__1__2 @ A @ B @ C ) @ ( c_ATP__Linkup_Osko__Relation__Xtotal__on__def__1__1 @ A @ B @ C ) @ C @ C ) @ B @ ( tc_prod @ C @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).
thf(140,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( C = B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C @ D ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_0) ).
thf(1000,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( C = B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C @ D ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(476,axiom,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Orderings_Otop__class_Otop @ A ) @ A ) @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__top__left_0) ).
thf(1726,plain,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Orderings_Otop__class_Otop @ A ) @ A ) @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).
thf(310,axiom,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ A @ ( hAPP @ ( c_Set_Oinsert @ A @ B ) @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertCI_1) ).
thf(1364,plain,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( c_in @ A @ ( hAPP @ ( c_Set_Oinsert @ A @ B ) @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(255,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ A @ D @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__rev__mp_0) ).
thf(1250,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ A @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(461,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__2 @ A @ B ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bex__UNIV_1) ).
thf(1694,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_ATP__Linkup_Osko__Set__Xbex__UNIV__1__2 @ A @ B ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(104,axiom,
! [B: $i,A: $i] :
( ( c_Relation_ODomain @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ B @ B )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__rtrancl_0) ).
thf(922,plain,
! [B: $i,A: $i] :
( ( c_Relation_ODomain @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ B @ B )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(332,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ A ) @ C ) @ D @ A )
| ~ ( c_lessequals @ C @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infI2_0) ).
thf(1413,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ A ) @ C ) @ D @ A )
| ~ ( c_lessequals @ C @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(156,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Relation_ORange @ B @ C @ D ) @ D ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ E @ A @ C @ D ) @ B @ ( tc_prod @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__iff_1) ).
thf(1034,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Relation_ORange @ B @ C @ D ) @ D ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ E @ A @ C @ D ) @ B @ ( tc_prod @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(412,axiom,
! [B: $i,A: $i] : ( c_Relation_Otrans @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__trancl_0) ).
thf(1583,plain,
! [B: $i,A: $i] : ( c_Relation_Otrans @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(279,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ ( tc_fun @ C @ tc_bool ) ) @ A ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__subset__iff_1) ).
thf(1304,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ ( tc_fun @ C @ tc_bool ) ) @ A ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(652,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__trans_0) ).
thf(2107,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)],[652]) ).
thf(231,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ A @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1 @ A @ B @ C @ D ) @ D @ D ) @ ( c_Transitive__Closure_Otrancl @ C @ D ) @ ( tc_prod @ D @ D ) ) )
| ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ D @ D ) @ C @ ( tc_prod @ D @ D ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ D @ D ) @ ( c_Transitive__Closure_Otrancl @ C @ D ) @ ( tc_prod @ D @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tranclE_0) ).
thf(1203,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ A @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclE__1__1 @ A @ B @ C @ D ) @ D @ D ) @ ( c_Transitive__Closure_Otrancl @ C @ D ) @ ( tc_prod @ D @ D ) ) )
| ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ D @ D ) @ C @ ( tc_prod @ D @ D ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ D @ D ) @ ( c_Transitive__Closure_Otrancl @ C @ D ) @ ( tc_prod @ D @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(115,axiom,
! [B: $i,A: $i] :
( ( c_Relation_Oirrefl @ A @ B )
| ( hBOOL @ ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1 @ A @ B ) @ ( c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1 @ A @ B ) @ B @ B ) @ A @ ( tc_prod @ B @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_irrefl__def_1) ).
thf(944,plain,
! [B: $i,A: $i] :
( ( c_Relation_Oirrefl @ A @ B )
| ( hBOOL @ ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1 @ A @ B ) @ ( c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1 @ A @ B ) @ B @ B ) @ A @ ( tc_prod @ B @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(357,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ A ) @ C ) @ D @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infI1_0) ).
thf(1467,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ A ) @ C ) @ D @ A )
| ~ ( c_lessequals @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(43,axiom,
! [B: $i,A: $i] :
( ( c_Relation_Oconverse @ ( c_Relation_OId__on @ A @ B ) @ B @ B )
= ( c_Relation_OId__on @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__Id__on_0) ).
thf(795,plain,
! [B: $i,A: $i] :
( ( c_Relation_Oconverse @ ( c_Relation_OId__on @ A @ B ) @ B @ B )
= ( c_Relation_OId__on @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(560,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ( A = D )
| ~ ( hBOOL @ ( c_in @ A @ ( hAPP @ ( c_Set_Oinsert @ D @ C ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertE_0) ).
thf(1905,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ( A = D )
| ~ ( hBOOL @ ( c_in @ A @ ( hAPP @ ( c_Set_Oinsert @ D @ C ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).
thf(457,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Relation_OImage @ A @ B @ B ) @ ( hAPP @ ( c_Set_Oinsert @ C @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) )
!= ( hAPP @ ( c_Relation_OImage @ A @ B @ B ) @ ( hAPP @ ( c_Set_Oinsert @ D @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) ) )
| ( hBOOL @ ( c_in @ ( c_Pair @ C @ D @ B @ B ) @ A @ ( tc_prod @ B @ B ) ) )
| ~ ( hBOOL @ ( c_in @ D @ E @ B ) )
| ~ ( c_Equiv__Relations_Oequiv @ E @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__equiv__class_0) ).
thf(1684,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Relation_OImage @ A @ B @ B ) @ ( hAPP @ ( c_Set_Oinsert @ C @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) )
!= ( hAPP @ ( c_Relation_OImage @ A @ B @ B ) @ ( hAPP @ ( c_Set_Oinsert @ D @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) ) )
| ( hBOOL @ ( c_in @ ( c_Pair @ C @ D @ B @ B ) @ A @ ( tc_prod @ B @ B ) ) )
| ~ ( hBOOL @ ( c_in @ D @ E @ B ) )
| ~ ( c_Equiv__Relations_Oequiv @ E @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(375,axiom,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ A @ ( tc_fun @ B @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__lower1_0) ).
thf(1509,plain,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ A @ ( tc_fun @ B @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(598,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ D @ C @ C ) @ E @ ( tc_prod @ C @ C ) ) )
| ~ ( c_Relation_Orefl__on @ B @ E @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__onD1_0) ).
thf(1990,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ D @ C @ C ) @ E @ ( tc_prod @ C @ C ) ) )
| ~ ( c_Relation_Orefl__on @ B @ E @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[598]) ).
thf(298,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A ) @ C )
!= ( c_Orderings_Obot__class_Obot @ A ) )
| ( C
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__eq__bot__eq2_0) ).
thf(1340,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A ) @ C )
!= ( c_Orderings_Obot__class_Obot @ A ) )
| ( C
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(148,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ B @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ A ) @ D ) @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__greatest_0) ).
thf(1018,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ B @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ A ) @ D ) @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(584,axiom,
! [B: $i,A: $i] :
( ( c_Nitpick_Orefl_H @ A @ B )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ ( c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1 @ A @ B ) @ ( c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1 @ A @ B ) @ B @ B ) @ A @ ( tc_prod @ B @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nitpick_Orefl_H__def_1) ).
thf(1958,plain,
! [B: $i,A: $i] :
( ( c_Nitpick_Orefl_H @ A @ B )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ ( c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1 @ A @ B ) @ ( c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1 @ A @ B ) @ B @ B ) @ A @ ( tc_prod @ B @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).
thf(23,axiom,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Ortrancl @ ( c_Relation_Oconverse @ A @ B @ B ) @ B )
= ( c_Relation_Oconverse @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ B @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__converse_0) ).
thf(754,plain,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Ortrancl @ ( c_Relation_Oconverse @ A @ B @ B ) @ B )
= ( c_Relation_Oconverse @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ B @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(65,axiom,
! [A: $i] : ( c_Relation_Osingle__valued @ ( c_Relation_OId @ A ) @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_single__valued__Id_0) ).
thf(836,plain,
! [A: $i] : ( c_Relation_Osingle__valued @ ( c_Relation_OId @ A ) @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(447,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( hAPP @ A @ B ) @ C @ D ) )
| ~ ( hBOOL @ ( c_in @ B @ E @ F ) )
| ~ ( c_lessequals @ ( c_Set_Oimage @ A @ E @ F @ D ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__subset__iff_0) ).
thf(1662,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( hAPP @ A @ B ) @ C @ D ) )
| ~ ( hBOOL @ ( c_in @ B @ E @ F ) )
| ~ ( c_lessequals @ ( c_Set_Oimage @ A @ E @ F @ D ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(647,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/sandbox/benchmark/theBenchmark.p',cls_range__composition_0) ).
thf(2096,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)],[647]) ).
thf(125,axiom,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ C @ ( tc_fun @ B @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__lower2_0) ).
thf(968,plain,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ C @ ( tc_fun @ B @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(221,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Set_Oinsert @ A @ B ) @ ( hAPP @ ( c_Set_Oinsert @ C @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) )
!= ( hAPP @ ( c_Set_Oinsert @ D @ B ) @ ( hAPP @ ( c_Set_Oinsert @ E @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) ) )
| ( C = D )
| ( A = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_1) ).
thf(1181,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Set_Oinsert @ A @ B ) @ ( hAPP @ ( c_Set_Oinsert @ C @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) )
!= ( hAPP @ ( c_Set_Oinsert @ D @ B ) @ ( hAPP @ ( c_Set_Oinsert @ E @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) ) )
| ( C = D )
| ( A = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(74,axiom,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Otrancl @ A @ B )
= ( c_Relation_Orel__comp @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ A @ B @ B @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__unfold__right_0) ).
thf(855,plain,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Otrancl @ A @ B )
= ( c_Relation_Orel__comp @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ A @ B @ B @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(82,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( hAPP @ B @ E ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ E @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__lower_0) ).
thf(872,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( hAPP @ B @ E ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ E @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(127,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ D @ C ) )
| ( ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ ( tc_fun @ C @ tc_bool ) ) @ B )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_disjoint__iff__not__equal_0) ).
thf(971,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ D @ C ) )
| ( ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ ( tc_fun @ C @ tc_bool ) ) @ B )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(256,axiom,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Ortrancl @ A @ B )
= ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_OId @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ ( c_Relation_Orel__comp @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ A @ B @ B @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__unfold_0) ).
thf(1252,plain,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Ortrancl @ A @ B )
= ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_OId @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ ( c_Relation_Orel__comp @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ A @ B @ B @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(682,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__subset__iff_2) ).
thf(2175,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[682]) ).
thf(501,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ ( tc_fun @ B @ tc_bool ) ) @ D ) )
= ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( tc_fun @ B @ tc_bool ) ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Un__distrib_0) ).
thf(1780,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ ( tc_fun @ B @ tc_bool ) ) @ D ) )
= ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( tc_fun @ B @ tc_bool ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).
thf(186,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ B @ ( c_COMBK @ C @ A @ D ) @ D @ A )
= C )
| ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INF__const_0) ).
thf(1098,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ B @ ( c_COMBK @ C @ A @ D ) @ D @ A )
= C )
| ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(137,axiom,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A ) @ ( c_Orderings_Otop__class_Otop @ A ) )
= ( c_Orderings_Otop__class_Otop @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__top__right_0) ).
thf(993,plain,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A ) @ ( c_Orderings_Otop__class_Otop @ A ) )
= ( c_Orderings_Otop__class_Otop @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(394,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Order__Relation_Ostrict__linear__order__on @ A @ B @ C )
| ~ ( c_Relation_Ototal__on @ A @ B @ C )
| ~ ( c_Relation_Oirrefl @ B @ C )
| ~ ( c_Relation_Otrans @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_strict__linear__order__on__def_3) ).
thf(1547,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Order__Relation_Ostrict__linear__order__on @ A @ B @ C )
| ~ ( c_Relation_Ototal__on @ A @ B @ C )
| ~ ( c_Relation_Oirrefl @ B @ C )
| ~ ( c_Relation_Otrans @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(485,axiom,
class_Orderings_Otop @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Otop) ).
thf(1748,plain,
class_Orderings_Otop @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).
thf(5,negated_conjecture,
~ ( hBOOL @ ( c_in @ ( c_Pair @ v_a @ v_b @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_P @ v_i ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_4) ).
thf(712,plain,
~ ( hBOOL @ ( c_in @ ( c_Pair @ v_a @ v_b @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( hAPP @ v_P @ v_i ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(141,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( tc_fun @ B @ tc_bool ) ) @ D )
= ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ ( tc_fun @ B @ tc_bool ) ) @ D ) ) )
| ~ ( c_lessequals @ D @ A @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__assoc__eq_1) ).
thf(1003,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( tc_fun @ B @ tc_bool ) ) @ D )
= ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ ( tc_fun @ B @ tc_bool ) ) @ D ) ) )
| ~ ( c_lessequals @ D @ A @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(425,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
= ( c_Set_Oimage @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__is__image_1) ).
thf(1611,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)],[425]) ).
thf(210,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ C @ ( tc_fun @ B @ tc_bool ) ) @ A ) )
= ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Diff__cancel_0) ).
thf(1156,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ C @ ( tc_fun @ B @ tc_bool ) ) @ A ) )
= ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(631,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ A ) @ C ) @ A ) @ D )
= ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ A ) @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__assoc_0) ).
thf(2060,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ A ) @ C ) @ A ) @ D )
= ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ A ) @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[631]) ).
thf(326,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ ( tc_fun @ C @ tc_bool ) ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntE_1) ).
thf(1400,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ ( tc_fun @ C @ tc_bool ) ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(690,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_ATP__Linkup_Osko__Relation__XImage__iff__1__1 @ A @ B @ C @ D @ E ) @ A @ D ) )
| ~ ( hBOOL @ ( c_in @ B @ ( hAPP @ ( c_Relation_OImage @ C @ D @ E ) @ A ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__iff_0) ).
thf(2192,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_ATP__Linkup_Osko__Relation__XImage__iff__1__1 @ A @ B @ C @ D @ E ) @ A @ D ) )
| ~ ( hBOOL @ ( c_in @ B @ ( hAPP @ ( c_Relation_OImage @ C @ D @ E ) @ A ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[690]) ).
thf(89,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Wellfounded_Oacyclic @ ( hAPP @ ( c_Set_Oinsert @ ( c_Pair @ A @ B @ C @ C ) @ ( tc_prod @ C @ C ) ) @ D ) @ C )
| ( hBOOL @ ( c_in @ ( c_Pair @ B @ A @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
| ~ ( c_Wellfounded_Oacyclic @ D @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acyclic__insert_2) ).
thf(887,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Wellfounded_Oacyclic @ ( hAPP @ ( c_Set_Oinsert @ ( c_Pair @ A @ B @ C @ C ) @ ( tc_prod @ C @ C ) ) @ D ) @ C )
| ( hBOOL @ ( c_in @ ( c_Pair @ B @ A @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
| ~ ( c_Wellfounded_Oacyclic @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(404,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_Osingle__valued @ A @ B @ C )
| ~ ( c_Relation_Osingle__valued @ D @ B @ C )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ ( tc_prod @ B @ C ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_single__valued__subset_0) ).
thf(1566,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_Osingle__valued @ A @ B @ C )
| ~ ( c_Relation_Osingle__valued @ D @ B @ C )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ ( tc_prod @ B @ C ) @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(668,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ B @ tc_bool ) ) @ C )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
| ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty_1) ).
thf(2143,plain,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ B @ tc_bool ) ) @ C )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
| ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[668]) ).
thf(244,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ A )
| ( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A ) @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ A ) @ D ) )
= ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A ) @ C ) @ A ) @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__inf__distrib1_0) ).
thf(1230,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ A )
| ( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A ) @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ A ) @ D ) )
= ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A ) @ C ) @ A ) @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(365,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
| ~ ( c_Wellfounded_Oacyclic @ ( hAPP @ ( c_Set_Oinsert @ ( c_Pair @ B @ A @ C @ C ) @ ( tc_prod @ C @ C ) ) @ D ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acyclic__insert_1) ).
thf(1484,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
| ~ ( c_Wellfounded_Oacyclic @ ( hAPP @ ( c_Set_Oinsert @ ( c_Pair @ B @ A @ C @ C ) @ ( tc_prod @ C @ C ) ) @ D ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(675,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A ) @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ A ) @ D ) )
= ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ A ) @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__left__commute_0) ).
thf(2160,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A ) @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ A ) @ D ) )
= ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ A ) @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[675]) ).
thf(645,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ A @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1 @ B @ A @ C @ D ) @ D @ D ) @ B @ ( tc_prod @ D @ D ) ) )
| ( hBOOL @ ( c_in @ ( c_Pair @ A @ C @ D @ D ) @ B @ ( tc_prod @ D @ D ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ C @ D @ D ) @ ( c_Transitive__Closure_Otrancl @ B @ D ) @ ( tc_prod @ D @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__tranclE_0) ).
thf(2092,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ A @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1 @ B @ A @ C @ D ) @ D @ D ) @ B @ ( tc_prod @ D @ D ) ) )
| ( hBOOL @ ( c_in @ ( c_Pair @ A @ C @ D @ D ) @ B @ ( tc_prod @ D @ D ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ C @ D @ D ) @ ( c_Transitive__Closure_Otrancl @ B @ D ) @ ( tc_prod @ D @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[645]) ).
thf(341,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ ( c_Relation_OId @ B ) )
= ( c_Transitive__Closure_Ortrancl @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_reflcl__trancl_0) ).
thf(1432,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ ( c_Relation_OId @ B ) )
= ( c_Transitive__Closure_Ortrancl @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(41,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/sandbox/benchmark/theBenchmark.p',cls_image__image_0) ).
thf(791,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)],[41]) ).
thf(158,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( tc_fun @ t_a @ A ) ) @ C ) @ v_x )
= ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ B @ v_x ) @ A ) @ ( hAPP @ C @ v_x ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__fun__eq_0) ).
thf(1038,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( tc_fun @ t_a @ A ) ) @ C ) @ v_x )
= ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ B @ v_x ) @ A ) @ ( hAPP @ C @ v_x ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(7,negated_conjecture,
! [A: $i] :
( ( c_Relation_Oirrefl @ ( v_F @ A ) @ tc_Arrow__Order__Mirabelle_Oalt )
| ~ ( c_Relation_Ototal__on @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ tc_bool ) ) @ ( hAPP @ A @ ( hAPP @ v_x @ A ) ) @ tc_Arrow__Order__Mirabelle_Oalt )
| ~ ( c_Relation_Oirrefl @ ( hAPP @ A @ ( hAPP @ v_x @ A ) ) @ tc_Arrow__Order__Mirabelle_Oalt )
| ~ ( c_Relation_Otrans @ ( hAPP @ A @ ( hAPP @ v_x @ A ) ) @ tc_Arrow__Order__Mirabelle_Oalt ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_6) ).
thf(717,plain,
! [A: $i] :
( ( c_Relation_Oirrefl @ ( v_F @ A ) @ tc_Arrow__Order__Mirabelle_Oalt )
| ~ ( c_Relation_Ototal__on @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oalt @ tc_bool ) ) @ ( hAPP @ A @ ( hAPP @ v_x @ A ) ) @ tc_Arrow__Order__Mirabelle_Oalt )
| ~ ( c_Relation_Oirrefl @ ( hAPP @ A @ ( hAPP @ v_x @ A ) ) @ tc_Arrow__Order__Mirabelle_Oalt )
| ~ ( c_Relation_Otrans @ ( hAPP @ A @ ( hAPP @ v_x @ A ) ) @ tc_Arrow__Order__Mirabelle_Oalt ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(260,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnCI_1) ).
thf(1262,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(702,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Ototal__on @ A @ B @ C )
| ( hBOOL @ ( c_in @ ( c_ATP__Linkup_Osko__Relation__Xtotal__on__def__1__1 @ A @ B @ C ) @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_total__on__def_1) ).
thf(2219,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Ototal__on @ A @ B @ C )
| ( hBOOL @ ( c_in @ ( c_ATP__Linkup_Osko__Relation__Xtotal__on__def__1__1 @ A @ B @ C ) @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[702]) ).
thf(558,axiom,
! [B: $i,A: $i] : ( c_Relation_Osym @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ ( c_Relation_Oconverse @ A @ B @ B ) ) @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__Un__converse_0) ).
thf(1901,plain,
! [B: $i,A: $i] : ( c_Relation_Osym @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ ( c_Relation_Oconverse @ A @ B @ B ) ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).
thf(455,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ C @ B @ D @ E ) @ F @ ( tc_prod @ D @ E ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ C @ A @ D @ E ) @ F @ ( tc_prod @ D @ E ) ) )
| ~ ( c_Relation_Osingle__valued @ F @ D @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_single__valuedD_0) ).
thf(1679,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ C @ B @ D @ E ) @ F @ ( tc_prod @ D @ E ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ C @ A @ D @ E ) @ F @ ( tc_prod @ D @ E ) ) )
| ~ ( c_Relation_Osingle__valued @ F @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(410,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
!= ( hAPP @ ( c_Set_Oinsert @ B @ A ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__not__insert_0) ).
thf(1579,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) )
!= ( hAPP @ ( c_Set_Oinsert @ B @ A ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(469,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ A ) @ C ) @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__le2_0) ).
thf(1711,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ A ) @ C ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).
thf(371,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( c_Complete__Lattice_OSup__class_OSup @ ( hAPP @ ( c_Set_Oinsert @ B @ A ) @ ( hAPP @ ( c_Set_Oinsert @ C @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ) @ A )
= ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sup__binary_0) ).
thf(1499,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( c_Complete__Lattice_OSup__class_OSup @ ( hAPP @ ( c_Set_Oinsert @ B @ A ) @ ( hAPP @ ( c_Set_Oinsert @ C @ A ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ) ) @ A )
= ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(597,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( c_ATP__Linkup_Osko__Complete__Lattice__XINTER__UNIV__conv__2__1 @ B @ A @ C @ D ) )
!= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_bool ) ) )
| ( ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ B @ A @ C @ ( tc_fun @ D @ tc_bool ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INTER__UNIV__conv_I2_J_2) ).
thf(1987,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( c_ATP__Linkup_Osko__Complete__Lattice__XINTER__UNIV__conv__2__1 @ B @ A @ C @ D ) )
!= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_bool ) ) )
| ( ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ B @ A @ C @ ( tc_fun @ D @ tc_bool ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[597]) ).
thf(705,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( hAPP @ ( c_Relation_OImage @ B @ C @ D ) @ ( hAPP @ ( c_Set_Oinsert @ E @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ) @ D ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ E @ A @ C @ D ) @ B @ ( tc_prod @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__singleton__iff_1) ).
thf(2224,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( hAPP @ ( c_Relation_OImage @ B @ C @ D ) @ ( hAPP @ ( c_Set_Oinsert @ E @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ) @ D ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ E @ A @ C @ D ) @ B @ ( tc_prod @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[705]) ).
thf(516,axiom,
! [B: $i,A: $i] :
( ( class_Complete__Lattice_Ocomplete__lattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Complete__Lattice_Ocomplete__lattice @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Complete__Lattice_Ocomplete__lattice) ).
thf(1813,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)],[516]) ).
thf(277,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ D @ C ) )
| ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subsetD_0) ).
thf(1300,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ D @ C ) )
| ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(436,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( c_Complete__Lattice_OSup__class_OSup @ ( hAPP @ ( c_Set_Oinsert @ B @ A ) @ C ) @ A )
= ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A ) @ ( c_Complete__Lattice_OSup__class_OSup @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sup__insert_0) ).
thf(1637,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( ( c_Complete__Lattice_OSup__class_OSup @ ( hAPP @ ( c_Set_Oinsert @ B @ A ) @ C ) @ A )
= ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A ) @ ( c_Complete__Lattice_OSup__class_OSup @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(224,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( hAPP @ ( c_Set_Oinsert @ B @ C ) @ D ) @ ( tc_fun @ C @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ B @ A @ C ) )
| ~ ( c_lessequals @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( hAPP @ ( c_Set_Oinsert @ B @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ) @ D @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_3) ).
thf(1188,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( hAPP @ ( c_Set_Oinsert @ B @ C ) @ D ) @ ( tc_fun @ C @ tc_bool ) )
| ~ ( hBOOL @ ( c_in @ B @ A @ C ) )
| ~ ( c_lessequals @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( hAPP @ ( c_Set_Oinsert @ B @ C ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) ) ) @ D @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(223,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__empty__right_0) ).
thf(1186,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(67,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Orefl__on @ A @ B @ C )
| ~ ( c_Relation_Orefl__on @ A @ ( c_Relation_Oconverse @ B @ C @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__converse_0) ).
thf(840,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Orefl__on @ A @ B @ C )
| ~ ( c_Relation_Orefl__on @ A @ ( c_Relation_Oconverse @ B @ C @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(504,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ D @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntI_0) ).
thf(1785,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ D @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).
thf(286,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Set_Oinsert @ A @ B ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ D @ E @ ( tc_fun @ B @ tc_bool ) ) )
= ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( c_COMBB @ ( c_Set_Oinsert @ A @ B ) @ D @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) @ E ) @ E @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__extend__simps_I5_J_0) ).
thf(1317,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Set_Oinsert @ A @ B ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ D @ E @ ( tc_fun @ B @ tc_bool ) ) )
= ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( c_COMBB @ ( c_Set_Oinsert @ A @ B ) @ D @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) @ E ) @ E @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(524,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__subset__iff_0) ).
thf(1830,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).
thf(179,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ B @ C @ ( tc_fun @ D @ tc_bool ) )
!= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_bool ) ) )
| ( ( hAPP @ B @ E )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_bool ) ) )
| ~ ( hBOOL @ ( c_in @ E @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INTER__UNIV__conv_I2_J_0) ).
thf(1085,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ B @ C @ ( tc_fun @ D @ tc_bool ) )
!= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_bool ) ) )
| ( ( hAPP @ B @ E )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_bool ) ) )
| ~ ( hBOOL @ ( c_in @ E @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(445,axiom,
! [B: $i,A: $i] : ( hBOOL @ ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ ( c_Relation_OId @ B ) @ ( tc_prod @ B @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pair__in__Id__conv_1) ).
thf(1658,plain,
! [B: $i,A: $i] : ( hBOOL @ ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ ( c_Relation_OId @ B ) @ ( tc_prod @ B @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(270,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) )
= ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__left__absorb_0) ).
thf(1285,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) )
= ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(481,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_Orefl__on @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ E ) @ B )
| ~ ( c_Relation_Orefl__on @ C @ E @ B )
| ~ ( c_Relation_Orefl__on @ A @ D @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__Un_0) ).
thf(1738,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_Orefl__on @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ E ) @ B )
| ~ ( c_Relation_Orefl__on @ C @ E @ B )
| ~ ( c_Relation_Orefl__on @ A @ D @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).
thf(573,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ C @ ( tc_prod @ B @ B ) ) )
| ~ ( c_Wellfounded_Owf @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__irrefl_0) ).
thf(1934,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ C @ ( tc_prod @ B @ B ) ) )
| ~ ( c_Wellfounded_Owf @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).
thf(18,axiom,
! [B: $i,A: $i] :
( ( c_Wellfounded_Oacyclic @ ( c_Relation_Oconverse @ A @ B @ B ) @ B )
| ~ ( c_Wellfounded_Oacyclic @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acyclic__converse_1) ).
thf(744,plain,
! [B: $i,A: $i] :
( ( c_Wellfounded_Oacyclic @ ( c_Relation_Oconverse @ A @ B @ B ) @ B )
| ~ ( c_Wellfounded_Oacyclic @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(496,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ A ) @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ A ) @ C ) )
= ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__left__idem_0) ).
thf(1766,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ A ) @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ A ) @ C ) )
= ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).
thf(655,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Relation_Orel__comp @ ( c_Relation_Oconverse @ A @ B @ B ) @ A @ B @ B @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) )
| ~ ( c_Relation_Orefl__on @ C @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__comp__subset_0) ).
thf(2113,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Relation_Orel__comp @ ( c_Relation_Oconverse @ A @ B @ B ) @ A @ B @ B @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) )
| ~ ( c_Relation_Orefl__on @ C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[655]) ).
thf(511,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Ototal__on @ A @ B @ C )
| ~ ( c_Relation_Ototal__on @ A @ ( c_Relation_Oconverse @ B @ C @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_total__on__converse_0) ).
thf(1802,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Ototal__on @ A @ B @ C )
| ~ ( c_Relation_Ototal__on @ A @ ( c_Relation_Oconverse @ B @ C @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).
thf(465,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( tc_fun @ B @ tc_bool ) ) @ C )
= ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__idemp_0) ).
thf(1702,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( tc_fun @ B @ tc_bool ) ) @ C )
= ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(239,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( c_lessequals @ B @ ( c_Complete__Lattice_OSup__class_OSup @ C @ A ) @ A )
| ~ ( hBOOL @ ( c_in @ B @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sup__upper_0) ).
thf(1221,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Complete__Lattice_Ocomplete__lattice @ A )
| ( c_lessequals @ B @ ( c_Complete__Lattice_OSup__class_OSup @ C @ A ) @ A )
| ~ ( hBOOL @ ( c_in @ B @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(164,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ A @ ( c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1 @ A @ B @ C @ D @ E @ F @ G ) @ E @ G ) @ C @ ( tc_prod @ E @ G ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ E @ F ) @ ( c_Relation_Orel__comp @ C @ D @ E @ G @ F ) @ ( tc_prod @ E @ F ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__compEpair_0) ).
thf(1052,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ A @ ( c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1 @ A @ B @ C @ D @ E @ F @ G ) @ E @ G ) @ C @ ( tc_prod @ E @ G ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ E @ F ) @ ( c_Relation_Orel__comp @ C @ D @ E @ G @ F ) @ ( tc_prod @ E @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(10,axiom,
! [B: $i,A: $i] :
( ( ( c_Relation_Orel__comp @ ( c_Relation_Oconverse @ A @ B @ B ) @ A @ B @ B @ B )
!= A )
| ( c_Equiv__Relations_Oequiv @ ( c_Relation_ODomain @ A @ B @ B ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comp__equivI_0) ).
thf(727,plain,
! [B: $i,A: $i] :
( ( ( c_Relation_Orel__comp @ ( c_Relation_Oconverse @ A @ B @ B ) @ A @ B @ B @ B )
!= A )
| ( c_Equiv__Relations_Oequiv @ ( c_Relation_ODomain @ A @ B @ B ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(509,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ A ) @ C )
= C )
| ~ ( c_lessequals @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__absorb2_0) ).
thf(1797,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ A ) @ C )
= C )
| ~ ( c_lessequals @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).
thf(143,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ D @ ( tc_fun @ B @ tc_bool ) ) @ E ) @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_lessequals @ E @ C @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__mono_0) ).
thf(1008,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ D @ ( tc_fun @ B @ tc_bool ) ) @ E ) @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_lessequals @ E @ C @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(472,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A ) @ C ) @ A ) @ D )
= ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A ) @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I6_J_0) ).
thf(1717,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A ) @ C ) @ A ) @ D )
= ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A ) @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).
thf(314,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( c_lessequals @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ A ) @ C ) @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I2_J_0) ).
thf(1372,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( c_lessequals @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ A ) @ C ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(84,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__greatest_0) ).
thf(876,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(76,axiom,
! [B: $i,A: $i] :
( ( c_Relation_Osym @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ B )
| ~ ( c_Relation_Osym @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__rtrancl_0) ).
thf(859,plain,
! [B: $i,A: $i] :
( ( c_Relation_Osym @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ B )
| ~ ( c_Relation_Osym @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(629,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ A @ ( tc_fun @ C @ tc_bool ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__empty_0) ).
thf(2056,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ A @ ( tc_fun @ C @ tc_bool ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[629]) ).
thf(307,axiom,
! [B: $i,A: $i] :
~ ( hBOOL @ ( c_in @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__iff_0) ).
thf(1358,plain,
! [B: $i,A: $i] :
~ ( hBOOL @ ( c_in @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(556,axiom,
! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_top1I_0) ).
thf(1898,plain,
! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).
thf(258,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A ) @ C )
!= ( c_Orderings_Obot__class_Obot @ A ) )
| ( B
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__eq__bot__eq1_0) ).
thf(1257,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A ) @ C )
!= ( c_Orderings_Obot__class_Obot @ A ) )
| ( B
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(304,axiom,
class_Lattices_Olattice @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olattice) ).
thf(1353,plain,
class_Lattices_Olattice @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(583,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A ) @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A ) @ C ) )
= ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I8_J_0) ).
thf(1955,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A ) @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A ) @ C ) )
= ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).
thf(486,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ B @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ A ) @ C ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infE_1) ).
thf(1749,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ B @ C @ A )
| ~ ( c_lessequals @ B @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ A ) @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).
thf(339,axiom,
! [B: $i,A: $i] :
~ ( hBOOL @ ( c_in @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_emptyE_0) ).
thf(1427,plain,
! [B: $i,A: $i] :
~ ( hBOOL @ ( c_in @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(549,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Relation_ODomain @ B @ C @ D ) @ C ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ E @ C @ D ) @ B @ ( tc_prod @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DomainI_0) ).
thf(1881,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Relation_ODomain @ B @ C @ D ) @ C ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ E @ C @ D ) @ B @ ( tc_prod @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).
thf(265,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 @ A @ B @ C ) @ A @ C ) )
| ~ ( hBOOL @ ( c_in @ D @ A @ C ) )
| ~ ( c_Wellfounded_Owf @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wfE__min_0) ).
thf(1272,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 @ A @ B @ C ) @ A @ C ) )
| ~ ( hBOOL @ ( c_in @ D @ A @ C ) )
| ~ ( c_Wellfounded_Owf @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(136,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( c_COMBB @ B @ C @ D @ ( tc_fun @ E @ tc_bool ) @ F ) @ F @ ( tc_fun @ E @ tc_bool ) )
= ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ ( c_Set_Oimage @ C @ A @ F @ D ) @ B @ D @ ( tc_fun @ E @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__extend__simps_I10_J_0) ).
thf(991,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( c_COMBB @ B @ C @ D @ ( tc_fun @ E @ tc_bool ) @ F ) @ F @ ( tc_fun @ E @ tc_bool ) )
= ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ ( c_Set_Oimage @ C @ A @ F @ D ) @ B @ D @ ( tc_fun @ E @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(428,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( hAPP @ ( c_Set_Oinsert @ A @ B ) @ C ) @ ( tc_fun @ B @ tc_bool ) ) @ D )
= ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ ( tc_fun @ B @ tc_bool ) ) @ D ) )
| ( hBOOL @ ( c_in @ A @ D @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__left_1) ).
thf(1617,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( hAPP @ ( c_Set_Oinsert @ A @ B ) @ C ) @ ( tc_fun @ B @ tc_bool ) ) @ D )
= ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ ( tc_fun @ B @ tc_bool ) ) @ D ) )
| ( hBOOL @ ( c_in @ A @ D @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(576,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ B @ tc_bool ) ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__absorb_0) ).
thf(1940,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ B @ tc_bool ) ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).
thf(336,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup1CI_0) ).
thf(1421,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(624,axiom,
class_Lattices_Oupper__semilattice @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oupper__semilattice) ).
thf(2045,plain,
class_Lattices_Oupper__semilattice @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[624]) ).
thf(588,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( tc_fun @ B @ tc_bool ) ) @ C )
= ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ ( tc_fun @ B @ tc_bool ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__commute_0) ).
thf(1966,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( tc_fun @ B @ tc_bool ) ) @ C )
= ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ ( tc_fun @ B @ tc_bool ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).
thf(580,axiom,
class_HOL_Oord @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__HOL_Oord) ).
thf(1949,plain,
class_HOL_Oord @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).
thf(518,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ B @ A @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) )
| ~ ( c_Wellfounded_Owf @ D @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__asym_0) ).
thf(1817,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ B @ A @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) )
| ~ ( c_Wellfounded_Owf @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).
thf(531,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ ( tc_fun @ B @ tc_bool ) ) @ E ) @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_lessequals @ C @ E @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__mono_0) ).
thf(1844,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ ( tc_fun @ B @ tc_bool ) ) @ E ) @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_lessequals @ C @ E @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).
thf(691,axiom,
! [B: $i,A: $i] :
( ( c_Relation_Otrans @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ ( c_Relation_OId @ B ) ) @ B )
| ~ ( c_Relation_Oantisym @ A @ B )
| ~ ( c_Relation_Otrans @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__diff__Id_0) ).
thf(2194,plain,
! [B: $i,A: $i] :
( ( c_Relation_Otrans @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ A @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ ( c_Relation_OId @ B ) ) @ B )
| ~ ( c_Relation_Oantisym @ A @ B )
| ~ ( c_Relation_Otrans @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[691]) ).
thf(380,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( c_in @ ( c_ATP__Linkup_Osko__Set__Xball__UNIV__1__1 @ A @ C ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ball__UNIV_0) ).
thf(1517,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( c_in @ ( c_ATP__Linkup_Osko__Set__Xball__UNIV__1__1 @ A @ C ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(26,axiom,
! [B: $i,A: $i] : ( c_Relation_Osym @ ( c_Relation_OId__on @ A @ B ) @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__Id__on_0) ).
thf(759,plain,
! [B: $i,A: $i] : ( c_Relation_Osym @ ( c_Relation_OId__on @ A @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(198,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ A ) @ D ) @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supI1_0) ).
thf(1126,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( c_lessequals @ B @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ A ) @ D ) @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(542,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Transitive__Closure_Ortrancl @ B @ C ) @ ( tc_prod @ C @ C ) ) )
| ~ ( hBOOL @ ( c_in @ A @ B @ ( tc_prod @ C @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_r__into__rtrancl_0) ).
thf(1866,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Transitive__Closure_Ortrancl @ B @ C ) @ ( tc_prod @ C @ C ) ) )
| ~ ( hBOOL @ ( c_in @ A @ B @ ( tc_prod @ C @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).
thf(479,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ C @ B ) )
| ~ ( c_lessequals @ C @ A @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_predicate1D_0) ).
thf(1734,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ C @ B ) )
| ~ ( c_lessequals @ C @ A @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).
thf(190,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ C ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ C @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1 @ A @ D @ E ) @ E @ E ) @ D @ ( tc_prod @ E @ E ) ) )
| ~ ( c_Wellfounded_Owf @ D @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__induct_0) ).
thf(1108,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ C ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ C @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1 @ A @ D @ E ) @ E @ E ) @ D @ ( tc_prod @ E @ E ) ) )
| ~ ( c_Wellfounded_Owf @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(602,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ ( c_Relation_Oconverse @ D @ C @ C ) @ C ) @ ( tc_prod @ C @ C ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Relation_Oconverse @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ C @ C ) @ ( tc_prod @ C @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__converseI_0) ).
thf(1998,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ ( c_Relation_Oconverse @ D @ C @ C ) @ C ) @ ( tc_prod @ C @ C ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Relation_Oconverse @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ C @ C ) @ ( tc_prod @ C @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[602]) ).
thf(565,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ B @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ A ) @ D ) @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__inf__iff_2) ).
thf(1918,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( c_lessequals @ B @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ A ) @ D ) @ A )
| ~ ( c_lessequals @ B @ D @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).
thf(285,axiom,
! [A: $i] : ( c_lessequals @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( tc_fun @ A @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__empty_1) ).
thf(1316,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)],[285]) ).
thf(288,axiom,
! [B: $i,A: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot1E_0) ).
thf(1321,plain,
! [B: $i,A: $i] :
~ ( hBOOL @ ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(563,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1 @ A @ C @ D ) ) )
| ~ ( c_Wellfounded_Owf @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__def_1) ).
thf(1913,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1 @ A @ C @ D ) ) )
| ~ ( c_Wellfounded_Owf @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).
thf(237,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( ( hAPP @ ( c_HOL_Ominus__class_Ominus @ B @ A ) @ C )
!= ( hAPP @ ( c_HOL_Ominus__class_Ominus @ D @ A ) @ E ) )
| ( c_lessequals @ C @ B @ A )
| ~ ( c_lessequals @ E @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__eqI_1) ).
thf(1216,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_OrderedGroup_Opordered__ab__group__add @ A )
| ( ( hAPP @ ( c_HOL_Ominus__class_Ominus @ B @ A ) @ C )
!= ( hAPP @ ( c_HOL_Ominus__class_Ominus @ D @ A ) @ E ) )
| ( c_lessequals @ C @ B @ A )
| ~ ( c_lessequals @ E @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(91,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ E @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ E @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__trans_0) ).
thf(891,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ E @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ E @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(349,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Set_Oinsert @ ( hAPP @ A @ B ) @ C ) @ ( c_Set_Oimage @ A @ D @ E @ C ) )
= ( c_Set_Oimage @ A @ D @ E @ C ) )
| ~ ( hBOOL @ ( c_in @ B @ D @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__image_0) ).
thf(1448,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Set_Oinsert @ ( hAPP @ A @ B ) @ C ) @ ( c_Set_Oimage @ A @ D @ E @ C ) )
= ( c_Set_Oimage @ A @ D @ E @ C ) )
| ~ ( hBOOL @ ( c_in @ B @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(688,axiom,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ A ) @ ( c_Orderings_Obot__class_Obot @ A ) )
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__bot__right_0) ).
thf(2187,plain,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ A ) @ ( c_Orderings_Obot__class_Obot @ A ) )
= ( c_Orderings_Obot__class_Obot @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[688]) ).
thf(144,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ D @ C @ ( tc_fun @ B @ tc_bool ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__extend__simps_I2_J_0) ).
thf(1010,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_bool ) ) @ D @ C @ ( tc_fun @ B @ tc_bool ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(321,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ ( tc_fun @ B @ tc_bool ) ) @ D ) )
= ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ B @ tc_bool ) ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__left__commute_0) ).
thf(1390,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ ( tc_fun @ B @ tc_bool ) ) @ D ) )
= ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ B @ tc_bool ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(69,axiom,
! [B: $i,A: $i] :
( ( c_Relation_Orel__comp @ A @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ B @ B @ B )
= ( c_Relation_Orel__comp @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ A @ B @ B @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_r__comp__rtrancl__eq_0) ).
thf(844,plain,
! [B: $i,A: $i] :
( ( c_Relation_Orel__comp @ A @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ B @ B @ B )
= ( c_Relation_Orel__comp @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ A @ B @ B @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(706,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
| ( A = B )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__eq__or__trancl_0) ).
thf(2226,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
| ( A = B )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[706]) ).
thf(291,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oimage @ A @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ ( c_Set_Oimage @ A @ E @ C @ D ) ) @ ( c_Set_Oimage @ A @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ B @ ( tc_fun @ C @ tc_bool ) ) @ E ) @ C @ D ) @ ( tc_fun @ D @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__diff__subset_0) ).
thf(1326,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( c_Set_Oimage @ A @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ ( c_Set_Oimage @ A @ E @ C @ D ) ) @ ( c_Set_Oimage @ A @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ B @ ( tc_fun @ C @ tc_bool ) ) @ E ) @ C @ D ) @ ( tc_fun @ D @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(123,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_Set_Oinsert @ C @ B ) @ D ) )
= ( hAPP @ ( c_Set_Oinsert @ C @ B ) @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( tc_fun @ B @ tc_bool ) ) @ D ) ) )
| ~ ( hBOOL @ ( c_in @ C @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__right_0) ).
thf(963,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_Set_Oinsert @ C @ B ) @ D ) )
= ( hAPP @ ( c_Set_Oinsert @ C @ B ) @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( tc_fun @ B @ tc_bool ) ) @ D ) ) )
| ~ ( hBOOL @ ( c_in @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(681,axiom,
class_Orderings_Oorder @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Oorder) ).
thf(2174,plain,
class_Orderings_Oorder @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[681]) ).
thf(452,axiom,
! [B: $i,A: $i] : ( c_Relation_Otrans @ ( c_Relation_OId__on @ A @ B ) @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__Id__on_0) ).
thf(1674,plain,
! [B: $i,A: $i] : ( c_Relation_Otrans @ ( c_Relation_OId__on @ A @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(364,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Set_Oinsert @ A @ B ) @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ C @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_Set_Oinsert @ A @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) ) )
= C )
| ~ ( hBOOL @ ( c_in @ A @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff_0) ).
thf(1481,plain,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Set_Oinsert @ A @ B ) @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ C @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_Set_Oinsert @ A @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) ) )
= C )
| ~ ( hBOOL @ ( c_in @ A @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(484,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A ) @ C )
= B )
| ~ ( c_lessequals @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__absorb1_0) ).
thf(1745,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A ) @ C )
= B )
| ~ ( c_lessequals @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).
thf(536,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ E @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ E @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__trans_0) ).
thf(1854,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ E @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ E @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).
thf(267,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ B @ tc_bool ) ) @ C )
= C )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__absorb1_0) ).
thf(1276,plain,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ B @ tc_bool ) ) @ C )
= C )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(416,axiom,
! [B: $i,A: $i] :
~ ( hBOOL @ ( c_in @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ex__in__conv_0) ).
thf(1590,plain,
! [B: $i,A: $i] :
~ ( hBOOL @ ( c_in @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(53,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_Oconverse @ ( c_Relation_Orel__comp @ A @ B @ C @ D @ E ) @ C @ E )
= ( c_Relation_Orel__comp @ ( c_Relation_Oconverse @ B @ D @ E ) @ ( c_Relation_Oconverse @ A @ C @ D ) @ E @ D @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__rel__comp_0) ).
thf(813,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_Oconverse @ ( c_Relation_Orel__comp @ A @ B @ C @ D @ E ) @ C @ E )
= ( c_Relation_Orel__comp @ ( c_Relation_Oconverse @ B @ D @ E ) @ ( c_Relation_Oconverse @ A @ C @ D ) @ E @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(319,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Relation_OImage @ A @ B @ B ) @ ( hAPP @ ( c_Set_Oinsert @ C @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) )
= ( hAPP @ ( c_Relation_OImage @ A @ B @ B ) @ ( hAPP @ ( c_Set_Oinsert @ D @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ C @ D @ B @ B ) @ A @ ( tc_prod @ B @ B ) ) )
| ~ ( c_Equiv__Relations_Oequiv @ E @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__class__eq_0) ).
thf(1385,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Relation_OImage @ A @ B @ B ) @ ( hAPP @ ( c_Set_Oinsert @ C @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) )
= ( hAPP @ ( c_Relation_OImage @ A @ B @ B ) @ ( hAPP @ ( c_Set_Oinsert @ D @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ C @ D @ B @ B ) @ A @ ( tc_prod @ B @ B ) ) )
| ~ ( c_Equiv__Relations_Oequiv @ E @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(474,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( hAPP @ ( c_Set_Oinsert @ A @ B ) @ C ) @ ( tc_fun @ B @ tc_bool ) ) @ D )
= ( hAPP @ ( c_Set_Oinsert @ A @ B ) @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ ( tc_fun @ B @ tc_bool ) ) @ D ) ) )
| ~ ( hBOOL @ ( c_in @ A @ D @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__left_0) ).
thf(1721,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( hAPP @ ( c_Set_Oinsert @ A @ B ) @ C ) @ ( tc_fun @ B @ tc_bool ) ) @ D )
= ( hAPP @ ( c_Set_Oinsert @ A @ B ) @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ ( tc_fun @ B @ tc_bool ) ) @ D ) ) )
| ~ ( hBOOL @ ( c_in @ A @ D @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(93,axiom,
! [A: $i] :
( ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UNIV__not__empty_0) ).
thf(896,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)],[93]) ).
thf(648,axiom,
! [B: $i,A: $i] :
( ( c_Relation_Otrans @ ( c_Relation_Oconverse @ A @ B @ B ) @ B )
| ~ ( c_Relation_Otrans @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__converse_1) ).
thf(2098,plain,
! [B: $i,A: $i] :
( ( c_Relation_Otrans @ ( c_Relation_Oconverse @ A @ B @ B ) @ B )
| ~ ( c_Relation_Otrans @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[648]) ).
thf(20,axiom,
! [B: $i,A: $i] :
( ( c_Relation_ODomain @ ( c_Relation_OId__on @ A @ B ) @ B @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__Id__on_0) ).
thf(748,plain,
! [B: $i,A: $i] :
( ( c_Relation_ODomain @ ( c_Relation_OId__on @ A @ B ) @ B @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(116,axiom,
! [B: $i,A: $i] : ( c_Relation_Orefl__on @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Transitive__Closure_Ortrancl @ B @ A ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__rtrancl_0) ).
thf(946,plain,
! [B: $i,A: $i] : ( c_Relation_Orefl__on @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ ( c_Transitive__Closure_Ortrancl @ B @ A ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(187,axiom,
! [B: $i,A: $i] :
( ( c_Relation_Otrans @ A @ B )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XtransI__1__1 @ A @ B ) @ ( c_ATP__Linkup_Osko__Relation__XtransI__1__3 @ A @ B ) @ B @ B ) @ A @ ( tc_prod @ B @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_transI_2) ).
thf(1101,plain,
! [B: $i,A: $i] :
( ( c_Relation_Otrans @ A @ B )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XtransI__1__1 @ A @ B ) @ ( c_ATP__Linkup_Osko__Relation__XtransI__1__3 @ A @ B ) @ B @ B ) @ A @ ( tc_prod @ B @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(433,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ C @ D ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
| ( A = B )
| ( A = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mktop_5) ).
thf(1629,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ C @ D ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
| ( A = B )
| ( A = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(605,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( c_in @ A @ B @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ D @ A ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ B @ D @ C @ ( tc_fun @ F @ tc_bool ) ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INF1__E_0) ).
thf(2004,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( c_in @ A @ B @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ D @ A ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ B @ D @ C @ ( tc_fun @ F @ tc_bool ) ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[605]) ).
thf(383,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Relation_Orel__comp @ A @ B @ C @ D @ E ) @ ( c_Relation_Orel__comp @ F @ G @ C @ D @ E ) @ ( tc_fun @ ( tc_prod @ C @ E ) @ tc_bool ) )
| ~ ( c_lessequals @ B @ G @ ( tc_fun @ ( tc_prod @ D @ E ) @ tc_bool ) )
| ~ ( c_lessequals @ A @ F @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__comp__mono_0) ).
thf(1523,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Relation_Orel__comp @ A @ B @ C @ D @ E ) @ ( c_Relation_Orel__comp @ F @ G @ C @ D @ E ) @ ( tc_fun @ ( tc_prod @ C @ E ) @ tc_bool ) )
| ~ ( c_lessequals @ B @ G @ ( tc_fun @ ( tc_prod @ D @ E ) @ tc_bool ) )
| ~ ( c_lessequals @ A @ F @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(662,axiom,
! [B: $i,A: $i] :
( ( c_Relation_Otrans @ A @ B )
| ~ ( c_Relation_Otrans @ ( c_Relation_Oconverse @ A @ B @ B ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__converse_0) ).
thf(2130,plain,
! [B: $i,A: $i] :
( ( c_Relation_Otrans @ A @ B )
| ~ ( c_Relation_Otrans @ ( c_Relation_Oconverse @ A @ B @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[662]) ).
thf(607,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ C @ D ) )
| ~ ( hBOOL @ ( hAPP @ A @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1I_0) ).
thf(2009,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ C @ D ) )
| ~ ( hBOOL @ ( hAPP @ A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[607]) ).
thf(154,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty__right_0) ).
thf(1030,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(459,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Set_Oinsert @ A @ B ) @ ( hAPP @ ( c_Set_Oinsert @ C @ B ) @ D ) )
= ( hAPP @ ( c_Set_Oinsert @ C @ B ) @ ( hAPP @ ( c_Set_Oinsert @ A @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__commute_0) ).
thf(1689,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Set_Oinsert @ A @ B ) @ ( hAPP @ ( c_Set_Oinsert @ C @ B ) @ D ) )
= ( hAPP @ ( c_Set_Oinsert @ C @ B ) @ ( hAPP @ ( c_Set_Oinsert @ A @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(622,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 @ B @ D @ C ) @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) )
| ~ ( hBOOL @ ( c_in @ E @ B @ C ) )
| ~ ( c_Wellfounded_Owf @ D @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__eq__minimal_1) ).
thf(2041,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 @ B @ D @ C ) @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) )
| ~ ( hBOOL @ ( c_in @ E @ B @ C ) )
| ~ ( c_Wellfounded_Owf @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[622]) ).
thf(500,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A ) @ C ) @ A ) @ D )
= ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A ) @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__assoc_0) ).
thf(1777,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A ) @ C ) @ A ) @ D )
= ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A ) @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).
thf(345,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ ( c_Product__Type_OSigma @ E @ F @ C @ D ) @ ( tc_prod @ C @ D ) ) )
| ~ ( hBOOL @ ( c_in @ B @ ( hAPP @ F @ A ) @ D ) )
| ~ ( hBOOL @ ( c_in @ A @ E @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SigmaI_0) ).
thf(1440,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ ( c_Product__Type_OSigma @ E @ F @ C @ D ) @ ( tc_prod @ C @ D ) ) )
| ~ ( hBOOL @ ( c_in @ B @ ( hAPP @ F @ A ) @ D ) )
| ~ ( hBOOL @ ( c_in @ A @ E @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(176,axiom,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ A ) @ A ) @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__bot__left_0) ).
thf(1077,plain,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Orderings_Obot__class_Obot @ A ) @ A ) @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(378,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ ( hAPP @ ( c_Set_Oinsert @ D @ C ) @ A ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_1) ).
thf(1513,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ ( hAPP @ ( c_Set_Oinsert @ D @ C ) @ A ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(94,axiom,
! [B: $i,A: $i] :
( ( c_Relation_Otrans @ A @ B )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__Xtrans__def__1__1 @ A @ B ) @ ( c_ATP__Linkup_Osko__Relation__Xtrans__def__1__3 @ A @ B ) @ B @ B ) @ A @ ( tc_prod @ B @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__def_3) ).
thf(899,plain,
! [B: $i,A: $i] :
( ( c_Relation_Otrans @ A @ B )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__Xtrans__def__1__1 @ A @ B ) @ ( c_ATP__Linkup_Osko__Relation__Xtrans__def__1__3 @ A @ B ) @ B @ B ) @ A @ ( tc_prod @ B @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(63,axiom,
! [B: $i,A: $i] :
( ( c_Relation_Osym @ ( c_Relation_Oconverse @ A @ B @ B ) @ B )
| ~ ( c_Relation_Osym @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__converse_1) ).
thf(832,plain,
! [B: $i,A: $i] :
( ( c_Relation_Osym @ ( c_Relation_Oconverse @ A @ B @ B ) @ B )
| ~ ( c_Relation_Osym @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(600,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ D @ C @ E ) @ ( c_Product__Type_OSigma @ B @ F @ C @ E ) @ ( tc_prod @ C @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SigmaD1_0) ).
thf(1994,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ D @ C @ E ) @ ( c_Product__Type_OSigma @ B @ F @ C @ E ) @ ( tc_prod @ C @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[600]) ).
thf(612,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( hAPP @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_1) ).
thf(2019,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( hAPP @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[612]) ).
thf(281,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ A @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup1CI_1) ).
thf(1308,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(693,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A @ B ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_2) ).
thf(2198,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ A @ B ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[693]) ).
thf(686,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ ( c_Product__Type_OSigma @ E @ F @ C @ D ) @ ( tc_prod @ C @ D ) ) )
| ~ ( hBOOL @ ( c_in @ B @ ( hAPP @ F @ A ) @ D ) )
| ~ ( hBOOL @ ( c_in @ A @ E @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__Sigma__iff_2) ).
thf(2183,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ ( c_Product__Type_OSigma @ E @ F @ C @ D ) @ ( tc_prod @ C @ D ) ) )
| ~ ( hBOOL @ ( c_in @ B @ ( hAPP @ F @ A ) @ D ) )
| ~ ( hBOOL @ ( c_in @ A @ E @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[686]) ).
thf(235,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ E @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ E @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__into__trancl1_0) ).
thf(1212,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ E @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ E @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(554,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Relation_ORange @ B @ C @ D ) @ D ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ E @ A @ C @ D ) @ B @ ( tc_prod @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_RangeI_0) ).
thf(1893,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Relation_ORange @ B @ C @ D ) @ D ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ E @ A @ C @ D ) @ B @ ( tc_prod @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).
thf(620,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1 @ A @ C @ D ) ) )
| ~ ( c_Wellfounded_Owf @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__induct_1) ).
thf(2036,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__induct__1__1 @ A @ C @ D ) ) )
| ~ ( c_Wellfounded_Owf @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[620]) ).
thf(347,axiom,
! [B: $i,A: $i] :
( ( class_Lattices_Odistrib__lattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Odistrib__lattice @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Odistrib__lattice) ).
thf(1444,plain,
! [B: $i,A: $i] :
( ( class_Lattices_Odistrib__lattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Odistrib__lattice @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(346,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Relation_Oconverse @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ C @ C ) @ ( tc_prod @ C @ C ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ ( c_Relation_Oconverse @ D @ C @ C ) @ C ) @ ( tc_prod @ C @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__converseD_0) ).
thf(1442,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Relation_Oconverse @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ C @ C ) @ ( tc_prod @ C @ C ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ ( c_Relation_Oconverse @ D @ C @ C ) @ C ) @ ( tc_prod @ C @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(2,negated_conjecture,
! [A: $i] : ( c_Relation_Oirrefl @ ( hAPP @ v_P @ A ) @ tc_Arrow__Order__Mirabelle_Oalt ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(716,plain,
! [A: $i] : ( c_Relation_Oirrefl @ ( hAPP @ v_P @ A ) @ tc_Arrow__Order__Mirabelle_Oalt ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(212,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Oantisym @ A @ B )
| ~ ( c_Relation_Oantisym @ C @ B )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__subset_0) ).
thf(1161,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Oantisym @ A @ B )
| ~ ( c_Relation_Oantisym @ C @ B )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(46,axiom,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Ortrancl @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ B )
= ( c_Transitive__Closure_Ortrancl @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__rtrancl__absorb_0) ).
thf(800,plain,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Ortrancl @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ B )
= ( c_Transitive__Closure_Ortrancl @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(561,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( tc_fun @ B @ tc_bool ) ) @ D )
= ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ ( tc_fun @ B @ tc_bool ) ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__assoc_0) ).
thf(1908,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( tc_fun @ B @ tc_bool ) ) @ D )
= ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ ( tc_fun @ B @ tc_bool ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).
thf(201,axiom,
! [A: $i] :
( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( 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 ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty_2) ).
thf(1133,plain,
! [A: $i] :
( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( 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 ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(377,axiom,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ A @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( tc_fun @ B @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__upper1_0) ).
thf(1512,plain,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ A @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ ( tc_fun @ B @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(673,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Recdef_Ocut @ A @ B @ C @ D @ E ) @ F )
= ( hAPP @ A @ F ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ F @ C @ D @ D ) @ B @ ( tc_prod @ D @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cut__apply_0) ).
thf(2155,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Recdef_Ocut @ A @ B @ C @ D @ E ) @ F )
= ( hAPP @ A @ F ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ F @ C @ D @ D ) @ B @ ( tc_prod @ D @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[673]) ).
thf(118,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( c_COMBK @ B @ ( tc_fun @ C @ tc_bool ) @ D ) @ D @ ( tc_fun @ C @ tc_bool ) )
= B )
| ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__constant_1) ).
thf(950,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( c_COMBK @ B @ ( tc_fun @ C @ tc_bool ) @ D ) @ D @ ( tc_fun @ C @ tc_bool ) )
= B )
| ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(709,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ B @ A @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ ( c_Relation_Oconverse @ D @ C @ C ) @ C ) @ ( tc_prod @ C @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__converseD_0) ).
thf(2233,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ B @ A @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ ( c_Relation_Oconverse @ D @ C @ C ) @ C ) @ ( tc_prod @ C @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[709]) ).
thf(56,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Oconverse @ ( c_Relation_Oconverse @ A @ B @ C ) @ C @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__converse_0) ).
thf(818,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Oconverse @ ( c_Relation_Oconverse @ A @ B @ C ) @ C @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(547,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1 @ A @ B @ C @ D ) @ C @ D @ D ) @ A @ ( tc_prod @ D @ D ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ B @ C @ D @ D ) @ ( c_Transitive__Closure_Otrancl @ A @ D ) @ ( tc_prod @ D @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tranclD2_1) ).
thf(1876,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1 @ A @ B @ C @ D ) @ C @ D @ D ) @ A @ ( tc_prod @ D @ D ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ B @ C @ D @ D ) @ ( c_Transitive__Closure_Otrancl @ A @ D ) @ ( tc_prod @ D @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).
thf(385,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) @ D )
= ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__extend__simps_I3_J_0) ).
thf(1527,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ B @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) @ D )
= ( hAPP @ ( c_HOL_Ominus__class_Ominus @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(253,axiom,
! [A: $i] : ( hBOOL @ ( c_in @ ( c_ATP__Linkup_Osko__Set__XUNIV__witness__1__1 @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UNIV__witness_0) ).
thf(1248,plain,
! [A: $i] : ( hBOOL @ ( c_in @ ( c_ATP__Linkup_Osko__Set__XUNIV__witness__1__1 @ A ) @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(491,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ A @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1 @ B @ A @ C @ D ) @ D @ D ) @ ( c_Transitive__Closure_Ortrancl @ B @ D ) @ ( tc_prod @ D @ D ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ C @ D @ D ) @ ( c_Transitive__Closure_Otrancl @ B @ D ) @ ( tc_prod @ D @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tranclD2_0) ).
thf(1757,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ A @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1 @ B @ A @ C @ D ) @ D @ D ) @ ( c_Transitive__Closure_Ortrancl @ B @ D ) @ ( tc_prod @ D @ D ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ C @ D @ D ) @ ( c_Transitive__Closure_Otrancl @ B @ D ) @ ( tc_prod @ D @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).
thf(79,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ A ) @ C )
= B )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__inf_0) ).
thf(865,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ A ) @ C )
= B )
| ~ ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(438,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ A )
| ( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ A ) @ C ) @ A ) @ D )
= ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A ) @ D ) @ A ) @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__inf__distrib2_0) ).
thf(1642,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ A )
| ( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ A ) @ C ) @ A ) @ D )
= ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A ) @ D ) @ A ) @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).
thf(650,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ C @ ( tc_fun @ B @ tc_bool ) ) @ A ) )
= C )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__partition_0) ).
thf(2102,plain,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ C @ ( tc_fun @ B @ tc_bool ) ) @ A ) )
= C )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[650]) ).
thf(22,axiom,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Otrancl @ ( c_Relation_Oconverse @ A @ B @ B ) @ B )
= ( c_Relation_Oconverse @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ B @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__converse_0) ).
thf(752,plain,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Otrancl @ ( c_Relation_Oconverse @ A @ B @ B ) @ B )
= ( c_Relation_Oconverse @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ B @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(343,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ( hBOOL @ ( c_in @ A @ D @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ ( tc_fun @ C @ tc_bool ) ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnE_0) ).
thf(1436,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ( hBOOL @ ( c_in @ A @ D @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ ( tc_fun @ C @ tc_bool ) ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(284,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_lessequals @ C @ D @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__subset__iff_2) ).
thf(1314,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ B @ tc_bool ) ) @ C ) @ D @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_lessequals @ C @ D @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(444,axiom,
class_Complete__Lattice_Ocomplete__lattice @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Complete__Lattice_Ocomplete__lattice) ).
thf(1657,plain,
class_Complete__Lattice_Ocomplete__lattice @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(50,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_ORange @ ( c_Relation_Oconverse @ A @ B @ C ) @ C @ B )
= ( c_Relation_ODomain @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__converse_0) ).
thf(807,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_ORange @ ( c_Relation_Oconverse @ A @ B @ C ) @ C @ B )
= ( c_Relation_ODomain @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(61,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Wellfounded_Owf @ ( c_Relation_Oinv__image @ A @ B @ C @ D ) @ D )
| ~ ( c_Wellfounded_Owf @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__inv__image_0) ).
thf(828,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Wellfounded_Owf @ ( c_Relation_Oinv__image @ A @ B @ C @ D ) @ D )
| ~ ( c_Wellfounded_Owf @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(4,negated_conjecture,
hBOOL @ ( c_in @ ( c_Pair @ v_a @ v_b @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( v_F @ v_P ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
thf(720,plain,
hBOOL @ ( c_in @ ( c_Pair @ v_a @ v_b @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( v_F @ v_P ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(120,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( tc_fun @ t_a @ A ) ) @ C ) @ v_x )
= ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( hAPP @ B @ v_x ) @ A ) @ ( hAPP @ C @ v_x ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__fun__eq_0) ).
thf(955,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( tc_fun @ t_a @ A ) ) @ C ) @ v_x )
= ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( hAPP @ B @ v_x ) @ A ) @ ( hAPP @ C @ v_x ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(296,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Relation_OImage @ A @ B @ B ) @ ( hAPP @ ( c_Set_Oinsert @ C @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) )
!= ( hAPP @ ( c_Relation_OImage @ A @ B @ B ) @ ( hAPP @ ( c_Set_Oinsert @ D @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) ) )
| ~ ( hBOOL @ ( c_in @ D @ E @ B ) )
| ~ ( hBOOL @ ( c_in @ C @ E @ B ) )
| ~ ( c_Equiv__Relations_Oequiv @ E @ A @ B )
| ( hBOOL @ ( c_in @ ( c_Pair @ C @ D @ B @ B ) @ A @ ( tc_prod @ B @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__equiv__class__iff_0) ).
thf(1335,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Relation_OImage @ A @ B @ B ) @ ( hAPP @ ( c_Set_Oinsert @ C @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) )
!= ( hAPP @ ( c_Relation_OImage @ A @ B @ B ) @ ( hAPP @ ( c_Set_Oinsert @ D @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) ) )
| ~ ( hBOOL @ ( c_in @ D @ E @ B ) )
| ~ ( hBOOL @ ( c_in @ C @ E @ B ) )
| ~ ( c_Equiv__Relations_Oequiv @ E @ A @ B )
| ( hBOOL @ ( c_in @ ( c_Pair @ C @ D @ B @ B ) @ A @ ( tc_prod @ B @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(636,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ A ) @ C )
!= ( c_Orderings_Otop__class_Otop @ A ) )
| ( C
= ( c_Orderings_Otop__class_Otop @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__eq__top__eq2_0) ).
thf(2070,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Obounded__lattice @ A )
| ( ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ A ) @ C )
!= ( c_Orderings_Otop__class_Otop @ A ) )
| ( C
= ( c_Orderings_Otop__class_Otop @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[636]) ).
thf(217,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( c_lessequals @ B @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A ) @ C ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I3_J_0) ).
thf(1172,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( c_lessequals @ B @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A ) @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(331,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A ) @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A ) @ C ) )
= ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__left__idem_0) ).
thf(1410,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A ) @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A ) @ C ) )
= ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(166,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( c_COMBB @ ( c_Set_Oinsert @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) @ ( tc_fun @ C @ tc_bool ) @ E ) @ E @ ( tc_fun @ C @ tc_bool ) )
= ( hAPP @ ( c_Set_Oinsert @ B @ C ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ D @ E @ ( tc_fun @ C @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( c_in @ F @ A @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__insert__distrib_0) ).
thf(1056,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( c_COMBB @ ( c_Set_Oinsert @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) @ ( tc_fun @ C @ tc_bool ) @ E ) @ E @ ( tc_fun @ C @ tc_bool ) )
= ( hAPP @ ( c_Set_Oinsert @ B @ C ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ D @ E @ ( tc_fun @ C @ tc_bool ) ) ) )
| ~ ( hBOOL @ ( c_in @ F @ A @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(506,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ D @ E @ ( tc_fun @ B @ tc_bool ) ) )
= ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( c_COMBB @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ B @ tc_bool ) ) @ D @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) @ E ) @ E @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__INT__distrib_0) ).
thf(1789,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ B @ tc_bool ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ D @ E @ ( tc_fun @ B @ tc_bool ) ) )
= ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ C @ ( c_COMBB @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ B @ tc_bool ) ) @ D @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ B @ tc_bool ) @ E ) @ E @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).
thf(704,axiom,
! [B: $i,A: $i] : ( c_Relation_Orefl__on @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_bool ) ) @ ( c_Relation_OId @ A ) ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__reflcl_0) ).
thf(2223,plain,
! [B: $i,A: $i] : ( c_Relation_Orefl__on @ ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_bool ) ) @ ( c_Relation_OId @ A ) ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[704]) ).
thf(122,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
| ( B = D )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ C @ D ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mktop_2) ).
thf(960,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) )
| ( B = D )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ C @ D ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(360,axiom,
! [B: $i,A: $i] :
( ( c_Relation_Oantisym @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ ( c_Relation_OId @ B ) ) @ B )
| ~ ( c_Relation_Oantisym @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__reflcl_1) ).
thf(1473,plain,
! [B: $i,A: $i] :
( ( c_Relation_Oantisym @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ ( c_Relation_OId @ B ) ) @ B )
| ~ ( c_Relation_Oantisym @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(613,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( hAPP @ ( c_Set_Oinsert @ B @ C ) @ D ) @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insertI2_0) ).
thf(2021,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( hAPP @ ( c_Set_Oinsert @ B @ C ) @ D ) @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[613]) ).
thf(632,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( c_in @ B @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_0) ).
thf(2063,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( c_in @ B @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[632]) ).
thf(483,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Set_Oinsert @ A @ B ) @ ( hAPP @ ( c_Set_Oinsert @ C @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) )
!= ( hAPP @ ( c_Set_Oinsert @ D @ B ) @ ( hAPP @ ( c_Set_Oinsert @ E @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) ) )
| ( C = D )
| ( C = E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_3) ).
thf(1742,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Set_Oinsert @ A @ B ) @ ( hAPP @ ( c_Set_Oinsert @ C @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) )
!= ( hAPP @ ( c_Set_Oinsert @ D @ B ) @ ( hAPP @ ( c_Set_Oinsert @ E @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) ) )
| ( C = D )
| ( C = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).
thf(107,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( tc_fun @ B @ tc_bool ) ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__absorb_0) ).
thf(928,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( tc_fun @ B @ tc_bool ) ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(593,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( c_COMBB @ ( c_HOL_Ominus__class_Ominus @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) @ ( tc_fun @ C @ tc_bool ) @ A ) @ A @ ( tc_fun @ C @ tc_bool ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__simps_I4_J_0) ).
thf(1977,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( c_COMBB @ ( c_HOL_Ominus__class_Ominus @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) @ ( tc_fun @ C @ tc_bool ) @ A ) @ A @ ( tc_fun @ C @ tc_bool ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[593]) ).
thf(263,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ C ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ C @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1 @ A @ D @ E ) @ E @ E ) @ D @ ( tc_prod @ E @ E ) ) )
| ~ ( c_Wellfounded_Owf @ D @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__def_0) ).
thf(1268,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ C ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ C @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__def__1__1 @ A @ D @ E ) @ E @ E ) @ D @ ( tc_prod @ E @ E ) ) )
| ~ ( c_Wellfounded_Owf @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(387,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( c_lessequals @ B @ A @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__eq__subset_2) ).
thf(1532,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)],[387]) ).
thf(389,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ ( c_Relation_Oconverse @ D @ C @ C ) @ C ) @ ( tc_prod @ C @ C ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ B @ A @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__converseI_0) ).
thf(1537,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ ( c_Relation_Oconverse @ D @ C @ C ) @ C ) @ ( tc_prod @ C @ C ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ B @ A @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(411,axiom,
class_Lattices_Olower__semilattice @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olower__semilattice) ).
thf(1582,plain,
class_Lattices_Olower__semilattice @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(396,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Transitive__Closure_Ortrancl @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) ) @ D ) @ C ) @ ( tc_prod @ C @ C ) ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_Transitive__Closure_Ortrancl @ B @ C ) @ ( tc_prod @ C @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__rtrancl__UnI_0) ).
thf(1550,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ ( c_Transitive__Closure_Ortrancl @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) ) @ D ) @ C ) @ ( tc_prod @ C @ C ) ) )
| ~ ( hBOOL @ ( c_in @ A @ ( c_Transitive__Closure_Ortrancl @ B @ C ) @ ( tc_prod @ C @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(98,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/sandbox/benchmark/theBenchmark.p',cls_Sup__UNIV_0) ).
thf(908,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)],[98]) ).
thf(58,axiom,
! [B: $i,A: $i] :
( ( c_Relation_Oantisym @ A @ B )
| ~ ( c_Relation_Oantisym @ ( c_Relation_Oconverse @ A @ B @ B ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__converse_0) ).
thf(822,plain,
! [B: $i,A: $i] :
( ( c_Relation_Oantisym @ A @ B )
| ~ ( c_Relation_Oantisym @ ( c_Relation_Oconverse @ A @ B @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(419,axiom,
! [B: $i,A: $i] :
( ( class_Lattices_Olattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Olattice @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olattice) ).
thf(1597,plain,
! [B: $i,A: $i] :
( ( class_Lattices_Olattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Olattice @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(559,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ A ) @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ A ) @ D ) )
= ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ A ) @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ A ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I3_J_0) ).
thf(1902,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ A ) @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ A ) @ D ) )
= ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ A ) @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ A ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).
thf(183,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ~ ( hBOOL @ ( c_in @ B @ D @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ A @ E @ ( tc_fun @ F @ tc_bool ) ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INF1__D_0) ).
thf(1093,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ~ ( hBOOL @ ( c_in @ B @ D @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ A @ E @ ( tc_fun @ F @ tc_bool ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(571,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__mono_0) ).
thf(1930,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).
thf(247,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( hAPP @ ( c_Relation_OImage @ A @ B @ C ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ E @ F @ ( tc_fun @ B @ tc_bool ) ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( c_COMBB @ ( c_Relation_OImage @ A @ B @ C ) @ E @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ C @ tc_bool ) @ F ) @ F @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__INT__subset_0) ).
thf(1236,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( hAPP @ ( c_Relation_OImage @ A @ B @ C ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ E @ F @ ( tc_fun @ B @ tc_bool ) ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ ( c_COMBB @ ( c_Relation_OImage @ A @ B @ C ) @ E @ ( tc_fun @ B @ tc_bool ) @ ( tc_fun @ C @ tc_bool ) @ F ) @ F @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(661,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( hAPP @ A @ B ) @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ A @ E @ ( tc_fun @ C @ tc_bool ) ) )
= ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ A @ E @ ( tc_fun @ C @ tc_bool ) ) )
| ~ ( hBOOL @ ( c_in @ B @ D @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__absorb_0) ).
thf(2127,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( hAPP @ A @ B ) @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ A @ E @ ( tc_fun @ C @ tc_bool ) ) )
= ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ D @ A @ E @ ( tc_fun @ C @ tc_bool ) ) )
| ~ ( hBOOL @ ( c_in @ B @ D @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[661]) ).
thf(72,axiom,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( c_lessequals @ B @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).
thf(850,plain,
! [B: $i,A: $i] :
( ~ ( class_Orderings_Opreorder @ A )
| ( c_lessequals @ B @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(470,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Oord @ A )
| ( c_lessequals @ ( hAPP @ B @ C ) @ ( hAPP @ D @ C ) @ A )
| ~ ( c_lessequals @ B @ D @ ( tc_fun @ E @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__funD_0) ).
thf(1713,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_HOL_Oord @ A )
| ( c_lessequals @ ( hAPP @ B @ C ) @ ( hAPP @ D @ C ) @ A )
| ~ ( c_lessequals @ B @ D @ ( tc_fun @ E @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(373,axiom,
! [B: $i,A: $i] :
( ( class_Orderings_Otop @ ( tc_fun @ A @ B ) )
| ~ ( class_Orderings_Otop @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Otop) ).
thf(1505,plain,
! [B: $i,A: $i] :
( ( class_Orderings_Otop @ ( tc_fun @ A @ B ) )
| ~ ( class_Orderings_Otop @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(430,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__eq__or__trancl_2) ).
thf(1621,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
| ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(423,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ B @ C @ ( tc_fun @ D @ tc_bool ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_bool ) ) )
| ( hBOOL @ ( c_in @ ( c_ATP__Linkup_Osko__Complete__Lattice__XINTER__UNIV__conv__2__1 @ A @ B @ C @ D ) @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INTER__UNIV__conv_I2_J_1) ).
thf(1606,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ B @ C @ ( tc_fun @ D @ tc_bool ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ D @ tc_bool ) ) )
| ( hBOOL @ ( c_in @ ( c_ATP__Linkup_Osko__Complete__Lattice__XINTER__UNIV__conv__2__1 @ A @ B @ C @ D ) @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(586,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Wellfounded_Owf @ A @ B )
| ~ ( c_Wellfounded_Owf @ ( hAPP @ ( c_Set_Oinsert @ ( c_Pair @ C @ D @ B @ B ) @ ( tc_prod @ B @ B ) ) @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__insert_0) ).
thf(1962,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Wellfounded_Owf @ A @ B )
| ~ ( c_Wellfounded_Owf @ ( hAPP @ ( c_Set_Oinsert @ ( c_Pair @ C @ D @ B @ B ) @ ( tc_prod @ B @ B ) ) @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).
thf(222,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ B @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DiffE_0) ).
thf(1184,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ A @ B @ C ) )
| ~ ( hBOOL @ ( c_in @ A @ ( hAPP @ ( c_HOL_Ominus__class_Ominus @ B @ ( tc_fun @ C @ tc_bool ) ) @ D ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(611,axiom,
! [B: $i,A: $i] : ( hBOOL @ ( c_in @ A @ ( hAPP @ ( c_Set_Oinsert @ A @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__iff_1) ).
thf(2018,plain,
! [B: $i,A: $i] : ( hBOOL @ ( c_in @ A @ ( hAPP @ ( c_Set_Oinsert @ A @ B ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[611]) ).
thf(533,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Otrans @ A @ B )
| ~ ( c_Order__Relation_Ostrict__linear__order__on @ C @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_strict__linear__order__on__def_0) ).
thf(1848,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Otrans @ A @ B )
| ~ ( c_Order__Relation_Ostrict__linear__order__on @ C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).
thf(34,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Orderings_Oorder @ A )
| ( B = C )
| ~ ( c_lessequals @ C @ B @ A )
| ~ ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_2) ).
thf(775,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)],[34]) ).
thf(497,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A ) @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ A ) @ C ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__inf__absorb_0) ).
thf(1769,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A ) @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ A ) @ C ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).
thf(180,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1 @ A @ B @ C ) @ B @ C @ C ) @ A @ ( tc_prod @ C @ C ) ) )
| ( hBOOL @ ( c_in @ B @ ( c_Wellfounded_Oacc @ A @ C ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__acc__down_0) ).
thf(1088,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1 @ A @ B @ C ) @ B @ C @ C ) @ A @ ( tc_prod @ C @ C ) ) )
| ( hBOOL @ ( c_in @ B @ ( c_Wellfounded_Oacc @ A @ C ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(643,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
| ~ ( c_lessequals @ A @ ( hAPP @ ( c_Relation_OImage @ C @ B @ B ) @ A ) @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_Wellfounded_Owf @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wfE__pf_0) ).
thf(2087,plain,
! [C: $i,B: $i,A: $i] :
( ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_bool ) ) )
| ~ ( c_lessequals @ A @ ( hAPP @ ( c_Relation_OImage @ C @ B @ B ) @ A ) @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_Wellfounded_Owf @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[643]) ).
thf(172,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( c_COMBB @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) @ ( tc_fun @ C @ tc_bool ) @ E ) @ E @ ( tc_fun @ C @ tc_bool ) )
= ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ D @ E @ ( tc_fun @ C @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__simps_I7_J_0) ).
thf(1069,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ ( c_COMBB @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) @ ( tc_fun @ C @ tc_bool ) @ E ) @ E @ ( tc_fun @ C @ tc_bool ) )
= ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ A @ D @ E @ ( tc_fun @ C @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(578,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ A ) @ C )
!= B )
| ( c_lessequals @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__inf_1) ).
thf(1944,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ A ) @ C )
!= B )
| ( c_lessequals @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).
thf(312,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( c_COMBK @ B @ ( tc_fun @ C @ tc_bool ) @ A ) @ A @ ( tc_fun @ C @ tc_bool ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__constant_0) ).
thf(1367,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Complete__Lattice_Ocomplete__lattice__class_OINFI @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_bool ) ) @ ( c_COMBK @ B @ ( tc_fun @ C @ tc_bool ) @ A ) @ A @ ( tc_fun @ C @ tc_bool ) )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(355,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_ORange @ ( hAPP @ ( c_Set_Oinsert @ ( c_Pair @ A @ B @ C @ D ) @ ( tc_prod @ C @ D ) ) @ E ) @ C @ D )
= ( hAPP @ ( c_Set_Oinsert @ B @ D ) @ ( c_Relation_ORange @ E @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__insert_0) ).
thf(1463,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_ORange @ ( hAPP @ ( c_Set_Oinsert @ ( c_Pair @ A @ B @ C @ D ) @ ( tc_prod @ C @ D ) ) @ E ) @ C @ D )
= ( hAPP @ ( c_Set_Oinsert @ B @ D ) @ ( c_Relation_ORange @ E @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(403,axiom,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) ) @ ( c_Transitive__Closure_Ortrancl @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ C ) @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__Un__subset_0) ).
thf(1565,plain,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) ) @ ( c_Transitive__Closure_Ortrancl @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ C ) @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(87,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Relation_OImage @ A @ B @ C ) @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ ( tc_fun @ B @ tc_bool ) ) @ E ) )
= ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( hAPP @ ( c_Relation_OImage @ A @ B @ C ) @ D ) @ ( tc_fun @ C @ tc_bool ) ) @ ( hAPP @ ( c_Relation_OImage @ A @ B @ C ) @ E ) ) )
| ~ ( c_Relation_Osingle__valued @ ( c_Relation_Oconverse @ A @ B @ C ) @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__Int__eq_0) ).
thf(882,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Relation_OImage @ A @ B @ C ) @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ ( tc_fun @ B @ tc_bool ) ) @ E ) )
= ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( hAPP @ ( c_Relation_OImage @ A @ B @ C ) @ D ) @ ( tc_fun @ C @ tc_bool ) ) @ ( hAPP @ ( c_Relation_OImage @ A @ B @ C ) @ E ) ) )
| ~ ( c_Relation_Osingle__valued @ ( c_Relation_Oconverse @ A @ B @ C ) @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(683,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ C @ ( tc_prod @ B @ B ) ) )
| ~ ( c_Relation_Oirrefl @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_irrefl__def_0) ).
thf(2177,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( hBOOL @ ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ C @ ( tc_prod @ B @ B ) ) )
| ~ ( c_Relation_Oirrefl @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[683]) ).
thf(146,axiom,
! [B: $i,A: $i] :
( ( c_Relation_Otrans @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ ( c_Relation_OId @ B ) ) @ B )
| ~ ( c_Relation_Otrans @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__reflclI_0) ).
thf(1014,plain,
! [B: $i,A: $i] :
( ( c_Relation_Otrans @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ ( c_Relation_OId @ B ) ) @ B )
| ~ ( c_Relation_Otrans @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(334,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( hAPP @ ( c_Relation_OImage @ A @ B @ C ) @ D ) @ ( hAPP @ ( c_Relation_OImage @ E @ B @ C ) @ F ) @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ D @ F @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_lessequals @ A @ E @ ( tc_fun @ ( tc_prod @ B @ C ) @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__mono_0) ).
thf(1417,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( hAPP @ ( c_Relation_OImage @ A @ B @ C ) @ D ) @ ( hAPP @ ( c_Relation_OImage @ E @ B @ C ) @ F ) @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ D @ F @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_lessequals @ A @ E @ ( tc_fun @ ( tc_prod @ B @ C ) @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(544,axiom,
! [A: $i] :
( ( c_Relation_ODomain @ ( c_Relation_OId @ A ) @ A @ A )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__Id_0) ).
thf(1870,plain,
! [A: $i] :
( ( c_Relation_ODomain @ ( c_Relation_OId @ A ) @ A @ A )
= ( c_Orderings_Otop__class_Otop @ ( tc_fun @ A @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).
thf(31069,plain,
$false,
inference(cvc4,[status(thm)],[2163,1036,2094,760,1729,1899,893,1850,1982,941,1179,1295,1586,809,1024,1469,1369,1190,2109,1454,2031,1559,1105,1237,846,1950,1549,1554,1110,2077,977,1924,2231,1808,1205,1142,878,1971,1486,1158,762,2117,1406,730,1290,741,1073,1544,2014,1041,861,1655,1137,1310,715,2141,1872,1233,1327,1640,1063,1458,1164,797,2168,1260,1761,913,1354,2146,1507,930,1095,1196,1835,2046,782,1613,1243,1782,885,1046,1650,1645,1724,1475,2067,1529,1228,1254,1287,1709,1985,1298,719,1323,917,802,1826,1279,1992,1059,1330,1860,1264,2217,2185,1577,1832,934,1545,1800,2169,1147,2049,770,1398,1115,1568,2158,1362,1922,817,1892,1379,1319,1704,870,1479,1609,969,1347,1572,1815,1494,924,1465,2027,789,2090,1632,1828,1151,1020,1677,1960,966,1489,2237,1415,1302,756,1664,2105,1811,1682,834,1858,1864,2122,1283,2073,1169,1377,2190,734,1886,1119,1394,2137,1351,1345,1405,1201,1521,2205,1696,1975,981,766,1843,2058,2002,998,1604,2011,920,942,1691,1438,793,1306,1199,1153,1338,1915,2000,2083,1736,714,1868,798,1163,1274,1223,746,1343,778,1519,1123,1824,815,2132,1570,1174,1502,1751,820,1883,1560,1423,1938,1365,1920,1968,852,1296,1687,2213,757,2211,1128,1392,974,1012,1032,1602,1819,1624,2200,830,889,2179,1787,2181,1740,1910,842,1402,1592,1804,1328,1121,1064,1856,1425,1006,1878,1755,989,857,1360,1936,1234,1541,874,2115,1762,2100,1270,1772,1794,1953,1096,1672,2080,1584,1700,1214,1889,1419,1028,1082,2023,1964,1942,1659,901,1075,2053,2196,1791,2172,2038,1446,1016,1207,2085,837,1324,1249,1131,1552,1050,911,2006,1947,1852,1874,1429,1599,1715,1720,1979,1759,2125,1588,985,1451,738,1539,1456,1382,1266,2153,1192,1932,1627,1525,1434,2203,938,1241,2043,1071,953,718,1732,926,2208,805,1846,1054,1515,2221,1026,1895,1167,773,1996,1764,1754,1595,1374,2235,906,1135,1648,750,1510,1698,1103,2033,2149,1219,824,904,1833,732,1620,1752,2016,1388,743,826,1535,958,1226,2134,1615,1784,1652,1929,1139,1669,936,2029,1707,1312,787,713,1635,1239,1332,1092,804,947,1224,1356,1675,2166,1090,1194,2079,1408,2214,1349,996,1492,1144,880,764,979,1209,2119,2151,2229,784,1117,1574,1806,1048,736,863,2065,1667,811,1471,2111,1821,1862,848,1838,915,1022,1293,1177,2025,1080,1556,1460,932,1061,983,1926,768,780,2139,986,1113,1477,1496,1973,2069,1562,1841,1396,2051,1044,1245,1066,868,1775,1000,1726,1364,1250,1694,922,1413,1034,1583,1304,2107,1203,944,1467,795,1905,1684,1509,1990,1340,1018,1958,754,836,1662,2096,968,1181,855,872,971,1252,2175,1780,1098,993,1547,1748,712,1003,1611,1156,2060,1400,2192,887,1566,2143,1230,1484,2160,2092,1432,791,1038,717,1262,2219,1901,1679,1579,1711,1499,1987,2224,1813,1300,1637,1188,1186,840,1785,1317,1830,1085,1658,1285,1738,1934,744,1766,2113,1802,1702,1221,1052,727,1797,1008,1717,1372,876,859,2056,1358,1898,1257,1353,1955,1749,1427,1881,1272,991,1617,1940,1421,2045,1966,1949,1817,1844,2194,1517,759,1126,1866,1734,1108,1998,1918,1316,1321,1913,1216,891,1448,2187,1010,1390,844,2226,1326,963,2174,1674,1481,1745,1854,1276,1590,813,1385,1721,896,2098,748,946,1101,1629,2004,1523,2130,2009,1030,1689,2041,1777,1440,1077,1513,899,832,1994,2019,1308,2198,2183,1212,1893,2036,1444,1442,716,1161,800,1908,1133,1512,2155,950,2233,818,1876,1527,1248,1757,865,1642,2102,752,1436,1314,1657,807,828,720,955,1335,2070,1172,1410,1056,1789,2223,960,1473,2021,2063,1742,928,1977,1268,1532,1537,1582,1550,908,822,1597,1902,1093,1930,1236,2127,850,1713,1505,1621,1606,1962,1184,2018,1848,775,1769,1088,2087,1069,1944,1367,1463,1565,882,2177,1014,1417,1870]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : SCT020-1 : TPTP v8.1.2. Released v4.1.0.
% 0.11/0.16 % Command : run_Leo-III %s %d
% 0.16/0.37 % Computer : n013.cluster.edu
% 0.16/0.37 % Model : x86_64 x86_64
% 0.16/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.37 % Memory : 8042.1875MB
% 0.16/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.37 % CPULimit : 300
% 0.16/0.37 % WCLimit : 300
% 0.16/0.37 % DateTime : Thu May 18 15:30:21 EDT 2023
% 0.16/0.37 % CPUTime :
% 0.85/0.86 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.71/1.12 % [INFO] Parsing done (263ms).
% 1.71/1.13 % [INFO] Running in sequential loop mode.
% 2.58/1.35 % [INFO] eprover registered as external prover.
% 2.58/1.35 % [INFO] cvc4 registered as external prover.
% 2.58/1.35 % [INFO] Scanning for conjecture ...
% 3.02/1.50 % [INFO] Found a conjecture and 704 axioms. Running axiom selection ...
% 3.80/1.66 % [INFO] Axiom selection finished. Selected 702 axioms (removed 2 axioms).
% 4.66/1.85 % [INFO] Problem is propositional (TPTP CNF).
% 4.66/1.86 % [INFO] Type checking passed.
% 4.66/1.86 % [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 ...
% 104.51/21.02 % External prover 'cvc4' found a proof!
% 104.51/21.02 % [INFO] Killing All external provers ...
% 104.51/21.03 % Time passed: 20500ms (effective reasoning time: 19892ms)
% 104.51/21.03 % 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)>
% 104.51/21.03 % Axioms used in derivation (702): cls_trancl__converseD_0, cls_inf__sup__aci_I2_J_0, cls_Diff__cancel_0, cls_converse__tranclE_1, cls_in__mktop_1, cls_Int__absorb2_0, cls_subset__insert_1, cls_Diff__iff_2, cls_rtrancl__idemp_0, cls_bex__UNIV_2, cls_bot__fun__eq_0, cls_equiv__class__eq__iff_0, cls_sym__conv__converse__eq_1, cls_cuts__eq_1, cls_top__fun__eq_0, cls_inf__sup__absorb_0, cls_Int__Un__distrib_0, clsarity_fun__Lattices_Olower__semilattice, cls_Range__Un__eq_0, cls_sup__ge1_0, cls_image__constant_0, cls_INT__simps_I7_J_0, cls_insertE_0, cls_rtrancl__converseD_0, cls_wf__subset_0, cls_insert__inter__insert_0, cls_Un__Diff_0, cls_congruent_Ocongruent_0, cls_Un__subset__iff_0, cls_splitD_H_0, cls_order__eq__iff_0, cls_total__on__def_0, cls_converseI_0, cls_equalityI_0, cls_Id__onE_0, cls_single__valuedD_0, cls_wf__acyclic_0, cls_sup__top__left_0, cls_Image__INT__eq_0, cls_subset__empty_1, cls_subset__image__iff_2, cls_trancl__subset__Sigma__aux_0, cls_Image__singleton__iff_0, cls_empty__is__image_1, cls_wfE__min_0, cls_single__valued__Id__on_0, cls_strict__linear__order__on__def_0, cls_le__funD_0, cls_image__mono_0, cls_tranclD2_0, cls_sup__bot__right_0, cls_insert__code_1, cls_Un__empty__left_0, cls_INT__extend__simps_I5_J_0, cls_trancl_Ocases_0, cls_trans__def_1, cls_ball__UNIV_2, cls_INT__D_0, clsarity_bool__Lattices_Olower__semilattice, cls_Id__O__R_0, cls_le__iff__inf_1, cls_Un__upper1_0, clsarity_fun__Orderings_Oorder, cls_COMBK__def_0, cls_distrib__sup__le_0, cls_Int__mono_0, cls_Range__def_0, cls_inf__sup__aci_I6_J_0, cls_Id__on__eqI_0, cls_Un__commute_0, cls_acc_Oinduct_2, cls_irrefl__def_0, cls_acc__wfD_0, cls_UnCI_1, cls_tranclD_0, cls_Diff__Un_0, cls_Int__insert__left_0, cls_insert__absorb_0, cls_comp__equivI_0, cls_empty__iff_0, cls_trans__diff__Id_0, cls_le__inf__iff_1, clsarity_bool__HOL_Ominus, cls_mem__def_1, cls_wf__inv__image_0, cls_equiv__class__self_0, cls_Int__subset__iff_2, cls_Domain__iff_0, cls_Diff__subset__conv_0, cls_Domain__rtrancl_0, cls_Int__Un__distrib2_0, cls_rtrancl__trans_0, cls_inf1E_1, cls_Diff__triv_0, cls_wf__union__compatible_0, cls_insert__subset_0, cls_Int__absorb1_0, cls_sup__inf__distrib2_0, clsarity_fun__Lattices_Oupper__semilattice, cls_antisymD_0, cls_refl__on__converse_0, cls_le__sup__iff_0, cls_wf__induct__rule_0, cls_Image__Un_0, cls_in__mkbot_4, cls_INT__simps_I4_J_0, cls_insert__iff_1, cls_refl__Id_0, cls_inf__sup__distrib1_0, cls_Diff__insert_0, cls_set__rev__mp_0, cls_insert__Diff__if_1, cls_inf__left__commute_0, cls_Times__subset__cancel2_1, cls_acc_Oinducts_0, cls_transI_0, cls_COMBB__def_0, cls_INT__absorb_0, cls_congruent2_Ocongruent2_0, cls_inf__commute_0, cls_trans__converse_1, cls_subset__insert__iff_2, cls_INT__insert__distrib_0, cls_Range__Id__on_0, cls_refl__on__Id__on_0, clsarity_fun__Orderings_Otop, cls_Un__left__commute_0, cls_wf__converse__trancl_0, cls_DomainE_0, cls_INTER__UNIV__conv_I2_J_2, cls_single__valued__Id_0, cls_rtrancl__trancl__absorb_0, cls_rtrancl__into__trancl1_0, cls_INF__leI_0, clsarity_bool__HOL_Oord, cls_set__mp_0, cls_cut__apply_0, cls_Un__Int__distrib2_0, cls_bex__UNIV_1, cls_Int__empty__right_0, cls_INT__extend__simps_I3_J_0, cls_Image__iff_0, cls_sym__Id__on_0, cls_sym__Id_0, cls_equiv__class__eq__iff_3, cls_le__supI_0, cls_Un__subset__iff_1, cls_rtrancl__unfold_0, cls_Un__empty_2, cls_le__iff__sup_1, cls_INT__subset__iff_0, cls_inf__fun__eq_0, cls_rel__compEpair_0, cls_rtrancl__mono_0, cls_INT__empty_0, cls_total__on__def_3, cls_antisym__converse_0, cls_Image__subset_0, cls_empty__is__image_0, cls_order__eq__refl_0, cls_rangeI_0, cls_converse__rtrancl__into__rtrancl_0, cls_wfE__min_1, cls_Image__empty_0, cls_range__composition_0, clsarity_fun__Orderings_Obot, cls_Image__iff_1, cls_le__supE_1, cls_le__iff__sup_0, cls_wf__insert_0, cls_Domain__Id_0, cls_rtrancl__reflcl_0, cls_rev__image__eqI_0, cls_INT__constant_0, cls_Diff__UNIV_0, cls_in__mktop_3, cls_rel__comp__distrib2_0, cls_wf__induct_1, cls_Sup__UNIV_0, cls_tranclE_1, cls_wf__acc__iff_1, cls_sym__trancl_0, cls_r__into__trancl_H_0, cls_acc__wfI_0, cls_Un__absorb2_0, cls_trancl__into__trancl2_0, cls_inf__sup__aci_I8_J_0, cls_Un__empty__right_0, cls_insert__ident_0, cls_image__constant__conv_1, cls_Image__Id__on_0, cls_Range__converse_0, cls_cuts__eq_0, cls_UNIV__eq__I_0, cls_Un__UNIV__right_0, cls_SigmaI_0, clsarity_bool__Orderings_Oorder, cls_bot__least_0, cls_INTER__UNIV__conv_I2_J_1, cls_rtrancl__eq__or__trancl_0, cls_wf__induct__rule_1, cls_Sigma__Diff__distrib1_0, cls_sup__eq__bot__eq2_0, cls_refl__on__def_1, cls_total__on__diff__Id_1, cls_Int__insert__right_1, cls_sym__Un_0, cls_r__r__into__trancl_0, cls_trancl_Ocases_1, cls_wf__trancl_0, cls_Sup__singleton_0, cls_trans__rtrancl_0, cls_RangeE_0, cls_antisym__reflcl_1, cls_Range__def__raw_0, cls_antisym__Id__on_0, cls_UnCI_0, cls_not__acc__down_1, cls_Un__upper2_0, cls_Image__INT__subset_0, cls_inf__top__right_0, cls_rtrancl__converse_0, cls_INTER__UNIV__conv_I1_J_2, cls_subset__iff_0, cls_insert__code_2, cls_INT__extend__simps_I10_J_0, cls_wf__comp__self_0, cls_trans__O__subset_0, clsarity_fun__HOL_Oord, cls_in__mkbot_3, cls_rev__predicate1D_0, cls_converse__Un_0, cls_inf__eq__top__eq1_0, cls_insert__Diff__single_0, cls_singleton__iff_1, cls_r__comp__rtrancl__eq_0, cls_single__valued__rel__comp_0, cls_Diff__idemp_0, cls_trans__def_2, cls_subset__empty_0, cls_rel__comp__distrib_0, cls_equiv__class__eq_0, cls_sym__converse_1, cls_wf__eq__minimal_0, cls_image__insert_0, cls_equiv_Otrans_0, cls_acc__downwards__aux_0, cls_inf__absorb2_0, cls_wf__def_1, cls_tranclD_1, cls_UNIV__not__empty_0, cls_strict__linear__order__on__def_1, cls_Range__iff_0, cls_acc__induct_2, cls_doubleton__eq__iff_2, cls_subset__insert__iff_3, cls_diff__single__insert_0, cls_Range__iff_1, cls_wf__comp__self_1, clsarity_bool__Lattices_Oupper__semilattice, cls_Sup__binary_0, cls_ball__UNIV_1, cls_Un__insert__left_0, cls_inf__sup__ord_I2_J_0, cls_pair__in__Id__conv_0, cls_wf__irrefl_0, cls_rtrancl__Un__rtrancl_0, cls_IdE_0, cls_SigmaD2_0, cls_set__eq__subset_2, cls_Un__mono_0, cls_Int__insert__left_1, cls_insert__subset_1, cls_Int__empty__left_0, cls_Image__singleton__iff_1, cls_INT__iff_0, cls_Un__INT__distrib_0, cls_INT__extend__simps_I2_J_0, cls_Range__Diff__subset_0, cls_Id__on__iff_0, cls_Range__insert_0, cls_sym__inv__image_0, cls_ex__in__conv_0, cls_sup__commute_0, cls_inf__sup__aci_I3_J_0, cls_trancl__reflcl_0, cls_trancl__domain_0, cls_converse__Id__on_0, cls_le__inf__iff_0, cls_Int__subset__iff_1, cls_Domain__Diff__subset_0, cls_refl__rtrancl_0, cls_rtrancl__reflcl__absorb_0, cls_DomainI_0, cls_transI_1, cls_Un__subset__iff_2, clsarity_fun__Lattices_Olattice, cls_INT__lower_0, cls_Un__empty_0, cls_linorder__linear_0, cls_Range__rtrancl_0, cls_total__on__def_5, cls_wf__asym_0, cls_in__mktop_5, cls_Int__assoc_0, cls_acc_Oinduct_1, cls_order__antisym_0, cls_order__trans_0, cls_acc__downwards_0, cls_wf__eq__minimal_1, 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cls_sup__top__right_0, cls_Diff__insert2_0, cls_sup__least_0, cls_subset__refl_0, cls_tranclE_0, cls_rev__ImageI_0, cls_Domain__converse_0, cls_trancl__converseI_0, cls_empty__subsetI_0, cls_top__greatest_0, cls_doubleton__eq__iff_0, cls_inf__sup__aci_I1_J_0, cls_trans__Id_0, cls_Un__absorb1_0, cls_sym__converse_0, cls_sup1E_0, cls_in__inv__image_1, cls_distrib__inf__le_0, cls_Int__commute_0, cls_Un__UNIV__left_0, cls_Sup__upper_0, cls_wfE__pf_0, cls_converse__iff_1, cls_refl__onD_0, cls_Pair__eq_0, cls_rtranclE_0, cls_singletonE_0, cls_Nitpick_Ortrancl__def_0, cls_image__diff__subset_0, cls_Image__mono_0, cls_Int__Diff_0, cls_image__iff_2, cls_insertCI_0, cls_le__infE_0, cls_image__Int__subset_0, cls_pair__in__Id__conv_1, cls_INT__simps_I2_J_1, cls_le__inf__iff_2, cls_tranclD2_1, cls_subset__equiv__class_0, cls_Un__Diff__cancel_0, cls_image__Un_0, cls_insert__Diff_0, cls_total__on__empty_0, cls_trans__def_3, cls_UNIV__I_0, cls_DiffE_0, cls_R__O__Id_0, cls_trancl__into__rtrancl_0, 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cls_antisym__Id_0, cls_trancl__rtrancl__absorb_0, cls_order__antisym__conv_0, cls_equiv_Osym_0, cls_total__on__def_1, cls_Int__lower1_0, cls_INT__extend__simps_I2_J_1, cls_trancl__range_0, cls_INTER__UNIV__conv_I1_J_1, cls_refl__on__converse_1, cls_strict__linear__order__on__def_2, cls_refl__onD1_0, clsarity_bool__Lattices_Obounded__lattice, cls_inf__sup__ord_I1_J_0, cls_le__infI_0, cls_Nitpick_Orefl_H__def_0, cls_Domain__Id__on_0, cls_equiv__type_0, cls_transI_2, clsarity_bool__Lattices_Olattice, cls_subset__insert__iff_4, cls_Int__subset__iff_0, cls_bot__empty__eq_0, cls_eq__eqI_0, cls_rtrancl__subset_0, cls_rtrancl__into__trancl2_0, cls_Un__Int__distrib_0, cls_Not__Domain__rtrancl_0, cls_converse__rel__comp_0, cls_acyclic__insert_2, cls_insert__subset_2, cls_le__supI1_0, cls_rtrancl__converseI_0, cls_sup__left__idem_0, cls_subsetD_0, cls_symD_0, cls_sym__def_0, cls_inf__idem_0, cls_single__valued__confluent_0, cls_inf__bot__left_0, cls_inf1I_0, cls_equiv_Orefl__on_0, cls_le__eqI_0, 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clsarity_bool__Complete__Lattice_Ocomplete__lattice, cls_tfl__wf__induct_0, cls_in__mktop_2, cls_INF1__E_0, cls_IntI_0, cls_in__inv__image_0, cls_inf__greatest_0, cls_Sup__empty_0, cls_Diff__empty_0, cls_Times__Un__distrib1_0, cls_Un__left__absorb_0, cls_converse__tranclE_0, cls_le__iff__inf_0, cls_rtrancl__eq__or__trancl_2, cls_insert__times__insert_0, cls_eq__eqI_1, cls_singleton__inject_0, cls_irrefl__diff__Id_0, cls_tfl__wf__induct_1, cls_Times__eq__cancel2_0, cls_Un__empty_1, cls_subset__insert_0, cls_sup__idem_0, cls_Times__Diff__distrib1_0, cls_emptyE_0, cls_antisym__subset_0, cls_acyclic__insert_0, cls_inf__sup__ord_I3_J_0, cls_congruent2__implies__congruent_0, cls_inf__sup__aci_I5_J_0, cls_INT__insert_0, cls_sup__eq__bot__eq1_0, cls_comm__monoid__add_Ononempty__iff_2, cls_trancl_Or__into__trancl_0, cls_Diff__Int_0, cls_rtrancl_Ortrancl__into__rtrancl_0, clsarity_fun__Orderings_Opreorder, cls_IntE_1, cls_rtrancl__subset__rtrancl_0, cls_trancl__unfold__right_0, cls_Int__greatest_0, cls_INT__Un_0, cls_Domain__insert_0, cls_sup__ge2_0, cls_sym__Un__converse_0, cls_sym__conv__converse__eq_0, cls_IntE_0, cls_in__mkbot_5, cls_Un__least_0, cls_in__rtrancl__UnI_0, cls_trancl__rtrancl__trancl_0, cls_sup1CI_0, cls_subset__Un__eq_1, cls_sup__left__commute_0, cls_in__rel__def_1, cls_rel__comp__subset__Sigma_0, cls_sym__trans__comp__subset_0, cls_le__infE_1, cls_Int__UNIV__left_0, cls_trans__trancl_0, cls_r__into__rtrancl_0, cls_rtrancl__idemp__self__comp_0, cls_insertCI_1, cls_doubleton__eq__iff_4, cls_wf__insert_2, clsarity_bool__Lattices_Odistrib__lattice, cls_mem__Sigma__iff_2, cls_image__eqI_0, cls_acc__downward_0, cls_acc__induct__rule_1, cls_subset__UNIV_0, cls_trancl__mono_0, cls_acyclic__subset_0, cls_rtrancl__Un__subset_0, cls_image__subset__iff_0, cls_acc__induct_0, cls_inf__le1_0, cls_rel__comp__mono_0, cls_refl__on__comp__subset_0, cls_inf__left__idem_0, cls_rtranclD_0, cls_mem__splitI_0, cls_single__valued__subset_0, cls_acc_OaccI_1, cls_Diff__subset__conv_1, cls_insert__code_0, cls_le__eqI_1, cls_INT__simps_I2_J_0, cls_INF__const_0, cls_acc_Oinducts_1, cls_trancl__unfold_0, cls_Transitive__Closure_Otrancl__into__trancl_0, cls_antisym__def_0, cls_Image__Int__eq_0, cls_total__on__converse_0, cls_trancl__trans_0, cls_INT__extend__simps_I7_J_0, cls_Un__Diff__Int_0, cls_subset__insertI_0, cls_Domain__mono_0, cls_Diff__Int2_0, cls_equiv__class__nondisjoint_0, cls_Un__Image_0, cls_DiffE_1, cls_le__infI2_0, cls_insert__image_0, cls_bex__UNIV_0, cls_Un__Int__assoc__eq_0, cls_refl__on__def_0, cls_INT__E_0, cls_insert__iff_2, cls_image__image_0, cls_Diff__insert__absorb_0, cls_Diff__partition_0, cls_equiv__comp__eq_0, cls_Domain__iff_1, cls_sup__bot__left_0, cls_acc__induct__rule_0, cls_disjoint__iff__not__equal_0, cls_INF1__D_0, cls_strict__linear__order__on__def_3, cls_Not__Domain__rtrancl_1, cls_wf__insert_1, cls_sup__inf__distrib1_0, cls_Nitpick_Orefl_H__def_1, cls_inf__top__left_0, cls_insert__commute_0, cls_trancl__subset__Sigma_0, cls_rtranclE_1, cls_INTER__UNIV__conv_I1_J_0, cls_equiv__class__eq__iff_2, cls_image__is__empty_0, cls_INT__constant_1, cls_Un__insert__right_0, cls_acyclic__impl__antisym__rtrancl_0, cls_equalityE_0, cls_inf__sup__distrib2_0, cls_trancl__converse_0, cls_imageI_0, clsarity_fun__HOL_Ominus, cls_acyclic__converse_1, cls_wf__Un_0, cls_antisym__converse_1, cls_total__on__def_2, cls_Pair__eq_1, clsarity_fun__Lattices_Odistrib__lattice, cls_wf__union__merge_1, cls_trans__def_0, cls_O__assoc_0, cls_inf__bot__right_0, cls_sup__absorb1_0, cls_not__acc__down_0, cls_rel__compEpair_1, cls_ball__empty_0, cls_Int__insert__right_0, cls_eq__equiv__class__iff_1, cls_empty__Diff_0, cls_acc__induct__rule_2, cls_tfl__cut__apply_0, cls_subset__insert__iff_1, clsarity_bool__Orderings_Otop, cls_in__mkbot_0, cls_Diff__subset_0, cls_predicate1D_0, cls_inf1E_0
% 104.51/21.03 % No. of inferences in proof: 1423
% 104.51/21.03 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 20500 ms resp. 19892 ms w/o parsing
% 105.62/21.37 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 105.62/21.37 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------