%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SCT023-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:27:02 AM UTC 2026
% Result : Unsatisfiable 29.43s 8.38s
% Output : Refutation 32.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 592
% Syntax : Number of formulae : 1185 ( 347 unt; 0 typ; 0 def)
% Number of atoms : 2486 ( 531 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 20627 (1212 ~;1301 |; 0 &;18114 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 11 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 92 ( 90 usr; 10 con; 0-6 aty)
% Number of variables : 4222 ( 0 ^;4222 !; 0 ?;4222 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_Relation_Otrans_decl,type,
c_Relation_Otrans: $i > $i > $o ).
thf(hAPP_decl,type,
hAPP: $i > $i > $i ).
thf(v_P_decl,type,
v_P: $i ).
thf(tc_Arrow__Order__Mirabelle_Oalt_decl,type,
tc_Arrow__Order__Mirabelle_Oalt: $i ).
thf(c_in_decl,type,
c_in: $i > $i > $i > $o ).
thf(c_Pair_decl,type,
c_Pair: $i > $i > $i > $i > $i ).
thf(tc_prod_decl,type,
tc_prod: $i > $i > $i ).
thf(v_a_decl,type,
v_a: $i ).
thf(v_b_decl,type,
v_b: $i ).
thf(v_F_decl,type,
v_F: $i > $i ).
thf(v_i_decl,type,
v_i: $i ).
thf(class_Lattices_Oupper__semilattice_decl,type,
class_Lattices_Oupper__semilattice: $i > $o ).
thf(c_Lattices_Oupper__semilattice__class_Osup_decl,type,
c_Lattices_Oupper__semilattice__class_Osup: $i > $i > $i > $i ).
thf(class_Orderings_Obot_decl,type,
class_Orderings_Obot: $i > $o ).
thf(tc_fun_decl,type,
tc_fun: $i > $i > $i ).
thf(class_Lattices_Odistrib__lattice_decl,type,
class_Lattices_Odistrib__lattice: $i > $o ).
thf(tc_bool_decl,type,
tc_bool: $i ).
thf(class_Lattices_Olattice_decl,type,
class_Lattices_Olattice: $i > $o ).
thf(c_Lattices_Olower__semilattice__class_Oinf_decl,type,
c_Lattices_Olower__semilattice__class_Oinf: $i > $i > $i > $i ).
thf(class_Lattices_Olower__semilattice_decl,type,
class_Lattices_Olower__semilattice: $i > $o ).
thf(class_Lattices_Obounded__lattice_decl,type,
class_Lattices_Obounded__lattice: $i > $o ).
thf(c_HOL_Ominus__class_Ominus_decl,type,
c_HOL_Ominus__class_Ominus: $i > $i > $i > $i ).
thf(c_Relation_Orel__comp_decl,type,
c_Relation_Orel__comp: $i > $i > $i > $i > $i > $i ).
thf(c_Relation_Oconverse_decl,type,
c_Relation_Oconverse: $i > $i > $i > $i ).
thf(c_Equiv__Relations_Oequiv_decl,type,
c_Equiv__Relations_Oequiv: $i > $i > $i > $o ).
thf(c_Relation_ODomain_decl,type,
c_Relation_ODomain: $i > $i > $i > $i ).
thf(c_Transitive__Closure_Ortrancl_decl,type,
c_Transitive__Closure_Ortrancl: $i > $i > $i ).
thf(c_Transitive__Closure_Otrancl_decl,type,
c_Transitive__Closure_Otrancl: $i > $i > $i ).
thf(c_Relation_OId_decl,type,
c_Relation_OId: $i > $i ).
thf(c_Set_Oinsert_decl,type,
c_Set_Oinsert: $i > $i > $i > $i ).
thf(c_Orderings_Obot__class_Obot_decl,type,
c_Orderings_Obot__class_Obot: $i > $i ).
thf(c_lessequals_decl,type,
c_lessequals: $i > $i > $i > $o ).
thf(c_Relation_Osym_decl,type,
c_Relation_Osym: $i > $i > $o ).
thf(c_Set_Oimage_decl,type,
c_Set_Oimage: $i > $i > $i > $i > $i ).
thf(c_Relation_Ototal__on_decl,type,
c_Relation_Ototal__on: $i > $i > $i > $o ).
thf(c_Order__Relation_Ostrict__linear__order__on_decl,type,
c_Order__Relation_Ostrict__linear__order__on: $i > $i > $i > $o ).
thf(c_Relation_ORange_decl,type,
c_Relation_ORange: $i > $i > $i > $i ).
thf(c_Relation_OImage_decl,type,
c_Relation_OImage: $i > $i > $i > $i > $i ).
thf(c_Wellfounded_Owf_decl,type,
c_Wellfounded_Owf: $i > $i > $o ).
thf(c_Wellfounded_Oacyclic_decl,type,
c_Wellfounded_Oacyclic: $i > $i > $o ).
thf(c_Product__Type_OSigma_decl,type,
c_Product__Type_OSigma: $i > $i > $i > $i > $i ).
thf(c_COMBK_decl,type,
c_COMBK: $i > $i > $i > $i ).
thf(class_OrderedGroup_Opordered__ab__group__add_decl,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
thf(c_Relation_Oantisym_decl,type,
c_Relation_Oantisym: $i > $i > $o ).
thf(class_HOL_Oord_decl,type,
class_HOL_Oord: $i > $o ).
thf(c_Relation_OId__on_decl,type,
c_Relation_OId__on: $i > $i > $i ).
thf(class_OrderedGroup_Oab__group__add_decl,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
thf(c_Relation_Orefl__on_decl,type,
c_Relation_Orefl__on: $i > $i > $i > $o ).
thf(c_Relation_Oinv__image_decl,type,
c_Relation_Oinv__image: $i > $i > $i > $i > $i ).
thf(c_Relation_Oirrefl_decl,type,
c_Relation_Oirrefl: $i > $i > $o ).
thf(c_Relation_Osingle__valued_decl,type,
c_Relation_Osingle__valued: $i > $i > $i > $o ).
thf(v_r_decl,type,
v_r: $i ).
thf(t_a_decl,type,
t_a: $i ).
thf(t_b_decl,type,
t_b: $i ).
thf(class_Orderings_Olinorder_decl,type,
class_Orderings_Olinorder: $i > $o ).
thf(hBOOL_decl,type,
hBOOL: $i > $o ).
thf(c_Equiv__Relations_Ocongruent2_decl,type,
c_Equiv__Relations_Ocongruent2: $i > $i > $i > $i > $i > $i > $o ).
thf(c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1_decl,type,
c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1: $i > $i > $i > $i > $i ).
thf(c_Wellfounded_Oacc_decl,type,
c_Wellfounded_Oacc: $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Relation__XtransI__1__1_decl,type,
c_ATP__Linkup_Osko__Relation__XtransI__1__1: $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Relation__XtransI__1__2_decl,type,
c_ATP__Linkup_Osko__Relation__XtransI__1__2: $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1_decl,type,
c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1: $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1_decl,type,
c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1: $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1_decl,type,
c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1: $i > $i > $i > $i ).
thf(c_Nitpick_Orefl_H_decl,type,
c_Nitpick_Orefl_H: $i > $i > $o ).
thf(c_Recdef_Ocut_decl,type,
c_Recdef_Ocut: $i > $i > $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1_decl,type,
c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1: $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1_decl,type,
c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1: $i > $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1_decl,type,
c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1: $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Relation__XImageE__1__1_decl,type,
c_ATP__Linkup_Osko__Relation__XImageE__1__1: $i > $i > $i > $i > $i > $i ).
thf(c_Arrow__Order__Mirabelle_Omkbot_decl,type,
c_Arrow__Order__Mirabelle_Omkbot: $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1_decl,type,
c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1: $i > $i > $i > $i ).
thf(c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1_decl,type,
c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1: $i > $i > $i ).
thf(c_split_decl,type,
c_split: $i > $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Relation__Xtrans__def__1__1_decl,type,
c_ATP__Linkup_Osko__Relation__Xtrans__def__1__1: $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Relation__Xtrans__def__1__3_decl,type,
c_ATP__Linkup_Osko__Relation__Xtrans__def__1__3: $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Product__Type__XSigma__mono__1__1_decl,type,
c_ATP__Linkup_Osko__Product__Type__XSigma__mono__1__1: $i > $i > $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Relation__XDomainE__1__1_decl,type,
c_ATP__Linkup_Osko__Relation__XDomainE__1__1: $i > $i > $i > $i > $i ).
thf(c_Arrow__Order__Mirabelle_Omktop_decl,type,
c_Arrow__Order__Mirabelle_Omktop: $i > $i > $i ).
thf(v_sko__Wellfounded__Xacc__Xinduct__1_decl,type,
v_sko__Wellfounded__Xacc__Xinduct__1: $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1_decl,type,
c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1: $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Relation__Xtrans__def__1__2_decl,type,
c_ATP__Linkup_Osko__Relation__Xtrans__def__1__2: $i > $i > $i ).
thf(c_Equiv__Relations_Ocongruent_decl,type,
c_Equiv__Relations_Ocongruent: $i > $i > $i > $i > $o ).
thf(v_sko__Wellfounded__Xacc__Xinducts__1_decl,type,
v_sko__Wellfounded__Xacc__Xinducts__1: $i > $i > $i ).
thf(c_FunDef_Oin__rel_decl,type,
c_FunDef_Oin__rel: $i > $i > $i > $i > $i > $o ).
thf(c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1_decl,type,
c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1: $i > $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Relation__XImage__iff__1__1_decl,type,
c_ATP__Linkup_Osko__Relation__XImage__iff__1__1: $i > $i > $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Relation__XtransI__1__3_decl,type,
c_ATP__Linkup_Osko__Relation__XtransI__1__3: $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Relation__XRange__iff__1__1_decl,type,
c_ATP__Linkup_Osko__Relation__XRange__iff__1__1: $i > $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Relation__XRangeE__1__1_decl,type,
c_ATP__Linkup_Osko__Relation__XRangeE__1__1: $i > $i > $i > $i > $i ).
thf(404,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( B @ ( A @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_r__into__rtrancl_0) ).
thf(1454,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( B @ ( A @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(237,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( C @ ( B @ c_Relation_Oconverse ) ) @ ( A @ c_Relation_Ototal__on ) ) )
| ( C @ ( B @ ( A @ c_Relation_Ototal__on ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_total__on__converse_0) ).
thf(1105,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( C @ ( B @ c_Relation_Oconverse ) ) @ ( A @ c_Relation_Ototal__on ) ) )
| ( C @ ( B @ ( A @ c_Relation_Ototal__on ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(533,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( G @ ( H @ ( F @ c_Equiv__Relations_Oequiv ) ) )
| ~ ( E @ ( D @ ( G @ ( B @ ( A @ ( H @ c_Equiv__Relations_Ocongruent2 ) ) ) ) ) )
| ~ ( G @ ( F @ ( C @ c_in ) ) )
| ( E @ ( D @ ( C @ ( B @ hAPP ) @ ( A @ c_Equiv__Relations_Ocongruent ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_congruent2__implies__congruent_0) ).
thf(1729,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( G @ ( H @ ( F @ c_Equiv__Relations_Oequiv ) ) )
| ~ ( E @ ( D @ ( G @ ( B @ ( A @ ( H @ c_Equiv__Relations_Ocongruent2 ) ) ) ) ) )
| ~ ( G @ ( F @ ( C @ c_in ) ) )
| ( E @ ( D @ ( C @ ( B @ hAPP ) @ ( A @ c_Equiv__Relations_Ocongruent ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).
thf(227,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
!= ( A @ ( C @ ( B @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__not__insert_0) ).
thf(1083,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
!= ( A @ ( C @ ( B @ c_Set_Oinsert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(271,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
!= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__not__empty_0) ).
thf(1179,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
!= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(83,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ ( A @ c_COMBK ) ) @ c_Set_Oimage ) ) ) )
= ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__constant__conv_0) ).
thf(777,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ ( A @ c_COMBK ) ) @ c_Set_Oimage ) ) ) )
= ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(25,axiom,
tc_bool @ class_Lattices_Oupper__semilattice,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oupper__semilattice) ).
thf(645,plain,
tc_bool @ class_Lattices_Oupper__semilattice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(137,axiom,
! [B: $i,A: $i] : ( B @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Relation_Osym ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sym__Un__converse_0) ).
thf(892,plain,
! [B: $i,A: $i] : ( B @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Relation_Osym ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(465,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ ( B @ tc_prod ) @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
| ~ ( C @ ( B @ ( D @ c_Relation_Osingle__valued ) ) )
| ( C @ ( B @ ( A @ c_Relation_Osingle__valued ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_single__valued__subset_0) ).
thf(1586,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ ( B @ tc_prod ) @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
| ~ ( C @ ( B @ ( D @ c_Relation_Osingle__valued ) ) )
| ( C @ ( B @ ( A @ c_Relation_Osingle__valued ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(424,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ c_Wellfounded_Oacyclic ) )
| ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
| ( B @ ( A @ c_Wellfounded_Oacyclic ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acyclic__subset_0) ).
thf(1501,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ c_Wellfounded_Oacyclic ) )
| ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
| ( B @ ( A @ c_Wellfounded_Oacyclic ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(266,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_Orderings_Obot__class_Obot ) )
| ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
!= ( A @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Lattices_Obounded__lattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__eq__bot__eq2_0) ).
thf(1168,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_Orderings_Obot__class_Obot ) )
| ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
!= ( A @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Lattices_Obounded__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(75,axiom,
! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__subset_0) ).
thf(760,plain,
! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(300,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( D @ ( C @ ( B @ ( A @ c_Relation_Oinv__image ) ) ) @ c_Relation_Oconverse ) ) )
= ( D @ ( C @ ( B @ ( C @ ( C @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_Oinv__image ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_converse__inv__image_0) ).
thf(1237,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( D @ ( C @ ( B @ ( A @ c_Relation_Oinv__image ) ) ) @ c_Relation_Oconverse ) ) )
= ( D @ ( C @ ( B @ ( C @ ( C @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_Oinv__image ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(115,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__disjoint_0) ).
thf(846,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(18,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__left__commute_0) ).
thf(628,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(204,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Transitive__Closure_Otrancl ) )
= ( B @ ( B @ ( B @ ( A @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_Relation_Orel__comp ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trancl__unfold__right_0) ).
thf(1031,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Transitive__Closure_Otrancl ) )
= ( B @ ( B @ ( B @ ( A @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_Relation_Orel__comp ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(138,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( tc_bool @ ( D @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Relation_Oconverse ) ) )
= ( tc_bool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ ( C @ ( B @ c_Relation_Oconverse ) ) @ ( D @ ( C @ ( A @ c_Relation_Oconverse ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_converse__Un_0) ).
thf(893,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( tc_bool @ ( D @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Relation_Oconverse ) ) )
= ( tc_bool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ ( C @ ( B @ c_Relation_Oconverse ) ) @ ( D @ ( C @ ( A @ c_Relation_Oconverse ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(585,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ c_Relation_Oantisym ) )
| ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_antisym__def_0) ).
thf(1840,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ c_Relation_Oantisym ) )
| ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[585]) ).
thf(34,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Lattices_Olattice )
| ( B @ ( A @ tc_fun ) @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olower__semilattice) ).
thf(666,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Lattices_Olattice )
| ( B @ ( A @ tc_fun ) @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(573,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( B @ c_in ) ) )
| ( E @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__eqI_0) ).
thf(1818,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( B @ c_in ) ) )
| ( E @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).
thf(262,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( D @ c_lessequals ) ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
!= ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Int__assoc__eq_0) ).
thf(1158,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( D @ c_lessequals ) ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
!= ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(192,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G @ ( E @ ( C @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Relation_Orel__comp ) ) ) ) @ c_Relation_Orel__comp ) ) ) ) )
= ( G @ ( D @ ( C @ ( G @ ( E @ ( D @ ( F @ ( B @ c_Relation_Orel__comp ) ) ) ) @ ( A @ c_Relation_Orel__comp ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_O__assoc_0) ).
thf(1005,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G @ ( E @ ( C @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Relation_Orel__comp ) ) ) ) @ c_Relation_Orel__comp ) ) ) ) )
= ( G @ ( D @ ( C @ ( G @ ( E @ ( D @ ( F @ ( B @ c_Relation_Orel__comp ) ) ) ) @ ( A @ c_Relation_Orel__comp ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(40,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Diff_0) ).
thf(683,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(220,axiom,
! [B: $i,A: $i] : ( B @ ( B @ ( B @ ( A @ c_Relation_OId__on ) @ c_Relation_Osingle__valued ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_single__valued__Id__on_0) ).
thf(1068,plain,
! [B: $i,A: $i] : ( B @ ( B @ ( B @ ( A @ c_Relation_OId__on ) @ c_Relation_Osingle__valued ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(481,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( F @ c_in ) ) )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( E @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ ( D @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_COMBK ) ) @ ( E @ c_Product__Type_OSigma ) ) ) @ ( C @ ( D @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_COMBK ) ) @ ( A @ c_Product__Type_OSigma ) ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Times__subset__cancel2_1) ).
thf(1618,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( F @ c_in ) ) )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( E @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ ( D @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_COMBK ) ) @ ( E @ c_Product__Type_OSigma ) ) ) @ ( C @ ( D @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_COMBK ) ) @ ( A @ c_Product__Type_OSigma ) ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).
thf(187,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__insert__left_0) ).
thf(994,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Set_Oinsert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(389,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ ( B @ tc_prod ) @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( B @ ( D @ c_Relation_ODomain ) ) @ ( C @ ( B @ ( A @ c_Relation_ODomain ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Domain__mono_0) ).
thf(1422,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ ( B @ tc_prod ) @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( B @ ( D @ c_Relation_ODomain ) ) @ ( C @ ( B @ ( A @ c_Relation_ODomain ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(445,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ~ ( D @ ( B @ hAPP ) @ hBOOL )
| ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf1I_0) ).
thf(1544,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ~ ( D @ ( B @ hAPP ) @ hBOOL )
| ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(127,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( A @ c_in ) ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__insert__left_1) ).
thf(873,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( A @ c_in ) ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(129,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__least_0) ).
thf(878,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(563,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_in ) ) )
| ~ ( D @ ( C @ ( A @ c_in ) ) )
| ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__iff_2) ).
thf(1793,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_in ) ) )
| ~ ( D @ ( C @ ( A @ c_in ) ) )
| ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).
thf(209,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__eqI_0) ).
thf(1041,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(592,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( A @ ( C @ c_lessequals ) ) )
| ( tc_bool @ ( B @ tc_fun ) @ ( B @ ( C @ c_Wellfounded_Oacc ) @ ( B @ ( A @ c_Wellfounded_Oacc ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acc__subset_0) ).
thf(1855,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( A @ ( C @ c_lessequals ) ) )
| ( tc_bool @ ( B @ tc_fun ) @ ( B @ ( C @ c_Wellfounded_Oacc ) @ ( B @ ( A @ c_Wellfounded_Oacc ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[592]) ).
thf(281,axiom,
! [B: $i,A: $i] : ( B @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Relation_Osym ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sym__Int__converse_0) ).
thf(1200,plain,
! [B: $i,A: $i] : ( B @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Relation_Osym ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(254,axiom,
! [B: $i,A: $i] : ( A @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Relation_Ototal__on ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_total__on__empty_0) ).
thf(1142,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Relation_Ototal__on ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(316,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_Relation_Osym ) )
| ( B @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_Relation_Osym ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sym__rtrancl_0) ).
thf(1269,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_Relation_Osym ) )
| ( B @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_Relation_Osym ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(11,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( B @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__commute_0) ).
thf(614,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( B @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(38,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__assoc_0) ).
thf(677,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(332,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_Wellfounded_Oacyclic ) )
| ( B @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_Relation_Oantisym ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acyclic__impl__antisym__rtrancl_0) ).
thf(1305,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_Wellfounded_Oacyclic ) )
| ( B @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_Relation_Oantisym ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(2,negated_conjecture,
! [B: $i,A: $i] :
~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( B @ ( v_P @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(597,plain,
! [B: $i,A: $i] :
~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( B @ ( v_P @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(422,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( A @ c_in ) ) )
| ~ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
| ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Transitive__Closure_Otrancl ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trancl__mono_0) ).
thf(1497,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( A @ c_in ) ) )
| ~ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
| ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Transitive__Closure_Otrancl ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(476,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ c_Wellfounded_Owf ) )
| ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acc__wfD_0) ).
thf(1608,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ c_Wellfounded_Owf ) )
| ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).
thf(498,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( E @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( D @ hAPP ) @ ( C @ ( B @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_HOL_Oord ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__funD_0) ).
thf(1655,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( E @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( D @ hAPP ) @ ( C @ ( B @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_HOL_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).
thf(335,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ hAPP ) @ hBOOL )
| ( B @ ( C @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup1E_0) ).
thf(1310,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ hAPP ) @ hBOOL )
| ( B @ ( C @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(536,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( D @ ( B @ c_Relation_ORange ) ) @ ( A @ c_in ) ) )
| ( C @ ( D @ tc_prod ) @ ( B @ ( C @ ( D @ ( A @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__XRange__iff__1__1 ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Range__iff_0) ).
thf(1735,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( D @ ( B @ c_Relation_ORange ) ) @ ( A @ c_in ) ) )
| ( C @ ( D @ tc_prod ) @ ( B @ ( C @ ( D @ ( A @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__XRange__iff__1__1 ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).
thf(343,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ ( F @ ( H @ ( A @ ( G @ ( I @ c_Equiv__Relations_Ocongruent2 ) ) ) ) ) )
| ~ ( H @ ( H @ tc_prod ) @ ( I @ ( H @ ( H @ ( D @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( F @ ( F @ tc_prod ) @ ( G @ ( F @ ( F @ ( E @ ( C @ c_Pair ) ) ) @ c_in ) ) )
| ( ( C @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( E @ ( D @ ( A @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_congruent2_Ocongruent2_0) ).
thf(1327,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ ( F @ ( H @ ( A @ ( G @ ( I @ c_Equiv__Relations_Ocongruent2 ) ) ) ) ) )
| ~ ( H @ ( H @ tc_prod ) @ ( I @ ( H @ ( H @ ( D @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( F @ ( F @ tc_prod ) @ ( G @ ( F @ ( F @ ( E @ ( C @ c_Pair ) ) ) @ c_in ) ) )
| ( ( C @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( E @ ( D @ ( A @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(492,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl_Ortrancl__into__rtrancl_0) ).
thf(1640,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).
thf(165,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ c_Relation_Osym ) )
| ( D @ ( D @ ( C @ ( B @ ( A @ c_Relation_Oinv__image ) ) ) @ c_Relation_Osym ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sym__inv__image_0) ).
thf(945,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ c_Relation_Osym ) )
| ( D @ ( D @ ( C @ ( B @ ( A @ c_Relation_Oinv__image ) ) ) @ c_Relation_Osym ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(218,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Wellfounded_Owf ) )
| ( B @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( B @ ( B @ ( A @ ( C @ c_Relation_Orel__comp ) ) ) ) @ ( B @ ( B @ ( B @ ( A @ ( A @ c_Relation_Orel__comp ) ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Wellfounded_Owf ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__union__merge_0) ).
thf(1063,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Wellfounded_Owf ) )
| ( B @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( B @ ( B @ ( A @ ( C @ c_Relation_Orel__comp ) ) ) ) @ ( B @ ( B @ ( B @ ( A @ ( A @ c_Relation_Orel__comp ) ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Wellfounded_Owf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(356,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_in ) ) )
| ( D @ ( C @ ( A @ c_in ) ) )
| ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_DiffI_0) ).
thf(1354,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_in ) ) )
| ( D @ ( C @ ( A @ c_in ) ) )
| ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(427,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_in ) ) )
| ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__absorb_0) ).
thf(1507,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_in ) ) )
| ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(406,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( C @ ( C @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ c_COMBK ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Product__Type_OSigma ) ) ) )
= ( tc_bool @ ( E @ ( C @ tc_prod ) @ tc_fun ) @ ( E @ ( C @ ( C @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ c_COMBK ) ) @ ( B @ c_Product__Type_OSigma ) ) ) @ ( E @ ( C @ ( C @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ c_COMBK ) ) @ ( A @ c_Product__Type_OSigma ) ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Times__Diff__distrib1_0) ).
thf(1458,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( C @ ( C @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ c_COMBK ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Product__Type_OSigma ) ) ) )
= ( tc_bool @ ( E @ ( C @ tc_prod ) @ tc_fun ) @ ( E @ ( C @ ( C @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ c_COMBK ) ) @ ( B @ c_Product__Type_OSigma ) ) ) @ ( E @ ( C @ ( C @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ c_COMBK ) ) @ ( A @ c_Product__Type_OSigma ) ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(561,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_in ) ) )
| ~ ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bex__empty_0) ).
thf(1788,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_in ) ) )
| ~ ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[561]) ).
thf(391,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_Relation_Otrans ) )
| ( ( B @ ( A @ c_Transitive__Closure_Otrancl ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trancl__id_0) ).
thf(1426,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_Relation_Otrans ) )
| ( ( B @ ( A @ c_Transitive__Closure_Otrancl ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(264,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linorder__linear_0) ).
thf(1164,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(93,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_in ) ) )
| ( ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Set_Oinsert ) ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__Diff_0) ).
thf(797,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_in ) ) )
| ( ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Set_Oinsert ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(311,axiom,
! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__upper1_0) ).
thf(1260,plain,
! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(46,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( B @ c_in ) ) )
| ( ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Set_Oinsert ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__insert__right_0) ).
thf(698,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( B @ c_in ) ) )
| ( ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Set_Oinsert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(232,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__subset__conv_1) ).
thf(1095,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(279,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__mono_0) ).
thf(1196,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(582,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( E @ ( D @ ( A @ ( C @ c_Relation_OImage ) ) ) @ ( B @ c_in ) ) )
| ( D @ ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__XImageE__1__1 ) ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ImageE_1) ).
thf(1835,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( E @ ( D @ ( A @ ( C @ c_Relation_OImage ) ) ) @ ( B @ c_in ) ) )
| ( D @ ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__XImageE__1__1 ) ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[582]) ).
thf(190,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__infE_1) ).
thf(1001,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(494,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Omkbot ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( A = D )
| ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__mkbot_2) ).
thf(1645,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Omkbot ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( A = D )
| ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).
thf(473,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( A = B )
| ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Omkbot ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__mkbot_5) ).
thf(1601,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( A = B )
| ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Omkbot ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).
thf(362,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_DiffE_1) ).
thf(1366,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(437,axiom,
! [B: $i,A: $i] : ( B @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ c_Relation_OId @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Relation_Oirrefl ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_irrefl__diff__Id_0) ).
thf(1529,plain,
! [B: $i,A: $i] : ( B @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ c_Relation_OId @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Relation_Oirrefl ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(542,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( E @ c_Equiv__Relations_Oequiv ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( A @ ( C @ ( C @ ( D @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ( ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) )
= ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equiv__class__eq__iff_0) ).
thf(1746,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( E @ c_Equiv__Relations_Oequiv ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( A @ ( C @ ( C @ ( D @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ( ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) )
= ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).
thf(141,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Relation_OImage ) ) ) )
= ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( D @ ( C @ ( A @ c_Relation_OImage ) ) ) @ ( E @ ( D @ ( B @ ( A @ c_Relation_OImage ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Image__Un_0) ).
thf(898,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Relation_OImage ) ) ) )
= ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( D @ ( C @ ( A @ c_Relation_OImage ) ) ) @ ( E @ ( D @ ( B @ ( A @ c_Relation_OImage ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(303,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__trans_0) ).
thf(1243,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(248,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_Equiv__Relations_Oequiv ) ) )
| ( B @ ( A @ c_Relation_Osym ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equiv_Osym_0) ).
thf(1127,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_Equiv__Relations_Oequiv ) ) )
| ( B @ ( A @ c_Relation_Osym ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(558,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( B @ ( A @ ( E @ c_FunDef_Oin__rel ) ) ) ) )
| ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__rel__def_0) ).
thf(1782,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( B @ ( A @ ( E @ c_FunDef_Oin__rel ) ) ) ) )
| ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).
thf(374,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( A @ c_in ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__rev__mp_0) ).
thf(1391,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( A @ c_in ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(460,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( E @ ( D @ c_Wellfounded_Oacc ) @ ( B @ c_in ) ) )
| ~ ( E @ ( E @ tc_prod ) @ ( D @ ( E @ ( E @ ( E @ ( D @ ( A @ c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 ) ) @ ( C @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acc__induct_1) ).
thf(1576,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( E @ ( D @ c_Wellfounded_Oacc ) @ ( B @ c_in ) ) )
| ~ ( E @ ( E @ tc_prod ) @ ( D @ ( E @ ( E @ ( E @ ( D @ ( A @ c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 ) ) @ ( C @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).
thf(531,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__eq__or__trancl_2) ).
thf(1724,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).
thf(412,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( F @ ( E @ c_Pair ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_split ) ) ) @ hAPP ) )
= ( F @ ( E @ ( A @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_split__case__cert_0) ).
thf(1475,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( F @ ( E @ c_Pair ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_split ) ) ) @ hAPP ) )
= ( F @ ( E @ ( A @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(432,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_Relation_Ototal__on ) ) )
| ( C @ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( C @ c_Relation_OId @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Relation_Ototal__on ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_total__on__diff__Id_1) ).
thf(1518,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_Relation_Ototal__on ) ) )
| ( C @ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( C @ c_Relation_OId @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Relation_Ototal__on ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(314,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Transitive__Closure_Ortrancl ) )
= ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( B @ ( B @ ( A @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_Relation_Orel__comp ) ) ) ) @ ( B @ c_Relation_OId @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__unfold_0) ).
thf(1265,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Transitive__Closure_Ortrancl ) )
= ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( B @ ( B @ ( A @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_Relation_Orel__comp ) ) ) ) @ ( B @ c_Relation_OId @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(522,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( C @ c_Relation_OId @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pair__in__Id__conv_0) ).
thf(1703,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( C @ c_Relation_OId @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).
thf(296,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__Int__distrib_0) ).
thf(1228,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(484,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( E @ ( B @ c_Relation_Orefl__on ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( E @ ( C @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_refl__onD1_0) ).
thf(1623,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( E @ ( B @ c_Relation_Orefl__on ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( E @ ( C @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).
thf(486,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( D @ ( C @ c_Wellfounded_Oacc ) @ ( B @ c_in ) ) )
| ( D @ ( D @ ( C @ c_Wellfounded_Oacc ) @ ( D @ ( C @ ( A @ c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 ) ) @ c_in ) ) )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acc__induct_0) ).
thf(1628,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( D @ ( C @ c_Wellfounded_Oacc ) @ ( B @ c_in ) ) )
| ( D @ ( D @ ( C @ c_Wellfounded_Oacc ) @ ( D @ ( C @ ( A @ c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 ) ) @ c_in ) ) )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).
thf(56,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( E @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__mono_0) ).
thf(719,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( E @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(87,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_Relation_Ototal__on ) ) )
| ( C @ ( C @ ( C @ ( B @ c_Relation_Oconverse ) ) @ ( A @ c_Relation_Ototal__on ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_total__on__converse_1) ).
thf(785,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_Relation_Ototal__on ) ) )
| ( C @ ( C @ ( C @ ( B @ c_Relation_Oconverse ) ) @ ( A @ c_Relation_Ototal__on ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(344,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( D @ tc_prod ) @ ( D @ ( B @ c_Transitive__Closure_Otrancl ) @ ( D @ ( D @ ( C @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( D @ ( D @ tc_prod ) @ ( B @ ( D @ ( D @ ( D @ ( C @ ( A @ ( B @ c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1 ) ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_tranclD_0) ).
thf(1330,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( D @ tc_prod ) @ ( D @ ( B @ c_Transitive__Closure_Otrancl ) @ ( D @ ( D @ ( C @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( D @ ( D @ tc_prod ) @ ( B @ ( D @ ( D @ ( D @ ( C @ ( A @ ( B @ c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1 ) ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(95,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Relation_ORange ) ) )
= ( B @ ( C @ ( C @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_ODomain ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Range__def_0) ).
thf(802,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Relation_ORange ) ) )
= ( B @ ( C @ ( C @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_ODomain ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(577,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( C @ tc_prod ) @ ( E @ ( C @ ( F @ ( B @ c_Product__Type_OSigma ) ) ) @ ( E @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SigmaD1_0) ).
thf(1826,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( C @ tc_prod ) @ ( E @ ( C @ ( F @ ( B @ c_Product__Type_OSigma ) ) ) @ ( E @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).
thf(158,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_Relation_ODomain ) ) )
= ( B @ ( B @ ( A @ c_Relation_ODomain ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trancl__domain_0) ).
thf(934,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_Relation_ODomain ) ) )
= ( B @ ( B @ ( A @ c_Relation_ODomain ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(167,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__left__absorb_0) ).
thf(949,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(214,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
| ~ ( D @ ( A @ ( B @ c_in ) ) )
| ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_diff__single__insert_0) ).
thf(1055,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
| ~ ( D @ ( A @ ( B @ c_in ) ) )
| ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(382,axiom,
! [B: $i,A: $i] : ( B @ ( B @ tc_prod ) @ ( B @ c_Relation_OId @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pair__in__Id__conv_1) ).
thf(1409,plain,
! [B: $i,A: $i] : ( B @ ( B @ tc_prod ) @ ( B @ c_Relation_OId @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(548,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( C @ ( A @ ( B @ c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1 ) ) @ c_in ) ) )
| ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acc_OaccI_1) ).
thf(1760,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( C @ ( A @ ( B @ c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1 ) ) @ c_in ) ) )
| ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[548]) ).
thf(329,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ c_Relation_Orefl__on ) ) )
| ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_COMBK ) ) @ ( B @ c_Product__Type_OSigma ) ) ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_refl__on__def_0) ).
thf(1298,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ c_Relation_Orefl__on ) ) )
| ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_COMBK ) ) @ ( B @ c_Product__Type_OSigma ) ) ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(341,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf1E_1) ).
thf(1323,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(13,axiom,
tc_bool @ class_Lattices_Odistrib__lattice,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Odistrib__lattice) ).
thf(619,plain,
tc_bool @ class_Lattices_Odistrib__lattice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(408,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = E )
| ( ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) )
!= ( D @ ( C @ ( F @ ( E @ c_Pair ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Pair__eq_0) ).
thf(1462,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = E )
| ( ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) )
!= ( D @ ( C @ ( F @ ( E @ c_Pair ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(216,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( C @ ( C @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ c_COMBK ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Product__Type_OSigma ) ) ) )
= ( tc_bool @ ( E @ ( C @ tc_prod ) @ tc_fun ) @ ( E @ ( C @ ( C @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ c_COMBK ) ) @ ( B @ c_Product__Type_OSigma ) ) ) @ ( E @ ( C @ ( C @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ c_COMBK ) ) @ ( A @ c_Product__Type_OSigma ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Times__Un__distrib1_0) ).
thf(1059,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( C @ ( C @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ c_COMBK ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Product__Type_OSigma ) ) ) )
= ( tc_bool @ ( E @ ( C @ tc_prod ) @ tc_fun ) @ ( E @ ( C @ ( C @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ c_COMBK ) ) @ ( B @ c_Product__Type_OSigma ) ) ) @ ( E @ ( C @ ( C @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ c_COMBK ) ) @ ( A @ c_Product__Type_OSigma ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(250,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= B )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__absorb_0) ).
thf(1132,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= B )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(368,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( B @ ( A @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Transitive__Closure_Otrancl ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_r__into__trancl_H_0) ).
thf(1379,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( B @ ( A @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Transitive__Closure_Otrancl ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(430,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( C @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Product__Type_OSigma ) ) ) )
= ( tc_bool @ ( E @ ( C @ tc_prod ) @ tc_fun ) @ ( E @ ( C @ ( D @ ( B @ c_Product__Type_OSigma ) ) ) @ ( E @ ( C @ ( D @ ( A @ c_Product__Type_OSigma ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sigma__Un__distrib1_0) ).
thf(1514,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( C @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Product__Type_OSigma ) ) ) )
= ( tc_bool @ ( E @ ( C @ tc_prod ) @ tc_fun ) @ ( E @ ( C @ ( D @ ( B @ c_Product__Type_OSigma ) ) ) @ ( E @ ( C @ ( D @ ( A @ c_Product__Type_OSigma ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(414,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__Xtrans__def__1__3 ) @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__Xtrans__def__1__1 ) @ c_Pair ) ) ) @ c_in ) ) )
| ( B @ ( A @ c_Relation_Otrans ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__def_3) ).
thf(1479,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__Xtrans__def__1__3 ) @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__Xtrans__def__1__1 ) @ c_Pair ) ) ) @ c_in ) ) )
| ( B @ ( A @ c_Relation_Otrans ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(242,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__partition_0) ).
thf(1115,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(456,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( t_a @ ( t_a @ ( D @ c_Wellfounded_Oacc ) @ ( B @ c_in ) ) )
| ~ ( t_a @ ( t_a @ tc_prod ) @ ( D @ ( t_a @ ( t_a @ ( D @ ( A @ v_sko__Wellfounded__Xacc__Xinduct__1 ) @ ( C @ c_Pair ) ) ) @ c_in ) ) )
| ( t_a @ ( t_a @ ( D @ c_Wellfounded_Oacc ) @ ( C @ c_in ) ) )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acc_Oinduct_0) ).
thf(1568,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( t_a @ ( t_a @ ( D @ c_Wellfounded_Oacc ) @ ( B @ c_in ) ) )
| ~ ( t_a @ ( t_a @ tc_prod ) @ ( D @ ( t_a @ ( t_a @ ( D @ ( A @ v_sko__Wellfounded__Xacc__Xinduct__1 ) @ ( C @ c_Pair ) ) ) @ c_in ) ) )
| ( t_a @ ( t_a @ ( D @ c_Wellfounded_Oacc ) @ ( C @ c_in ) ) )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).
thf(360,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( E @ ( C @ ( B @ ( D @ c_Set_Oimage ) ) ) @ ( A @ ( D @ hAPP ) @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__image__eqI_0) ).
thf(1362,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( E @ ( C @ ( B @ ( D @ c_Set_Oimage ) ) ) @ ( A @ ( D @ hAPP ) @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(298,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ c_Wellfounded_Owf ) )
| ( D @ ( D @ ( C @ ( B @ ( A @ c_Relation_Oinv__image ) ) ) @ c_Wellfounded_Owf ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__inv__image_0) ).
thf(1232,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ c_Wellfounded_Owf ) )
| ( D @ ( D @ ( C @ ( B @ ( A @ c_Relation_Oinv__image ) ) ) @ c_Wellfounded_Owf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(588,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( F @ c_in ) ) )
| ~ ( E @ ( D @ tc_prod ) @ ( B @ ( E @ ( D @ ( A @ ( F @ c_Pair ) ) ) @ c_in ) ) )
| ( E @ ( E @ ( D @ ( C @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__ImageI_0) ).
thf(1847,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( F @ c_in ) ) )
| ~ ( E @ ( D @ tc_prod ) @ ( B @ ( E @ ( D @ ( A @ ( F @ c_Pair ) ) ) @ c_in ) ) )
| ( E @ ( E @ ( D @ ( C @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[588]) ).
thf(176,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_lessequals ) ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__absorb1_0) ).
thf(969,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_lessequals ) ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(352,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( C @ ( C @ ( D @ c_Relation_Oconverse ) ) @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__converseD_0) ).
thf(1347,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( C @ ( C @ ( D @ c_Relation_Oconverse ) ) @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(458,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_Set_Oinsert ) ) @ c_Wellfounded_Owf ) )
| ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__insert_1) ).
thf(1572,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_Set_Oinsert ) ) @ c_Wellfounded_Owf ) )
| ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).
thf(418,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( A @ ( E @ c_Pair ) ) ) @ c_in ) ) )
| ( D @ ( D @ ( C @ ( B @ c_Relation_ORange ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_RangeI_0) ).
thf(1489,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( A @ ( E @ c_Pair ) ) ) @ c_in ) ) )
| ( D @ ( D @ ( C @ ( B @ c_Relation_ORange ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(527,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl__into__trancl_0) ).
thf(1714,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).
thf(89,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Int__distrib_0) ).
thf(789,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(365,axiom,
! [B: $i,A: $i] :
~ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ex__in__conv_0) ).
thf(1373,plain,
! [B: $i,A: $i] :
~ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(387,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1 ) @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1 ) @ c_Pair ) ) ) @ c_in ) ) )
| ( B @ ( A @ c_Relation_Oirrefl ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_irrefl__def_1) ).
thf(1418,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1 ) @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__Xirrefl__def__1__1 ) @ c_Pair ) ) ) @ c_in ) ) )
| ( B @ ( A @ c_Relation_Oirrefl ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(578,axiom,
! [C: $i,B: $i,A: $i] : ( B @ ( B @ tc_prod ) @ ( B @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl_Ortrancl__refl_0) ).
thf(1828,plain,
! [C: $i,B: $i,A: $i] : ( B @ ( B @ tc_prod ) @ ( B @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).
thf(259,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__mono_0) ).
thf(1151,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(370,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__trans_0) ).
thf(1383,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(97,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ ( C @ tc_prod ) @ tc_fun ) @ ( E @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( F @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( F @ ( E @ c_Relation_OImage ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Relation_OImage ) ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Image__mono_0) ).
thf(806,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ ( C @ tc_prod ) @ tc_fun ) @ ( E @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( F @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( F @ ( E @ c_Relation_OImage ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Relation_OImage ) ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(323,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( A @ c_in ) ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Set_Oinsert ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__insert__left_0) ).
thf(1283,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( A @ c_in ) ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Set_Oinsert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(331,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
!= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__empty_0) ).
thf(1302,plain,
! [C: $i,B: $i,A: $i] :
( ( A
= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
!= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(73,axiom,
! [B: $i,A: $i] :
( ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__empty_0) ).
thf(756,plain,
! [B: $i,A: $i] :
( ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(503,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oimage ) ) ) )
= ( E @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__insert_0) ).
thf(1664,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oimage ) ) ) )
= ( E @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_Set_Oinsert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).
thf(570,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_Relation_Otrans ) )
| ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_Otrans ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__converse_1) ).
thf(1811,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_Relation_Otrans ) )
| ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_Otrans ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[570]) ).
thf(402,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( F @ c_Equiv__Relations_Oequiv ) ) )
| ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( D @ c_Relation_OImage ) ) ) @ ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( D @ c_Relation_OImage ) ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( E @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equiv__class__nondisjoint_0) ).
thf(1450,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( F @ c_Equiv__Relations_Oequiv ) ) )
| ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( D @ c_Relation_OImage ) ) ) @ ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( D @ c_Relation_OImage ) ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( E @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(239,axiom,
! [B: $i,A: $i] :
( ( B @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ c_Relation_OId @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Transitive__Closure_Ortrancl ) )
= ( B @ ( A @ c_Transitive__Closure_Ortrancl ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__reflcl_0) ).
thf(1109,plain,
! [B: $i,A: $i] :
( ( B @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ c_Relation_OId @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Transitive__Closure_Ortrancl ) )
= ( B @ ( A @ c_Transitive__Closure_Ortrancl ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(488,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ c_Wellfounded_Owf ) )
| ~ ( C @ ( B @ ( E @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( C @ ( D @ ( B @ c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wfE__min_1) ).
thf(1632,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ c_Wellfounded_Owf ) )
| ~ ( C @ ( B @ ( E @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( C @ ( D @ ( B @ c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).
thf(346,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ c_in ) ) )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mem__def_0) ).
thf(1334,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ c_in ) ) )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(26,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( B @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I1_J_0) ).
thf(646,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( B @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(181,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= B )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__absorb1_0) ).
thf(981,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= B )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(586,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_Relation_Otrans ) )
| ( B @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ c_Relation_OId @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Relation_Otrans ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__reflclI_0) ).
thf(1843,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_Relation_Otrans ) )
| ( B @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ c_Relation_OId @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Relation_Otrans ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[586]) ).
thf(367,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_Relation_Otrans ) )
| ~ ( B @ ( A @ c_Relation_Oantisym ) )
| ( B @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ c_Relation_OId @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Relation_Otrans ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__diff__Id_0) ).
thf(1377,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_Relation_Otrans ) )
| ~ ( B @ ( A @ c_Relation_Oantisym ) )
| ( B @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ c_Relation_OId @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Relation_Otrans ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(124,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
!= B )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__inf_1) ).
thf(866,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
!= B )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(222,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( A @ c_in ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__subset_2) ).
thf(1072,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( A @ c_in ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(244,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ ( A @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distrib__inf__le_0) ).
thf(1119,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ ( A @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(354,axiom,
! [A: $i] : ( A @ ( A @ c_Relation_OId @ c_Relation_Otrans ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__Id_0) ).
thf(1351,plain,
! [A: $i] : ( A @ ( A @ c_Relation_OId @ c_Relation_Otrans ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(351,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( D @ ( C @ ( B @ c_Relation_ODomain ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Domain__iff_1) ).
thf(1345,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( D @ ( C @ ( B @ c_Relation_ODomain ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(394,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( D @ tc_prod ) @ ( B @ ( D @ ( D @ ( C @ ( F @ c_Pair ) ) ) @ c_in ) ) )
| ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Recdef_Ocut ) ) ) ) @ hAPP ) )
= ( F @ ( A @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_tfl__cut__apply_0) ).
thf(1433,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( D @ tc_prod ) @ ( B @ ( D @ ( D @ ( C @ ( F @ c_Pair ) ) ) @ c_in ) ) )
| ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Recdef_Ocut ) ) ) ) @ hAPP ) )
= ( F @ ( A @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(282,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( tc_bool @ ( E @ tc_fun ) @ ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( E @ ( D @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Set_Oimage ) ) ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__Int__subset_0) ).
thf(1201,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( tc_bool @ ( E @ tc_fun ) @ ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( E @ ( D @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Set_Oimage ) ) ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(434,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( A @ ( C @ c_Arrow__Order__Mirabelle_Omkbot ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( B = A )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__mkbot_4) ).
thf(1521,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( A @ ( C @ c_Arrow__Order__Mirabelle_Omkbot ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( B = A )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(454,axiom,
! [B: $i,A: $i] :
~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( A @ ( B @ c_Arrow__Order__Mirabelle_Omktop ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__mktop_1) ).
thf(1564,plain,
! [B: $i,A: $i] :
~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( A @ ( B @ c_Arrow__Order__Mirabelle_Omktop ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).
thf(289,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__inf__iff_1) ).
thf(1215,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(20,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I6_J_0) ).
thf(634,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(236,axiom,
! [A: $i] : ( A @ ( A @ c_Relation_OId @ c_Relation_Osym ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sym__Id_0) ).
thf(1104,plain,
! [A: $i] : ( A @ ( A @ c_Relation_OId @ c_Relation_Osym ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(519,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ c_Wellfounded_Oacyclic ) )
| ~ ( B @ ( B @ tc_prod ) @ ( B @ ( C @ c_Transitive__Closure_Otrancl ) @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acyclic__def_0) ).
thf(1697,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ c_Wellfounded_Oacyclic ) )
| ~ ( B @ ( B @ tc_prod ) @ ( B @ ( C @ c_Transitive__Closure_Otrancl ) @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).
thf(496,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
| ~ ( C @ ( D @ ( A @ c_in ) ) )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subsetD_0) ).
thf(1651,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
| ~ ( C @ ( D @ ( A @ c_in ) ) )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).
thf(285,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insertI2_0) ).
thf(1206,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(163,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
= ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( B @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_4) ).
thf(942,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
= ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( B @ c_Set_Oinsert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(516,axiom,
! [B: $i,A: $i] :
~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( A @ ( B @ c_Arrow__Order__Mirabelle_Omkbot ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__mkbot_1) ).
thf(1691,plain,
! [B: $i,A: $i] :
~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( A @ ( B @ c_Arrow__Order__Mirabelle_Omkbot ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).
thf(396,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( A @ c_Relation_Orefl__on ) ) )
| ~ ( C @ ( E @ ( B @ c_Relation_Orefl__on ) ) )
| ( C @ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( E @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Relation_Orefl__on ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_refl__on__Int_0) ).
thf(1438,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( A @ c_Relation_Orefl__on ) ) )
| ~ ( C @ ( E @ ( B @ c_Relation_Orefl__on ) ) )
| ( C @ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( E @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Relation_Orefl__on ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(91,axiom,
! [B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__empty__left_0) ).
thf(793,plain,
! [B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(152,axiom,
! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_Relation_OId__on ) @ ( A @ c_Relation_Orefl__on ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_refl__on__Id__on_0) ).
thf(925,plain,
! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_Relation_OId__on ) @ ( A @ c_Relation_Orefl__on ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(99,axiom,
! [B: $i,A: $i] :
( ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__empty__right_0) ).
thf(810,plain,
! [B: $i,A: $i] :
( ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(348,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( E @ ( A @ c_in ) ) )
| ~ ( D @ ( A @ ( F @ hAPP ) @ ( B @ c_in ) ) )
| ( D @ ( C @ tc_prod ) @ ( D @ ( C @ ( F @ ( E @ c_Product__Type_OSigma ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SigmaI_0) ).
thf(1338,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( E @ ( A @ c_in ) ) )
| ~ ( D @ ( A @ ( F @ hAPP ) @ ( B @ c_in ) ) )
| ( D @ ( C @ tc_prod ) @ ( D @ ( C @ ( F @ ( E @ c_Product__Type_OSigma ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(490,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__Xtrans__def__1__2 ) @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__Xtrans__def__1__1 ) @ c_Pair ) ) ) @ c_in ) ) )
| ( B @ ( A @ c_Relation_Otrans ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__def_1) ).
thf(1636,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__Xtrans__def__1__2 ) @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__Xtrans__def__1__1 ) @ c_Pair ) ) ) @ c_in ) ) )
| ( B @ ( A @ c_Relation_Otrans ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).
thf(223,axiom,
! [B: $i,A: $i] :
( ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ c_Relation_OId @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( B @ ( A @ c_Transitive__Closure_Ortrancl ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_reflcl__trancl_0) ).
thf(1074,plain,
! [B: $i,A: $i] :
( ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ c_Relation_OId @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( B @ ( A @ c_Transitive__Closure_Ortrancl ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(474,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ tc_prod ) @ ( B @ ( E @ ( D @ ( A @ ( C @ c_Pair ) ) ) @ c_in ) ) )
| ( E @ ( E @ ( D @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Image__singleton__iff_1) ).
thf(1604,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ tc_prod ) @ ( B @ ( E @ ( D @ ( A @ ( C @ c_Pair ) ) ) @ c_in ) ) )
| ( E @ ( E @ ( D @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(260,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
!= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ~ ( C @ ( D @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_disjoint__iff__not__equal_0) ).
thf(1153,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
!= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ~ ( C @ ( D @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(76,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( D @ ( E @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__eqI_0) ).
thf(761,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( D @ ( E @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(410,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( E @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_COMBK ) ) @ ( B @ c_Product__Type_OSigma ) ) ) @ ( E @ c_lessequals ) ) )
| ( A = D )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trancl__subset__Sigma__aux_0) ).
thf(1470,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( E @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_COMBK ) ) @ ( B @ c_Product__Type_OSigma ) ) ) @ ( E @ c_lessequals ) ) )
| ( A = D )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(524,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( E @ tc_prod ) @ ( D @ ( E @ ( B @ ( F @ c_Product__Type_OSigma ) ) ) @ ( D @ ( E @ ( A @ ( C @ c_Pair ) ) ) @ c_in ) ) )
| ( D @ ( C @ ( B @ hAPP ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SigmaD2_0) ).
thf(1708,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( E @ tc_prod ) @ ( D @ ( E @ ( B @ ( F @ c_Product__Type_OSigma ) ) ) @ ( D @ ( E @ ( A @ ( C @ c_Pair ) ) ) @ c_in ) ) )
| ( D @ ( C @ ( B @ hAPP ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).
thf(552,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( F @ c_in ) ) )
| ~ ( tc_bool @ ( E @ ( C @ tc_prod ) @ tc_fun ) @ ( E @ ( C @ ( C @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ c_COMBK ) ) @ ( B @ c_Product__Type_OSigma ) ) ) @ ( E @ ( C @ ( C @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ c_COMBK ) ) @ ( A @ c_Product__Type_OSigma ) ) ) @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Times__subset__cancel2_0) ).
thf(1768,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( F @ c_in ) ) )
| ~ ( tc_bool @ ( E @ ( C @ tc_prod ) @ tc_fun ) @ ( E @ ( C @ ( C @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ c_COMBK ) ) @ ( B @ c_Product__Type_OSigma ) ) ) @ ( E @ ( C @ ( C @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ c_COMBK ) ) @ ( A @ c_Product__Type_OSigma ) ) ) @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).
thf(53,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__Un_0) ).
thf(714,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(211,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D
= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( ( B @ ( C @ ( D @ ( C @ ( B @ ( A @ c_COMBK ) ) @ c_Set_Oimage ) ) ) )
= ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__constant__conv_1) ).
thf(1047,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D
= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( ( B @ ( C @ ( D @ ( C @ ( B @ ( A @ c_COMBK ) ) @ c_Set_Oimage ) ) ) )
= ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(215,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ ( A @ c_Relation_OId__on ) @ c_Relation_Oconverse ) ) )
= ( B @ ( A @ c_Relation_OId__on ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_converse__Id__on_0) ).
thf(1057,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ ( A @ c_Relation_OId__on ) @ c_Relation_Oconverse ) ) )
= ( B @ ( A @ c_Relation_OId__on ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(350,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ tc_prod ) @ ( D @ ( C @ ( E @ c_Relation_Oconverse ) ) @ ( C @ ( D @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_converseD_0) ).
thf(1343,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ tc_prod ) @ ( D @ ( C @ ( E @ c_Relation_Oconverse ) ) @ ( C @ ( D @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(199,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
= ( A @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oimage ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__is__image_1) ).
thf(1021,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
= ( A @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oimage ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(462,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( C @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Product__Type_OSigma ) ) ) )
= ( tc_bool @ ( E @ ( C @ tc_prod ) @ tc_fun ) @ ( E @ ( C @ ( D @ ( B @ c_Product__Type_OSigma ) ) ) @ ( E @ ( C @ ( D @ ( A @ c_Product__Type_OSigma ) ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sigma__Int__distrib1_0) ).
thf(1580,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( C @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Product__Type_OSigma ) ) ) )
= ( tc_bool @ ( E @ ( C @ tc_prod ) @ tc_fun ) @ ( E @ ( C @ ( D @ ( B @ c_Product__Type_OSigma ) ) ) @ ( E @ ( C @ ( D @ ( A @ c_Product__Type_OSigma ) ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).
thf(504,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( t_a @ ( t_a @ ( C @ c_Wellfounded_Oacc ) @ ( B @ c_in ) ) )
| ~ ( C @ ( A @ v_sko__Wellfounded__Xacc__Xinducts__1 ) @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acc_Oinducts_2) ).
thf(1666,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( t_a @ ( t_a @ ( C @ c_Wellfounded_Oacc ) @ ( B @ c_in ) ) )
| ~ ( C @ ( A @ v_sko__Wellfounded__Xacc__Xinducts__1 ) @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).
thf(417,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( A @ c_lessequals ) ) )
| ( C @ ( A @ ( D @ ( C @ ( F @ ( B @ ( A @ c_ATP__Linkup_Osko__Product__Type__XSigma__mono__1__1 ) ) ) ) @ c_in ) ) )
| ( tc_bool @ ( D @ ( C @ tc_prod ) @ tc_fun ) @ ( D @ ( C @ ( F @ ( E @ c_Product__Type_OSigma ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Product__Type_OSigma ) ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sigma__mono_0) ).
thf(1487,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( A @ c_lessequals ) ) )
| ( C @ ( A @ ( D @ ( C @ ( F @ ( B @ ( A @ c_ATP__Linkup_Osko__Product__Type__XSigma__mono__1__1 ) ) ) ) @ c_in ) ) )
| ( tc_bool @ ( D @ ( C @ tc_prod ) @ tc_fun ) @ ( D @ ( C @ ( F @ ( E @ c_Product__Type_OSigma ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Product__Type_OSigma ) ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(44,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__infI_0) ).
thf(693,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(101,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_Orderings_Obot__class_Obot @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Lattices_Obounded__lattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__bot__left_0) ).
thf(815,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_Orderings_Obot__class_Obot @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Lattices_Obounded__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(61,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__ord_I4_J_0) ).
thf(729,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(452,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_Equiv__Relations_Oequiv ) ) )
| ( B @ ( A @ c_Relation_Otrans ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equiv_Otrans_0) ).
thf(1560,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_Equiv__Relations_Oequiv ) ) )
| ( B @ ( A @ c_Relation_Otrans ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(372,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ c_Wellfounded_Owf ) )
| ~ ( C @ ( A @ ( D @ c_in ) ) )
| ( C @ ( A @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wfE__min_0) ).
thf(1387,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ c_Wellfounded_Owf ) )
| ~ ( C @ ( A @ ( D @ c_in ) ) )
| ( C @ ( A @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(146,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__mono_0) ).
thf(910,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(171,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Relation_Osym ) )
| ( ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) )
!= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sym__conv__converse__eq_1) ).
thf(957,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Relation_Osym ) )
| ( ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) )
!= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(293,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( D @ ( C @ ( E @ ( tc_bool @ ( D @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Relation_Orel__comp ) ) ) ) )
= ( tc_bool @ ( F @ ( C @ tc_prod ) @ tc_fun ) @ ( F @ ( D @ ( C @ ( E @ ( B @ c_Relation_Orel__comp ) ) ) ) @ ( F @ ( D @ ( C @ ( E @ ( A @ c_Relation_Orel__comp ) ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__comp__distrib2_0) ).
thf(1223,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( D @ ( C @ ( E @ ( tc_bool @ ( D @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Relation_Orel__comp ) ) ) ) )
= ( tc_bool @ ( F @ ( C @ tc_prod ) @ tc_fun ) @ ( F @ ( D @ ( C @ ( E @ ( B @ c_Relation_Orel__comp ) ) ) ) @ ( F @ ( D @ ( C @ ( E @ ( A @ c_Relation_Orel__comp ) ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(69,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_Wellfounded_Owf ) )
| ( B @ ( A @ c_Wellfounded_Oacyclic ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__acyclic_0) ).
thf(746,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_Wellfounded_Owf ) )
| ( B @ ( A @ c_Wellfounded_Oacyclic ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(230,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_Transitive__Closure_Ortrancl ) )
= ( B @ ( A @ c_Transitive__Closure_Ortrancl ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trancl__rtrancl__absorb_0) ).
thf(1091,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_Transitive__Closure_Ortrancl ) )
= ( B @ ( A @ c_Transitive__Closure_Ortrancl ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(246,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ ( B @ c_in ) ) )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert__iff_2) ).
thf(1123,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ ( B @ c_in ) ) )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(122,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__infI1_0) ).
thf(862,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(457,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( D @ tc_prod ) @ ( D @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( A @ c_in ) ) )
| ( D @ ( D @ tc_prod ) @ ( D @ ( tc_bool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Transitive__Closure_Ortrancl ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__rtrancl__UnI_0) ).
thf(1570,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( D @ tc_prod ) @ ( D @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( A @ c_in ) ) )
| ( D @ ( D @ tc_prod ) @ ( D @ ( tc_bool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Transitive__Closure_Ortrancl ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(268,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( B @ ( tc_bool @ ( C @ ( B @ tc_prod ) @ tc_fun ) @ ( D @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Relation_ODomain ) ) @ ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( B @ ( D @ c_Relation_ODomain ) ) @ ( C @ ( B @ ( A @ c_Relation_ODomain ) ) @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Domain__Diff__subset_0) ).
thf(1174,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( B @ ( tc_bool @ ( C @ ( B @ tc_prod ) @ tc_fun ) @ ( D @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Relation_ODomain ) ) @ ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( B @ ( D @ c_Relation_ODomain ) ) @ ( C @ ( B @ ( A @ c_Relation_ODomain ) ) @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(509,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( B = D )
| ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Omktop ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__mktop_3) ).
thf(1676,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( B = D )
| ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Omktop ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).
thf(290,axiom,
! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( A @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insertI_0) ).
thf(1217,plain,
! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( A @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(7,negated_conjecture,
! [C: $i,B: $i,A: $i] :
( ( B = A )
| ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( v_P @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( v_P @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_6) ).
thf(598,plain,
! [C: $i,B: $i,A: $i] :
( ( B = A )
| ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( v_P @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( v_P @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(544,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trancl__into__rtrancl_0) ).
thf(1751,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).
thf(103,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__least_0) ).
thf(820,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(576,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_Otrans ) )
| ( B @ ( A @ c_Relation_Otrans ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__converse_0) ).
thf(1824,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_Otrans ) )
| ( B @ ( A @ c_Relation_Otrans ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).
thf(364,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( E @ c_Equiv__Relations_Oequiv ) ) )
| ~ ( C @ ( E @ ( D @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( A @ ( C @ ( C @ ( D @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ( ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) )
!= ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__equiv__class_0) ).
thf(1370,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( E @ c_Equiv__Relations_Oequiv ) ) )
| ~ ( C @ ( E @ ( D @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( A @ ( C @ ( C @ ( D @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ( ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) )
!= ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(149,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Odistrib__lattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__inf__distrib2_0) ).
thf(916,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Odistrib__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(583,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( F @ c_in ) ) )
| ~ ( E @ ( D @ tc_prod ) @ ( B @ ( E @ ( D @ ( A @ ( F @ c_Pair ) ) ) @ c_in ) ) )
| ( E @ ( E @ ( D @ ( C @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Image__iff_2) ).
thf(1837,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( F @ c_in ) ) )
| ~ ( E @ ( D @ tc_prod ) @ ( B @ ( E @ ( D @ ( A @ ( F @ c_Pair ) ) ) @ c_in ) ) )
| ( E @ ( E @ ( D @ ( C @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[583]) ).
thf(17,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( B @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I5_J_0) ).
thf(625,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( B @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(328,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( C @ ( B @ c_Relation_Oconverse ) ) @ ( A @ c_Relation_Orefl__on ) ) )
| ( C @ ( B @ ( A @ c_Relation_Orefl__on ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_refl__on__converse_0) ).
thf(1296,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( C @ ( B @ c_Relation_Oconverse ) ) @ ( A @ c_Relation_Orefl__on ) ) )
| ( C @ ( B @ ( A @ c_Relation_Orefl__on ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(514,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( E @ ( D @ c_Wellfounded_Oacc ) @ ( B @ c_in ) ) )
| ~ ( E @ ( E @ tc_prod ) @ ( D @ ( E @ ( E @ ( E @ ( D @ ( A @ c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 ) ) @ ( C @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acc__induct__rule_1) ).
thf(1687,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( E @ ( D @ c_Wellfounded_Oacc ) @ ( B @ c_in ) ) )
| ~ ( E @ ( E @ tc_prod ) @ ( D @ ( E @ ( E @ ( E @ ( D @ ( A @ c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 ) ) @ ( C @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).
thf(135,axiom,
! [C: $i,B: $i,A: $i] : ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Transitive__Closure_Ortrancl ) @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__Un__subset_0) ).
thf(889,plain,
! [C: $i,B: $i,A: $i] : ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Transitive__Closure_Ortrancl ) @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(287,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
!= C )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__sup_1) ).
thf(1210,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
!= C )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(381,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_in ) ) )
| ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UnCI_1) ).
thf(1407,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_in ) ) )
| ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(489,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( E @ ( A @ c_in ) ) )
| ~ ( D @ ( A @ ( F @ hAPP ) @ ( B @ c_in ) ) )
| ( D @ ( C @ tc_prod ) @ ( D @ ( C @ ( F @ ( E @ c_Product__Type_OSigma ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mem__Sigma__iff_2) ).
thf(1634,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( E @ ( A @ c_in ) ) )
| ~ ( D @ ( A @ ( F @ hAPP ) @ ( B @ c_in ) ) )
| ( D @ ( C @ tc_prod ) @ ( D @ ( C @ ( F @ ( E @ c_Product__Type_OSigma ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).
thf(178,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ ( C @ tc_prod ) @ tc_fun ) @ ( F @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( E @ ( D @ tc_prod ) @ tc_fun ) @ ( G @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( E @ ( C @ tc_prod ) @ tc_fun ) @ ( E @ ( D @ ( C @ ( G @ ( F @ c_Relation_Orel__comp ) ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Relation_Orel__comp ) ) ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__comp__mono_0) ).
thf(974,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ ( C @ tc_prod ) @ tc_fun ) @ ( F @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( E @ ( D @ tc_prod ) @ tc_fun ) @ ( G @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( E @ ( C @ tc_prod ) @ tc_fun ) @ ( E @ ( D @ ( C @ ( G @ ( F @ c_Relation_Orel__comp ) ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Relation_Orel__comp ) ) ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(118,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ ( B @ ( B @ ( A @ ( A @ c_Relation_Orel__comp ) ) ) ) @ c_Wellfounded_Owf ) )
| ( B @ ( A @ c_Wellfounded_Owf ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__comp__self_1) ).
thf(852,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ ( B @ ( B @ ( A @ ( A @ c_Relation_Orel__comp ) ) ) ) @ c_Wellfounded_Owf ) )
| ( B @ ( A @ c_Wellfounded_Owf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(450,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( B @ ( C @ c_Arrow__Order__Mirabelle_Omktop ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( A = B )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__mktop_4) ).
thf(1555,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( B @ ( C @ c_Arrow__Order__Mirabelle_Omktop ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(225,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__commute_0) ).
thf(1079,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(202,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( tc_bool @ ( D @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Relation_Oconverse ) ) )
= ( tc_bool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ ( C @ ( B @ c_Relation_Oconverse ) ) @ ( D @ ( C @ ( A @ c_Relation_Oconverse ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_converse__Int_0) ).
thf(1027,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( tc_bool @ ( D @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Relation_Oconverse ) ) )
= ( tc_bool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ ( C @ ( B @ c_Relation_Oconverse ) ) @ ( D @ ( C @ ( A @ c_Relation_Oconverse ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(326,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_Equiv__Relations_Oequiv ) ) )
| ( ( B @ ( B @ ( B @ ( A @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_Orel__comp ) ) ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equiv__comp__eq_0) ).
thf(1291,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_Equiv__Relations_Oequiv ) ) )
| ( ( B @ ( B @ ( B @ ( A @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_Orel__comp ) ) ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(51,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( C @ ( B @ c_Relation_OId @ ( A @ c_Relation_Orel__comp ) ) ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_R__O__Id_0) ).
thf(710,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( C @ ( B @ c_Relation_OId @ ( A @ c_Relation_Orel__comp ) ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(539,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trancl__into__trancl2_0) ).
thf(1740,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).
thf(113,axiom,
! [A: $i] :
( ( A @ ( A @ ( A @ c_Relation_OId @ c_Relation_Oconverse ) ) )
= ( A @ c_Relation_OId ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_converse__Id_0) ).
thf(842,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ c_Relation_OId @ c_Relation_Oconverse ) ) )
= ( A @ c_Relation_OId ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(379,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( A @ c_Wellfounded_Oacc ) @ ( B @ c_in ) ) )
| ~ ( C @ ( C @ ( A @ c_Wellfounded_Oacc ) @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1 ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__acc__down_1) ).
thf(1402,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( A @ c_Wellfounded_Oacc ) @ ( B @ c_in ) ) )
| ~ ( C @ ( C @ ( A @ c_Wellfounded_Oacc ) @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1 ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(359,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_in ) ) )
| ~ ( D @ ( C @ ( A @ c_in ) ) )
| ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntI_0) ).
thf(1360,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_in ) ) )
| ~ ( D @ ( C @ ( A @ c_in ) ) )
| ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(255,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
= ( C @ ( B @ ( A @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__absorb2_0) ).
thf(1143,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
= ( C @ ( B @ ( A @ c_Set_Oinsert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(549,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_converse__rtrancl__into__rtrancl_0) ).
thf(1762,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[549]) ).
thf(568,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = F )
| ( ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) )
!= ( D @ ( C @ ( F @ ( E @ c_Pair ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Pair__eq_1) ).
thf(1804,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = F )
| ( ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) )
!= ( D @ ( C @ ( F @ ( E @ c_Pair ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).
thf(507,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ tc_prod ) @ ( A @ ( E @ ( D @ ( C @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ( E @ ( D @ ( C @ ( B @ ( A @ c_FunDef_Oin__rel ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__rel__def_1) ).
thf(1672,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ tc_prod ) @ ( A @ ( E @ ( D @ ( C @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ( E @ ( D @ ( C @ ( B @ ( A @ c_FunDef_Oin__rel ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).
thf(443,axiom,
! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__iff_1) ).
thf(1540,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(5,negated_conjecture,
! [A: $i] :
~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( v_P @ v_F @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_4) ).
thf(593,plain,
! [A: $i] :
~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( v_P @ v_F @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(125,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__assoc_0) ).
thf(869,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(546,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ c_Relation_Otrans ) )
| ( D @ ( D @ ( C @ ( B @ ( A @ c_Relation_Oinv__image ) ) ) @ c_Relation_Otrans ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__inv__image_0) ).
thf(1755,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ c_Relation_Otrans ) )
| ( D @ ( D @ ( C @ ( B @ ( A @ c_Relation_Oinv__image ) ) ) @ c_Relation_Otrans ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).
thf(185,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( A @ c_in ) ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__Diff1_0) ).
thf(989,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( A @ c_in ) ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(468,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( D @ ( C @ c_Pair ) ) ) @ c_Set_Oinsert ) ) @ c_Wellfounded_Oacyclic ) )
| ( B @ ( A @ c_Wellfounded_Oacyclic ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acyclic__insert_0) ).
thf(1592,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( D @ ( C @ c_Pair ) ) ) @ c_Set_Oinsert ) ) @ c_Wellfounded_Oacyclic ) )
| ( B @ ( A @ c_Wellfounded_Oacyclic ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
thf(67,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( D @ c_Equiv__Relations_Oequiv ) ) )
| ~ ( C @ ( D @ ( A @ c_in ) ) )
| ( C @ ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equiv__class__self_0) ).
thf(742,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( D @ c_Equiv__Relations_Oequiv ) ) )
| ~ ( C @ ( D @ ( A @ c_in ) ) )
| ( C @ ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(229,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_Osym ) )
| ( B @ ( A @ c_Relation_Osym ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sym__converse_0) ).
thf(1089,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_Osym ) )
| ( B @ ( A @ c_Relation_Osym ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(299,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_in ) ) )
| ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
!= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comm__monoid__add_Ononempty__iff_2) ).
thf(1234,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_in ) ) )
| ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
!= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(444,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( A = B )
| ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Omktop ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__mktop_5) ).
thf(1541,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( A = B )
| ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Omktop ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(590,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ c_Wellfounded_Owf ) )
| ~ ( B @ ( B @ tc_prod ) @ ( C @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__irrefl_0) ).
thf(1851,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ c_Wellfounded_Owf ) )
| ~ ( B @ ( B @ tc_prod ) @ ( C @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[590]) ).
thf(554,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( A = D )
| ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Omkbot ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__mkbot_3) ).
thf(1772,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( A = D )
| ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Omkbot ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).
thf(440,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_in ) ) )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntE_0) ).
thf(1534,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_in ) ) )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).
thf(197,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ c_Equiv__Relations_Oequiv ) ) )
| ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_COMBK ) ) @ ( B @ c_Product__Type_OSigma ) ) ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equiv__type_0) ).
thf(1017,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ c_Equiv__Relations_Oequiv ) ) )
| ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_COMBK ) ) @ ( B @ c_Product__Type_OSigma ) ) ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(366,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( D @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( B @ ( C @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acc__downward_0) ).
thf(1375,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( D @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( B @ ( C @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(245,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__sup__iff_0) ).
thf(1121,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(240,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Set_Oinsert ) ) )
= ( C @ ( B @ ( A @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__Diff__single_0) ).
thf(1111,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Set_Oinsert ) ) )
= ( C @ ( B @ ( A @ c_Set_Oinsert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(295,axiom,
! [B: $i,A: $i] : ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__refl_0) ).
thf(1227,plain,
! [B: $i,A: $i] : ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(252,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__insert2_0) ).
thf(1138,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(529,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( B @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) )
| ( A = D )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insertE_0) ).
thf(1719,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( B @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) )
| ( A = D )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).
thf(86,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__Int__distrib2_0) ).
thf(783,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(243,axiom,
! [B: $i,A: $i] : ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equalityE_0) ).
thf(1118,plain,
! [B: $i,A: $i] : ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(120,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( A @ c_in ) ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Set_Oinsert ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__Diff__if_1) ).
thf(857,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( A @ c_in ) ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Set_Oinsert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(377,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ c_Nitpick_Orefl_H ) )
| ( B @ ( B @ tc_prod ) @ ( C @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nitpick_Orefl_H__def_0) ).
thf(1397,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ c_Nitpick_Orefl_H ) )
| ( B @ ( B @ tc_prod ) @ ( C @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(132,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__greatest_0) ).
thf(884,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(500,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_lessequals ) ) )
| ~ ( B @ ( C @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_predicate1D_0) ).
thf(1659,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_lessequals ) ) )
| ~ ( B @ ( C @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).
thf(72,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_Relation_Osym ) )
| ( ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sym__conv__converse__eq_0) ).
thf(753,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_Relation_Osym ) )
| ( ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(272,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_Wellfounded_Owf ) )
| ( B @ ( B @ ( B @ ( B @ ( A @ ( A @ c_Relation_Orel__comp ) ) ) ) @ c_Wellfounded_Owf ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__comp__self_0) ).
thf(1182,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_Wellfounded_Owf ) )
| ( B @ ( B @ ( B @ ( B @ ( A @ ( A @ c_Relation_Orel__comp ) ) ) ) @ c_Wellfounded_Owf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(538,axiom,
! [B: $i,A: $i] : ( B @ ( B @ tc_prod ) @ ( B @ c_Relation_OId @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IdI_0) ).
thf(1739,plain,
! [B: $i,A: $i] : ( B @ ( B @ tc_prod ) @ ( B @ c_Relation_OId @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).
thf(390,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( D @ ( F @ ( E @ ( A @ c_Set_Oimage ) ) ) @ c_lessequals ) ) )
| ~ ( F @ ( E @ ( B @ c_in ) ) )
| ( D @ ( C @ ( B @ ( A @ hAPP ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__subset__iff_0) ).
thf(1424,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( D @ ( F @ ( E @ ( A @ c_Set_Oimage ) ) ) @ c_lessequals ) ) )
| ~ ( F @ ( E @ ( B @ c_in ) ) )
| ( D @ ( C @ ( B @ ( A @ hAPP ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(24,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__left__idem_0) ).
thf(642,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(385,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_r__r__into__trancl_0) ).
thf(1414,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(400,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_Set_Oinsert ) ) @ c_Wellfounded_Oacyclic ) )
| ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acyclic__insert_1) ).
thf(1446,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_Set_Oinsert ) ) @ c_Wellfounded_Oacyclic ) )
| ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(478,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trancl__trans_0) ).
thf(1612,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).
thf(541,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( G @ ( C @ tc_prod ) @ ( E @ ( G @ ( C @ ( H @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ ( G @ tc_prod ) @ ( F @ ( D @ ( G @ ( B @ ( H @ c_Pair ) ) ) @ c_in ) ) )
| ( D @ ( C @ tc_prod ) @ ( D @ ( G @ ( C @ ( F @ ( E @ c_Relation_Orel__comp ) ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__compI_0) ).
thf(1744,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( G @ ( C @ tc_prod ) @ ( E @ ( G @ ( C @ ( H @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ ( G @ tc_prod ) @ ( F @ ( D @ ( G @ ( B @ ( H @ c_Pair ) ) ) @ c_in ) ) )
| ( D @ ( C @ tc_prod ) @ ( D @ ( G @ ( C @ ( F @ ( E @ c_Relation_Orel__comp ) ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).
thf(49,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_Relation_Osym ) )
| ( B @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_Relation_Osym ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sym__trancl_0) ).
thf(706,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_Relation_Osym ) )
| ( B @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_Relation_Osym ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(420,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( A @ c_Relation_Orefl__on ) ) )
| ~ ( C @ ( E @ ( B @ c_Relation_Orefl__on ) ) )
| ( C @ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( E @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Relation_Orefl__on ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_refl__on__Un_0) ).
thf(1493,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( A @ c_Relation_Orefl__on ) ) )
| ~ ( C @ ( E @ ( B @ c_Relation_Orefl__on ) ) )
| ( C @ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( E @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Relation_Orefl__on ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(512,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( E @ ( D @ ( A @ ( C @ c_Relation_OImage ) ) ) @ ( B @ c_in ) ) )
| ( E @ ( D @ tc_prod ) @ ( C @ ( E @ ( D @ ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__XImage__iff__1__1 ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Image__iff_1) ).
thf(1683,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( E @ ( D @ ( A @ ( C @ c_Relation_OImage ) ) ) @ ( B @ c_in ) ) )
| ( E @ ( D @ tc_prod ) @ ( C @ ( E @ ( D @ ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__XImage__iff__1__1 ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).
thf(21,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Lattices_Odistrib__lattice )
| ( B @ ( A @ tc_fun ) @ class_Lattices_Odistrib__lattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Odistrib__lattice) ).
thf(637,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Lattices_Odistrib__lattice )
| ( B @ ( A @ tc_fun ) @ class_Lattices_Odistrib__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(464,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ c_Relation_Osym ) )
| ~ ( C @ ( B @ c_Relation_Osym ) )
| ( C @ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Relation_Osym ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sym__Un_0) ).
thf(1584,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ c_Relation_Osym ) )
| ~ ( C @ ( B @ c_Relation_Osym ) )
| ( C @ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Relation_Osym ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(111,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_HOL_Oord )
| ( B @ ( A @ tc_fun ) @ class_HOL_Oord ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__HOL_Oord) ).
thf(837,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_HOL_Oord )
| ( B @ ( A @ tc_fun ) @ class_HOL_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(313,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__ge2_0) ).
thf(1263,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(47,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_Orderings_Obot__class_Obot @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Lattices_Obounded__lattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__bot__right_0) ).
thf(701,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_Orderings_Obot__class_Obot @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Lattices_Obounded__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(258,axiom,
! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_Relation_OId__on ) @ c_Relation_Oantisym ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_antisym__Id__on_0) ).
thf(1150,plain,
! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_Relation_OId__on ) @ c_Relation_Oantisym ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(65,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__assoc_0) ).
thf(738,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(580,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ c_Wellfounded_Owf ) )
| ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__asym_0) ).
thf(1831,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ c_Wellfounded_Owf ) )
| ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[580]) ).
thf(29,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Lattices_Obounded__lattice )
| ( B @ ( A @ tc_fun ) @ class_Lattices_Obounded__lattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Obounded__lattice) ).
thf(654,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Lattices_Obounded__lattice )
| ( B @ ( A @ tc_fun ) @ class_Lattices_Obounded__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(505,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( t_a @ ( t_a @ ( D @ c_Wellfounded_Oacc ) @ ( B @ c_in ) ) )
| ~ ( t_a @ ( t_a @ tc_prod ) @ ( D @ ( t_a @ ( t_a @ ( D @ ( A @ v_sko__Wellfounded__Xacc__Xinducts__1 ) @ ( C @ c_Pair ) ) ) @ c_in ) ) )
| ( t_a @ ( t_a @ ( D @ c_Wellfounded_Oacc ) @ ( C @ c_in ) ) )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acc_Oinducts_0) ).
thf(1668,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( t_a @ ( t_a @ ( D @ c_Wellfounded_Oacc ) @ ( B @ c_in ) ) )
| ~ ( t_a @ ( t_a @ tc_prod ) @ ( D @ ( t_a @ ( t_a @ ( D @ ( A @ v_sko__Wellfounded__Xacc__Xinducts__1 ) @ ( C @ c_Pair ) ) ) @ c_in ) ) )
| ( t_a @ ( t_a @ ( D @ c_Wellfounded_Oacc ) @ ( C @ c_in ) ) )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).
thf(449,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Omktop ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( B = D )
| ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__mktop_2) ).
thf(1552,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Omktop ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( B = D )
| ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).
thf(277,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ ( A @ c_Relation_OId__on ) @ c_Relation_ORange ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Range__Id__on_0) ).
thf(1192,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ ( A @ c_Relation_OId__on ) @ c_Relation_ORange ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(212,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( C @ ( A @ ( D @ c_Set_Oinsert ) ) @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__subset_1) ).
thf(1050,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( C @ ( A @ ( D @ c_Set_Oinsert ) ) @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(182,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_Equiv__Relations_Oequiv ) ) )
| ( C @ ( B @ ( A @ c_Relation_Orefl__on ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equiv_Orefl__on_0) ).
thf(984,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_Equiv__Relations_Oequiv ) ) )
| ( C @ ( B @ ( A @ c_Relation_Orefl__on ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(57,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__supI_0) ).
thf(721,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(566,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( F @ c_Relation_Osingle__valued ) ) )
| ~ ( E @ ( D @ tc_prod ) @ ( F @ ( E @ ( D @ ( A @ ( C @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( E @ ( D @ tc_prod ) @ ( F @ ( E @ ( D @ ( B @ ( C @ c_Pair ) ) ) @ c_in ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_single__valuedD_0) ).
thf(1799,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( F @ c_Relation_Osingle__valued ) ) )
| ~ ( E @ ( D @ tc_prod ) @ ( F @ ( E @ ( D @ ( A @ ( C @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( E @ ( D @ tc_prod ) @ ( F @ ( E @ ( D @ ( B @ ( C @ c_Pair ) ) ) @ c_in ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).
thf(392,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_Set_Oinsert ) ) @ c_Relation_ODomain ) ) )
= ( C @ ( D @ ( C @ ( E @ c_Relation_ODomain ) ) @ ( A @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Domain__insert_0) ).
thf(1429,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_Set_Oinsert ) ) @ c_Relation_ODomain ) ) )
= ( C @ ( D @ ( C @ ( E @ c_Relation_ODomain ) ) @ ( A @ c_Set_Oinsert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(84,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__insert_0) ).
thf(779,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(375,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_prod ) @ ( B @ ( C @ ( C @ ( A @ ( C @ ( A @ ( B @ c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1 ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acc_OaccI_0) ).
thf(1393,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_prod ) @ ( B @ ( C @ ( C @ ( A @ ( C @ ( A @ ( B @ c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1 ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(435,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( C @ c_Relation_OId @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Relation_Ototal__on ) ) )
| ( C @ ( B @ ( A @ c_Relation_Ototal__on ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_total__on__diff__Id_0) ).
thf(1525,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( C @ c_Relation_OId @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Relation_Ototal__on ) ) )
| ( C @ ( B @ ( A @ c_Relation_Ototal__on ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(466,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__trancl__trancl_0) ).
thf(1588,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).
thf(234,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( B = D )
| ( ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
!= ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ c_Set_Oinsert ) ) @ ( D @ c_Set_Oinsert ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_3) ).
thf(1099,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( B = D )
| ( ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
!= ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ c_Set_Oinsert ) ) @ ( D @ c_Set_Oinsert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(438,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_COMBK ) ) @ hAPP ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBK__def_0) ).
thf(1530,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_COMBK ) ) @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).
thf(405,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ c_Wellfounded_Oacyclic ) )
| ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_Set_Oinsert ) ) @ c_Wellfounded_Oacyclic ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acyclic__insert_2) ).
thf(1456,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ c_Wellfounded_Oacyclic ) )
| ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_Set_Oinsert ) ) @ c_Wellfounded_Oacyclic ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(472,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( C @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Product__Type_OSigma ) ) ) )
= ( tc_bool @ ( E @ ( C @ tc_prod ) @ tc_fun ) @ ( E @ ( C @ ( D @ ( B @ c_Product__Type_OSigma ) ) ) @ ( E @ ( C @ ( D @ ( A @ c_Product__Type_OSigma ) ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sigma__Diff__distrib1_0) ).
thf(1599,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( C @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Product__Type_OSigma ) ) ) )
= ( tc_bool @ ( E @ ( C @ tc_prod ) @ tc_fun ) @ ( E @ ( C @ ( D @ ( B @ c_Product__Type_OSigma ) ) ) @ ( E @ ( C @ ( D @ ( A @ c_Product__Type_OSigma ) ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).
thf(305,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__subset__iff_2) ).
thf(1246,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(339,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( B @ c_in ) ) )
| ( ( E @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_Set_Oinsert ) ) )
= ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__image_0) ).
thf(1318,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( B @ c_in ) ) )
| ( ( E @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_Set_Oinsert ) ) )
= ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(283,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__supE_0) ).
thf(1202,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(302,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( D @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) )
| ~ ( C @ ( A @ ( B @ c_in ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert__iff_0) ).
thf(1241,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( D @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) )
| ~ ( C @ ( A @ ( B @ c_in ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(557,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( E @ c_Relation_Ototal__on ) ) )
| ~ ( C @ ( E @ ( B @ c_in ) ) )
| ~ ( C @ ( E @ ( A @ c_in ) ) )
| ( B = A )
| ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_total__on__def_0) ).
thf(1779,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( E @ c_Relation_Ototal__on ) ) )
| ~ ( C @ ( E @ ( B @ c_in ) ) )
| ~ ( C @ ( E @ ( A @ c_in ) ) )
| ( B = A )
| ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).
thf(518,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__XtransI__1__3 ) @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__XtransI__1__2 ) @ c_Pair ) ) ) @ c_in ) ) )
| ( B @ ( A @ c_Relation_Otrans ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_transI_1) ).
thf(1695,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__XtransI__1__3 ) @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__XtransI__1__2 ) @ c_Pair ) ) ) @ c_in ) ) )
| ( B @ ( A @ c_Relation_Otrans ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).
thf(502,axiom,
! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insertI1_0) ).
thf(1663,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).
thf(480,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ tc_prod ) @ ( E @ ( C @ ( D @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ( D @ ( C @ tc_prod ) @ ( C @ ( D @ ( E @ c_Relation_Oconverse ) ) @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_converse__iff_1) ).
thf(1616,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ tc_prod ) @ ( E @ ( C @ ( D @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ( D @ ( C @ tc_prod ) @ ( C @ ( D @ ( E @ c_Relation_Oconverse ) ) @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).
thf(81,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__Un__distrib_0) ).
thf(773,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(153,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( A @ c_Relation_OId @ c_Relation_OImage ) ) ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Image__Id_0) ).
thf(926,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( A @ c_Relation_OId @ c_Relation_OImage ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(228,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
!= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__Un__eq_1) ).
thf(1086,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
!= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(160,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( B @ ( tc_bool @ ( C @ ( B @ tc_prod ) @ tc_fun ) @ ( D @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Relation_ORange ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( B @ ( D @ c_Relation_ORange ) ) @ ( C @ ( B @ ( A @ c_Relation_ORange ) ) @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Range__Diff__subset_0) ).
thf(938,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( B @ ( tc_bool @ ( C @ ( B @ tc_prod ) @ tc_fun ) @ ( D @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Relation_ORange ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( B @ ( D @ c_Relation_ORange ) ) @ ( C @ ( B @ ( A @ c_Relation_ORange ) ) @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(324,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_singletonE_0) ).
thf(1286,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(206,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__is__Un_0) ).
thf(1035,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(275,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ ( C @ tc_prod ) @ tc_fun ) @ ( D @ ( C @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( H @ c_COMBK ) ) @ ( F @ c_Product__Type_OSigma ) ) ) @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( E @ ( D @ tc_prod ) @ tc_fun ) @ ( E @ ( D @ ( D @ ( tc_bool @ ( E @ tc_fun ) @ ( G @ c_COMBK ) ) @ ( H @ c_Product__Type_OSigma ) ) ) @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( E @ ( C @ tc_prod ) @ tc_fun ) @ ( E @ ( C @ ( C @ ( tc_bool @ ( E @ tc_fun ) @ ( G @ c_COMBK ) ) @ ( F @ c_Product__Type_OSigma ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Relation_Orel__comp ) ) ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__comp__subset__Sigma_0) ).
thf(1187,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ ( C @ tc_prod ) @ tc_fun ) @ ( D @ ( C @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( H @ c_COMBK ) ) @ ( F @ c_Product__Type_OSigma ) ) ) @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( E @ ( D @ tc_prod ) @ tc_fun ) @ ( E @ ( D @ ( D @ ( tc_bool @ ( E @ tc_fun ) @ ( G @ c_COMBK ) ) @ ( H @ c_Product__Type_OSigma ) ) ) @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( E @ ( C @ tc_prod ) @ tc_fun ) @ ( E @ ( C @ ( C @ ( tc_bool @ ( E @ tc_fun ) @ ( G @ c_COMBK ) ) @ ( F @ c_Product__Type_OSigma ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Relation_Orel__comp ) ) ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(37,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__assoc_0) ).
thf(674,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(169,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Set_Oimage ) ) ) )
= ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( E @ ( D @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__Un_0) ).
thf(953,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Set_Oimage ) ) ) )
= ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( E @ ( D @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(274,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__subset__iff_0) ).
thf(1185,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(32,axiom,
tc_bool @ class_Lattices_Obounded__lattice,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Obounded__lattice) ).
thf(662,plain,
tc_bool @ class_Lattices_Obounded__lattice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(55,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ c_Relation_ODomain ) ) @ ( D @ ( C @ ( A @ c_Relation_ODomain ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( D @ ( C @ ( tc_bool @ ( D @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Relation_ODomain ) ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Domain__Int__subset_0) ).
thf(718,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ c_Relation_ODomain ) ) @ ( D @ ( C @ ( A @ c_Relation_ODomain ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( D @ ( C @ ( tc_bool @ ( D @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Relation_ODomain ) ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(144,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_Relation_ORange ) ) )
= ( B @ ( B @ ( A @ c_Relation_ORange ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trancl__range_0) ).
thf(906,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_Relation_ORange ) ) )
= ( B @ ( B @ ( A @ c_Relation_ORange ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(320,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Transitive__Closure_Otrancl ) )
= ( B @ ( B @ ( B @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ ( A @ c_Relation_Orel__comp ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trancl__unfold__left_0) ).
thf(1278,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Transitive__Closure_Otrancl ) )
= ( B @ ( B @ ( B @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ ( A @ c_Relation_Orel__comp ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(105,axiom,
! [B: $i,A: $i] :
( ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__cancel_0) ).
thf(824,plain,
! [B: $i,A: $i] :
( ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(318,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Odistrib__lattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__inf__distrib1_0) ).
thf(1273,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Odistrib__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(447,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( C @ ( C @ ( D @ c_Relation_Oconverse ) ) @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( C @ ( C @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ c_Relation_Oconverse ) ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trancl__converseD_0) ).
thf(1548,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( C @ ( C @ ( D @ c_Relation_Oconverse ) ) @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( C @ ( C @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ c_Relation_Oconverse ) ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(470,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_in ) ) )
| ( D @ ( C @ ( A @ c_in ) ) )
| ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__iff_2) ).
thf(1595,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_in ) ) )
| ( D @ ( C @ ( A @ c_in ) ) )
| ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(63,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) )
| ( A
= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( A
= ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__singletonD_0) ).
thf(733,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) )
| ( A
= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( A
= ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(4,negated_conjecture,
tc_Arrow__Order__Mirabelle_Oalt @ ( v_P @ v_F @ c_Relation_Otrans ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_3) ).
thf(601,plain,
tc_Arrow__Order__Mirabelle_Oalt @ ( v_P @ v_F @ c_Relation_Otrans ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(251,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( A = E )
| ( ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
!= ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ c_Set_Oinsert ) ) @ ( D @ c_Set_Oinsert ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_0) ).
thf(1135,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( A = E )
| ( ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
!= ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ c_Set_Oinsert ) ) @ ( D @ c_Set_Oinsert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(495,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ ( A @ ( C @ c_Set_Oinsert ) ) @ hAPP ) @ hBOOL )
| ( C = B )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__code_0) ).
thf(1648,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ ( A @ ( C @ c_Set_Oinsert ) ) @ hAPP ) @ hBOOL )
| ( C = B )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).
thf(174,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert__iff_4) ).
thf(965,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(71,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_Orderings_Obot__class_Obot ) )
| ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
!= ( A @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Lattices_Obounded__lattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__eq__bot__eq1_0) ).
thf(750,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_Orderings_Obot__class_Obot ) )
| ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
!= ( A @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Lattices_Obounded__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(532,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_Relation_Otrans ) )
| ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( A @ ( B @ ( B @ ( B @ ( A @ ( A @ c_Relation_Orel__comp ) ) ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__O__subset_0) ).
thf(1727,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_Relation_Otrans ) )
| ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( A @ ( B @ ( B @ ( B @ ( A @ ( A @ c_Relation_Orel__comp ) ) ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).
thf(428,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ c_Wellfounded_Owf ) )
| ( C @ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Wellfounded_Owf ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__Int2_0) ).
thf(1510,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ c_Wellfounded_Owf ) )
| ( C @ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Wellfounded_Owf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(307,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Int__distrib2_0) ).
thf(1251,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(550,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( t_a @ ( t_a @ ( C @ c_Wellfounded_Oacc ) @ ( B @ c_in ) ) )
| ~ ( C @ ( A @ v_sko__Wellfounded__Xacc__Xinduct__1 ) @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acc_Oinduct_2) ).
thf(1764,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( t_a @ ( t_a @ ( C @ c_Wellfounded_Oacc ) @ ( B @ c_in ) ) )
| ~ ( C @ ( A @ v_sko__Wellfounded__Xacc__Xinduct__1 ) @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).
thf(581,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( A @ c_in ) ) )
| ( B @ ( B @ tc_prod ) @ ( B @ ( C @ c_Relation_OId__on ) @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Id__on__eqI_0) ).
thf(1833,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( A @ c_in ) ) )
| ( B @ ( B @ tc_prod ) @ ( B @ ( C @ c_Relation_OId__on ) @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[581]) ).
thf(193,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__Un__distrib2_0) ).
thf(1007,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(247,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( C @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_ORange ) ) )
= ( C @ ( B @ ( A @ c_Relation_ODomain ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Range__converse_0) ).
thf(1125,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( C @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_ORange ) ) )
= ( C @ ( B @ ( A @ c_Relation_ODomain ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(482,axiom,
! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_Relation_OId__on ) @ c_Relation_Otrans ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__Id__on_0) ).
thf(1620,plain,
! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_Relation_OId__on ) @ c_Relation_Otrans ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).
thf(106,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Diff__cancel_0) ).
thf(826,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(564,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ c_in ) ) )
| ( D @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__iff_2) ).
thf(1795,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ c_in ) ) )
| ( D @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).
thf(433,axiom,
! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insertCI_1) ).
thf(1520,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(309,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__le1_0) ).
thf(1256,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(559,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_Relation_Osym ) )
| ~ ( B @ ( A @ c_Relation_Otrans ) )
| ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( A @ ( B @ ( B @ ( B @ ( A @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_Orel__comp ) ) ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sym__trans__comp__subset_0) ).
thf(1784,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_Relation_Osym ) )
| ~ ( B @ ( A @ c_Relation_Otrans ) )
| ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( A @ ( B @ ( B @ ( B @ ( A @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_Orel__comp ) ) ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).
thf(373,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_in ) ) )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_DiffE_0) ).
thf(1389,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_in ) ) )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(425,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( C @ ( B @ c_Relation_ODomain ) ) @ ( A @ c_in ) ) )
| ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__XDomainE__1__1 ) ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_DomainE_0) ).
thf(1503,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( C @ ( B @ c_Relation_ODomain ) ) @ ( A @ c_in ) ) )
| ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__XDomainE__1__1 ) ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(560,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_Relation_Oantisym ) )
| ( B @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ c_Relation_OId @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Relation_Oantisym ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_antisym__reflcl_1) ).
thf(1786,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_Relation_Oantisym ) )
| ( B @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ c_Relation_OId @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Relation_Oantisym ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).
thf(159,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_Transitive__Closure_Otrancl ) )
= ( B @ ( A @ c_Transitive__Closure_Ortrancl ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__trancl__absorb_0) ).
thf(936,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_Transitive__Closure_Otrancl ) )
= ( B @ ( A @ c_Transitive__Closure_Ortrancl ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(317,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__subset__rtrancl_0) ).
thf(1271,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(336,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__code_2) ).
thf(1312,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(535,axiom,
! [B: $i,A: $i] :
~ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__iff_0) ).
thf(1733,plain,
! [B: $i,A: $i] :
~ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).
thf(238,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ ( C @ tc_prod ) @ tc_fun ) @ ( D @ ( C @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( E @ c_COMBK ) ) @ ( F @ c_Product__Type_OSigma ) ) ) @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( D @ tc_fun ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Relation_OImage ) ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Image__subset_0) ).
thf(1107,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ ( C @ tc_prod ) @ tc_fun ) @ ( D @ ( C @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( E @ c_COMBK ) ) @ ( F @ c_Product__Type_OSigma ) ) ) @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( D @ tc_fun ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Relation_OImage ) ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(301,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( E @ ( tc_bool @ ( D @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Relation_OImage ) ) ) )
= ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( E @ ( B @ c_Relation_OImage ) ) ) @ ( D @ ( C @ ( E @ ( A @ c_Relation_OImage ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Image_0) ).
thf(1239,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( E @ ( tc_bool @ ( D @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Relation_OImage ) ) ) )
= ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( E @ ( B @ c_Relation_OImage ) ) ) @ ( D @ ( C @ ( E @ ( A @ c_Relation_OImage ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(345,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( D @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acc__downwards_0) ).
thf(1332,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( D @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(166,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__greatest_0) ).
thf(947,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(491,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( F @ ( B @ ( A @ c_ATP__Linkup_Osko__Product__Type__XSigma__mono__1__1 ) ) ) ) @ ( F @ hAPP ) @ ( D @ ( C @ ( F @ ( B @ ( A @ c_ATP__Linkup_Osko__Product__Type__XSigma__mono__1__1 ) ) ) ) @ ( B @ hAPP ) @ c_lessequals ) ) )
| ( tc_bool @ ( D @ ( C @ tc_prod ) @ tc_fun ) @ ( D @ ( C @ ( F @ ( E @ c_Product__Type_OSigma ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Product__Type_OSigma ) ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sigma__mono_1) ).
thf(1638,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( F @ ( B @ ( A @ c_ATP__Linkup_Osko__Product__Type__XSigma__mono__1__1 ) ) ) ) @ ( F @ hAPP ) @ ( D @ ( C @ ( F @ ( B @ ( A @ c_ATP__Linkup_Osko__Product__Type__XSigma__mono__1__1 ) ) ) ) @ ( B @ hAPP ) @ c_lessequals ) ) )
| ( tc_bool @ ( D @ ( C @ tc_prod ) @ tc_fun ) @ ( D @ ( C @ ( F @ ( E @ c_Product__Type_OSigma ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Product__Type_OSigma ) ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).
thf(357,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ ( C @ ( B @ c_Relation_ODomain ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Not__Domain__rtrancl_1) ).
thf(1356,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ ( C @ ( B @ c_Relation_ODomain ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(10,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__left__idem_0) ).
thf(611,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(88,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( D @ ( A @ c_Set_Oinsert ) ) @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__mono_0) ).
thf(787,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( D @ ( A @ c_Set_Oinsert ) ) @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(150,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Wellfounded_Owf ) )
| ~ ( B @ ( A @ c_Wellfounded_Owf ) )
| ~ ( B @ ( C @ c_Wellfounded_Owf ) )
| ( ( tc_bool @ ( B @ tc_fun ) @ ( B @ ( B @ ( C @ c_Relation_ORange ) ) @ ( B @ ( B @ ( A @ c_Relation_ODomain ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
!= ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__Un_0) ).
thf(919,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Wellfounded_Owf ) )
| ~ ( B @ ( A @ c_Wellfounded_Owf ) )
| ~ ( B @ ( C @ c_Wellfounded_Owf ) )
| ( ( tc_bool @ ( B @ tc_fun ) @ ( B @ ( B @ ( C @ c_Relation_ORange ) ) @ ( B @ ( B @ ( A @ c_Relation_ODomain ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
!= ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(96,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
| ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__subset__conv_0) ).
thf(804,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
| ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(310,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( C @ ( C @ ( C @ ( A @ ( B @ c_Relation_Orel__comp ) ) ) ) @ ( C @ ( C @ ( C @ ( A @ ( A @ c_Relation_Orel__comp ) ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Wellfounded_Owf ) )
| ( C @ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Wellfounded_Owf ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__union__merge_1) ).
thf(1258,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( C @ ( C @ ( C @ ( A @ ( B @ c_Relation_Orel__comp ) ) ) ) @ ( C @ ( C @ ( C @ ( A @ ( A @ c_Relation_Orel__comp ) ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Wellfounded_Owf ) )
| ( C @ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Wellfounded_Owf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(48,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__commute_0) ).
thf(704,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(77,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ ( B @ c_in ) ) )
| ( ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__insert__right_1) ).
thf(764,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ ( B @ c_in ) ) )
| ( ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(278,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Diff__Int_0) ).
thf(1194,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(142,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( D @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__eqI_1) ).
thf(900,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( D @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(108,axiom,
! [A: $i] : ( A @ ( A @ c_Relation_OId @ c_Relation_Oantisym ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_antisym__Id_0) ).
thf(831,plain,
! [A: $i] : ( A @ ( A @ c_Relation_OId @ c_Relation_Oantisym ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(591,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( E @ ( B @ c_Relation_Orefl__on ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( E @ ( C @ ( C @ ( A @ ( D @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_refl__onD2_0) ).
thf(1853,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( E @ ( B @ c_Relation_Orefl__on ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( E @ ( C @ ( C @ ( A @ ( D @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[591]) ).
thf(322,axiom,
! [A: $i] : ( A @ ( A @ ( A @ c_Relation_OId @ c_Relation_Osingle__valued ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_single__valued__Id_0) ).
thf(1282,plain,
! [A: $i] : ( A @ ( A @ ( A @ c_Relation_OId @ c_Relation_Osingle__valued ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(64,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ c_Orderings_Obot__class_Obot @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Obot ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bot__least_0) ).
thf(736,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ c_Orderings_Obot__class_Obot @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(353,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__into__trancl1_0) ).
thf(1349,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(188,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= C )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__absorb2_0) ).
thf(996,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= C )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(530,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_Order__Relation_Ostrict__linear__order__on ) ) )
| ( B @ ( A @ c_Relation_Otrans ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_strict__linear__order__on__def_0) ).
thf(1722,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_Order__Relation_Ostrict__linear__order__on ) ) )
| ( B @ ( A @ c_Relation_Otrans ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).
thf(3,negated_conjecture,
tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( v_P @ v_F @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( v_b @ ( v_a @ c_Pair ) ) ) @ c_in ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(599,plain,
tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( v_P @ v_F @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( v_b @ ( v_a @ c_Pair ) ) ) @ c_in ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(333,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( E @ ( A @ c_Set_Oimage ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__diff__subset_0) ).
thf(1307,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( E @ ( A @ c_Set_Oimage ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(269,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( C @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_ODomain ) ) )
= ( C @ ( B @ ( A @ c_Relation_ORange ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Domain__converse_0) ).
thf(1175,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( C @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_ODomain ) ) )
= ( C @ ( B @ ( A @ c_Relation_ORange ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(459,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( C @ ( C @ ( tc_bool @ ( F @ tc_fun ) @ ( F @ ( E @ ( D @ c_Set_Oinsert ) ) @ c_COMBK ) ) @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Product__Type_OSigma ) ) ) )
= ( F @ ( C @ tc_prod ) @ ( tc_bool @ ( F @ ( C @ tc_prod ) @ tc_fun ) @ ( F @ ( C @ ( C @ ( tc_bool @ ( F @ tc_fun ) @ ( E @ c_COMBK ) ) @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Product__Type_OSigma ) ) ) @ ( F @ ( C @ ( C @ ( tc_bool @ ( F @ tc_fun ) @ ( F @ ( E @ ( D @ c_Set_Oinsert ) ) @ c_COMBK ) ) @ ( B @ c_Product__Type_OSigma ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( F @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__times__insert_0) ).
thf(1574,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( C @ ( C @ ( tc_bool @ ( F @ tc_fun ) @ ( F @ ( E @ ( D @ c_Set_Oinsert ) ) @ c_COMBK ) ) @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Product__Type_OSigma ) ) ) )
= ( F @ ( C @ tc_prod ) @ ( tc_bool @ ( F @ ( C @ tc_prod ) @ tc_fun ) @ ( F @ ( C @ ( C @ ( tc_bool @ ( F @ tc_fun ) @ ( E @ c_COMBK ) ) @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Product__Type_OSigma ) ) ) @ ( F @ ( C @ ( C @ ( tc_bool @ ( F @ tc_fun ) @ ( F @ ( E @ ( D @ c_Set_Oinsert ) ) @ c_COMBK ) ) @ ( B @ c_Product__Type_OSigma ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( F @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_Set_Oinsert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(195,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
!= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__empty_1) ).
thf(1011,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
!= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(130,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ c_Wellfounded_Owf ) )
| ~ ( C @ ( B @ c_Wellfounded_Owf ) )
| ~ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( A @ ( C @ ( C @ ( C @ ( B @ ( A @ c_Relation_Orel__comp ) ) ) ) @ c_lessequals ) ) )
| ( C @ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Wellfounded_Owf ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__union__compatible_0) ).
thf(880,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ c_Wellfounded_Owf ) )
| ~ ( C @ ( B @ c_Wellfounded_Owf ) )
| ~ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( A @ ( C @ ( C @ ( C @ ( B @ ( A @ c_Relation_Orel__comp ) ) ) ) @ c_lessequals ) ) )
| ( C @ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Wellfounded_Owf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(27,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= B )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__idem_0) ).
thf(649,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= B )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(136,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__sup__iff_2) ).
thf(890,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(19,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I8_J_0) ).
thf(631,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(74,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Transitive__Closure_Ortrancl ) )
= ( B @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Transitive__Closure_Ortrancl ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__Un__rtrancl_0) ).
thf(758,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Transitive__Closure_Ortrancl ) )
= ( B @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Transitive__Closure_Ortrancl ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(487,axiom,
! [C: $i,B: $i,A: $i] :
~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( A @ ( C @ c_Arrow__Order__Mirabelle_Omktop ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__mktop_0) ).
thf(1630,plain,
! [C: $i,B: $i,A: $i] :
~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( A @ ( C @ c_Arrow__Order__Mirabelle_Omktop ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).
thf(59,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_Order__Relation_Ostrict__linear__order__on ) ) )
| ( C @ ( B @ ( A @ c_Relation_Ototal__on ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_strict__linear__order__on__def_2) ).
thf(726,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_Order__Relation_Ostrict__linear__order__on ) ) )
| ( C @ ( B @ ( A @ c_Relation_Ototal__on ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(15,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( A @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I3_J_0) ).
thf(621,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( A @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(116,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ ( A @ c_Relation_OId__on ) @ c_Relation_ODomain ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Domain__Id__on_0) ).
thf(848,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ ( A @ c_Relation_OId__on ) @ c_Relation_ODomain ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(342,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ hAPP ) @ hBOOL )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_lessequals ) ) )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__predicate1D_0) ).
thf(1325,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ hAPP ) @ hBOOL )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_lessequals ) ) )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(35,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( B @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__commute_0) ).
thf(668,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( B @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(574,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( tc_bool @ ( D @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Relation_ODomain ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ c_Relation_ODomain ) ) @ ( D @ ( C @ ( A @ c_Relation_ODomain ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Domain__Un__eq_0) ).
thf(1820,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( tc_bool @ ( D @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Relation_ODomain ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ c_Relation_ODomain ) ) @ ( D @ ( C @ ( A @ c_Relation_ODomain ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).
thf(534,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( D @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( B @ ( C @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acc_Ocases_0) ).
thf(1731,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( D @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( B @ ( C @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[534]) ).
thf(1,negated_conjecture,
! [A: $i] : ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( v_P @ hAPP ) @ c_Relation_Otrans ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(594,plain,
! [A: $i] : ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( v_P @ hAPP ) @ c_Relation_Otrans ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(203,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_Wellfounded_Owf ) )
| ( B @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_Wellfounded_Owf ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__trancl_0) ).
thf(1029,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_Wellfounded_Owf ) )
| ( B @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_Wellfounded_Owf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(139,axiom,
! [B: $i,A: $i] : ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__subsetI_0) ).
thf(895,plain,
! [B: $i,A: $i] : ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(79,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Transitive__Closure_Otrancl ) )
= ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( B @ ( B @ ( A @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_Relation_Orel__comp ) ) ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trancl__unfold_0) ).
thf(769,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Transitive__Closure_Otrancl ) )
= ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( B @ ( B @ ( A @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_Relation_Orel__comp ) ) ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(407,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_Set_Oinsert ) ) @ c_Relation_ORange ) ) )
= ( D @ ( D @ ( C @ ( E @ c_Relation_ORange ) ) @ ( B @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Range__insert_0) ).
thf(1460,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_Set_Oinsert ) ) @ c_Relation_ORange ) ) )
= ( D @ ( D @ ( C @ ( E @ c_Relation_ORange ) ) @ ( B @ c_Set_Oinsert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(270,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__Int_0) ).
thf(1177,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(369,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( D @ ( C @ c_Wellfounded_Oacc ) @ ( B @ c_in ) ) )
| ( D @ ( D @ ( C @ c_Wellfounded_Oacc ) @ ( D @ ( C @ ( A @ c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 ) ) @ c_in ) ) )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acc__induct__rule_0) ).
thf(1381,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( D @ ( C @ c_Wellfounded_Oacc ) @ ( B @ c_in ) ) )
| ( D @ ( D @ ( C @ c_Wellfounded_Oacc ) @ ( D @ ( C @ ( A @ c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 ) ) @ c_in ) ) )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(157,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( A @ ( B @ ( A @ c_Relation_OId @ c_Relation_Orel__comp ) ) ) ) )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Id__O__R_0) ).
thf(932,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( A @ ( B @ ( A @ c_Relation_OId @ c_Relation_Orel__comp ) ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(217,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__inf__iff_0) ).
thf(1061,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(280,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__supI1_0) ).
thf(1198,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(288,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ c_Wellfounded_Owf ) )
| ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
| ( B @ ( A @ c_Wellfounded_Owf ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__subset_0) ).
thf(1213,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ c_Wellfounded_Owf ) )
| ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
| ( B @ ( A @ c_Wellfounded_Owf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(183,axiom,
! [B: $i,A: $i] : ( B @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_singleton__iff_1) ).
thf(986,plain,
! [B: $i,A: $i] : ( B @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(241,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_Relation_Orel__comp ) ) ) ) )
= ( B @ ( A @ c_Transitive__Closure_Ortrancl ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__idemp__self__comp_0) ).
thf(1113,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_Relation_Orel__comp ) ) ) ) )
= ( B @ ( A @ c_Transitive__Closure_Ortrancl ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(555,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
| ~ ( C @ ( D @ ( A @ c_in ) ) )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__iff_0) ).
thf(1775,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
| ~ ( C @ ( D @ ( A @ c_in ) ) )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).
thf(413,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( F @ tc_prod ) @ ( D @ ( F @ ( F @ ( B @ ( E @ hAPP ) @ ( A @ ( E @ hAPP ) @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( C @ ( F @ ( E @ ( D @ c_Relation_Oinv__image ) ) ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__inv__image_1) ).
thf(1477,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( F @ tc_prod ) @ ( D @ ( F @ ( F @ ( B @ ( E @ hAPP ) @ ( A @ ( E @ hAPP ) @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( C @ ( F @ ( E @ ( D @ c_Relation_Oinv__image ) ) ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(361,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Relation_OId__on ) @ ( C @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Id__on__iff_1) ).
thf(1364,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Relation_OId__on ) @ ( C @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(235,axiom,
( ( t_b @ ( t_a @ ( v_r @ c_Relation_ORange ) ) )
= ( t_a @ ( t_b @ ( t_b @ ( t_a @ ( v_r @ c_Relation_Oconverse ) ) @ c_Relation_ODomain ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Range__def__raw_0) ).
thf(1102,plain,
( ( t_b @ ( t_a @ ( v_r @ c_Relation_ORange ) ) )
= ( t_a @ ( t_b @ ( t_b @ ( t_a @ ( v_r @ c_Relation_Oconverse ) ) @ c_Relation_ODomain ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(151,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_in ) ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__insert__absorb_0) ).
thf(922,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_in ) ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(453,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ c_Relation_Otrans ) )
| ~ ( C @ ( B @ c_Relation_Oirrefl ) )
| ~ ( C @ ( B @ ( A @ c_Relation_Ototal__on ) ) )
| ( C @ ( B @ ( A @ c_Order__Relation_Ostrict__linear__order__on ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_strict__linear__order__on__def_3) ).
thf(1562,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ c_Relation_Otrans ) )
| ~ ( C @ ( B @ c_Relation_Oirrefl ) )
| ~ ( C @ ( B @ ( A @ c_Relation_Ototal__on ) ) )
| ( C @ ( B @ ( A @ c_Order__Relation_Ostrict__linear__order__on ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(147,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Transitive__Closure_Otrancl ) )
= ( B @ ( B @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_Relation_Oconverse ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trancl__converse_0) ).
thf(912,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Transitive__Closure_Otrancl ) )
= ( B @ ( B @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_Relation_Oconverse ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(41,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( B @ ( B @ ( A @ c_Relation_ODomain ) ) @ c_Equiv__Relations_Oequiv ) ) )
| ( ( B @ ( B @ ( B @ ( A @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_Orel__comp ) ) ) ) )
!= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comp__equivI_0) ).
thf(685,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( B @ ( B @ ( A @ c_Relation_ODomain ) ) @ c_Equiv__Relations_Oequiv ) ) )
| ( ( B @ ( B @ ( B @ ( A @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_Orel__comp ) ) ) ) )
!= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(267,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( E @ c_lessequals ) ) )
| ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__eqI_1) ).
thf(1171,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( E @ c_lessequals ) ) )
| ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(469,axiom,
! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_Relation_Otrans ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__trancl_0) ).
thf(1594,plain,
! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_Relation_Otrans ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).
thf(520,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Relation_OId__on ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Id__on__iff_0) ).
thf(1699,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Relation_OId__on ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).
thf(210,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__absorb2_0) ).
thf(1044,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(45,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= B )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__inf__absorb_0) ).
thf(695,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= B )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(304,axiom,
! [B: $i,A: $i] : ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( B @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ ( A @ c_COMBK ) ) @ ( A @ c_Product__Type_OSigma ) ) ) @ ( B @ ( A @ c_Relation_OId__on ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Id__on__subset__Times_0) ).
thf(1245,plain,
! [B: $i,A: $i] : ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( B @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ ( A @ c_COMBK ) ) @ ( A @ c_Product__Type_OSigma ) ) ) @ ( B @ ( A @ c_Relation_OId__on ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(224,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__absorb1_0) ).
thf(1076,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(569,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( D @ tc_prod ) @ ( D @ ( B @ c_Transitive__Closure_Otrancl ) @ ( D @ ( D @ ( C @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( D @ ( D @ tc_prod ) @ ( D @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( D @ ( D @ ( D @ ( C @ ( A @ ( B @ c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1 ) ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_tranclD2_0) ).
thf(1809,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( D @ tc_prod ) @ ( D @ ( B @ c_Transitive__Closure_Otrancl ) @ ( D @ ( D @ ( C @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( D @ ( D @ tc_prod ) @ ( D @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( D @ ( D @ ( D @ ( C @ ( A @ ( B @ c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1 ) ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[569]) ).
thf(265,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_Oantisym ) )
| ( B @ ( A @ c_Relation_Oantisym ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_antisym__converse_0) ).
thf(1166,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_Oantisym ) )
| ( B @ ( A @ c_Relation_Oantisym ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(286,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Relation_OImage ) ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Image__empty_0) ).
thf(1208,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Relation_OImage ) ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(164,axiom,
! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__lower1_0) ).
thf(944,plain,
! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(409,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( A = B )
| ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__eq__or__trancl_0) ).
thf(1467,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( A = B )
| ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(33,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I2_J_0) ).
thf(663,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(388,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
| ~ ( C @ ( D @ ( A @ c_in ) ) )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__mp_0) ).
thf(1420,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
| ~ ( C @ ( D @ ( A @ c_in ) ) )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(100,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= C )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__sup_0) ).
thf(812,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= C )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(226,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__ord_I3_J_0) ).
thf(1081,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(12,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Orderings_Obot )
| ( B @ ( A @ tc_fun ) @ class_Orderings_Obot ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Orderings_Obot) ).
thf(617,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Orderings_Obot )
| ( B @ ( A @ tc_fun ) @ class_Orderings_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(256,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( D @ c_lessequals ) ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Int__assoc__eq_1) ).
thf(1145,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( D @ c_lessequals ) ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(92,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__ord_I1_J_0) ).
thf(795,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(39,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I4_J_0) ).
thf(680,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(161,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( tc_bool @ ( E @ tc_fun ) @ ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( D @ ( C @ ( A @ c_Relation_OImage ) ) ) @ ( E @ ( D @ ( B @ ( A @ c_Relation_OImage ) ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Relation_OImage ) ) ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Image__Int__subset_0) ).
thf(939,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( tc_bool @ ( E @ tc_fun ) @ ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( D @ ( C @ ( A @ c_Relation_OImage ) ) ) @ ( E @ ( D @ ( B @ ( A @ c_Relation_OImage ) ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Relation_OImage ) ) ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(349,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( E @ ( B @ c_in ) ) )
| ~ ( C @ ( E @ ( D @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( A @ ( C @ ( C @ ( D @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( A @ ( E @ c_Equiv__Relations_Oequiv ) ) )
| ( ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) )
!= ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equiv__class__eq__iff_3) ).
thf(1340,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( E @ ( B @ c_in ) ) )
| ~ ( C @ ( E @ ( D @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( A @ ( C @ ( C @ ( D @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( A @ ( E @ c_Equiv__Relations_Oequiv ) ) )
| ( ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) )
!= ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(587,axiom,
! [B: $i,A: $i] :
~ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_emptyE_0) ).
thf(1845,plain,
! [B: $i,A: $i] :
~ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[587]) ).
thf(23,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Lattices_Olattice )
| ( B @ ( A @ tc_fun ) @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olattice) ).
thf(640,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Lattices_Olattice )
| ( B @ ( A @ tc_fun ) @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(201,axiom,
! [B: $i,A: $i] :
( ( B @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ c_Relation_OId @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Transitive__Closure_Ortrancl ) )
= ( B @ ( A @ c_Transitive__Closure_Ortrancl ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__r__diff__Id_0) ).
thf(1025,plain,
! [B: $i,A: $i] :
( ( B @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ c_Relation_OId @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Transitive__Closure_Ortrancl ) )
= ( B @ ( A @ c_Transitive__Closure_Ortrancl ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(261,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( B @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__sup__iff_1) ).
thf(1156,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( B @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(294,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__Int2_0) ).
thf(1225,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(134,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__subset__iff_1) ).
thf(887,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(455,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( F @ ( E @ ( C @ ( B @ c_Pair ) ) ) @ ( tc_bool @ ( G @ tc_fun ) @ ( F @ ( E @ ( A @ c_split ) ) ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_splitD_H_0) ).
thf(1566,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( F @ ( E @ ( C @ ( B @ c_Pair ) ) ) @ ( tc_bool @ ( G @ tc_fun ) @ ( F @ ( E @ ( A @ c_split ) ) ) @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(363,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__XtransI__1__2 ) @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__XtransI__1__1 ) @ c_Pair ) ) ) @ c_in ) ) )
| ( B @ ( A @ c_Relation_Otrans ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_transI_0) ).
thf(1368,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__XtransI__1__2 ) @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__XtransI__1__1 ) @ c_Pair ) ) ) @ c_in ) ) )
| ( B @ ( A @ c_Relation_Otrans ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(52,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__left__absorb_0) ).
thf(712,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(191,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ c_Relation_Osingle__valued ) ) )
| ~ ( E @ ( D @ ( B @ c_Relation_Osingle__valued ) ) )
| ( E @ ( C @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Relation_Orel__comp ) ) ) ) @ c_Relation_Osingle__valued ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_single__valued__rel__comp_0) ).
thf(1003,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ c_Relation_Osingle__valued ) ) )
| ~ ( E @ ( D @ ( B @ c_Relation_Osingle__valued ) ) )
| ( E @ ( C @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Relation_Orel__comp ) ) ) ) @ c_Relation_Osingle__valued ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(553,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( E @ ( B @ c_Equiv__Relations_Oequiv ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( E @ ( C @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equiv__class__eq__iff_1) ).
thf(1770,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( E @ ( B @ c_Equiv__Relations_Oequiv ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( E @ ( C @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).
thf(43,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) )
!= ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_singleton__inject_0) ).
thf(690,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) )
!= ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(431,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ c_Wellfounded_Owf ) )
| ~ ( C @ ( A @ ( D @ c_in ) ) )
| ( C @ ( A @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__eq__minimal_0) ).
thf(1516,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ c_Wellfounded_Owf ) )
| ~ ( C @ ( A @ ( D @ c_in ) ) )
| ( C @ ( A @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(545,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( t_a @ ( t_a @ ( D @ c_Wellfounded_Oacc ) @ ( B @ c_in ) ) )
| ~ ( t_a @ ( t_a @ tc_prod ) @ ( D @ ( t_a @ ( t_a @ ( D @ ( A @ v_sko__Wellfounded__Xacc__Xinduct__1 ) @ ( C @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acc_Oinduct_1) ).
thf(1753,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( t_a @ ( t_a @ ( D @ c_Wellfounded_Oacc ) @ ( B @ c_in ) ) )
| ~ ( t_a @ ( t_a @ tc_prod ) @ ( D @ ( t_a @ ( t_a @ ( D @ ( A @ v_sko__Wellfounded__Xacc__Xinduct__1 ) @ ( C @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).
thf(315,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( C @ ( D @ ( A @ c_Set_Oinsert ) ) @ c_lessequals ) ) )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__subset_0) ).
thf(1267,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( C @ ( D @ ( A @ c_Set_Oinsert ) ) @ c_lessequals ) ) )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(297,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( C @ ( B @ ( A @ c_Relation_OId__on ) @ c_Relation_OImage ) ) ) )
= ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Image__Id__on_0) ).
thf(1230,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( C @ ( B @ ( A @ c_Relation_OId__on ) @ c_Relation_OImage ) ) ) )
= ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(416,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = E )
| ~ ( C @ ( B @ ( F @ c_in ) ) )
| ( ( C @ ( D @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_COMBK ) ) @ ( A @ c_Product__Type_OSigma ) ) ) )
!= ( C @ ( D @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_COMBK ) ) @ ( E @ c_Product__Type_OSigma ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Times__eq__cancel2_0) ).
thf(1484,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = E )
| ~ ( C @ ( B @ ( F @ c_in ) ) )
| ( ( C @ ( D @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_COMBK ) ) @ ( A @ c_Product__Type_OSigma ) ) ) )
!= ( C @ ( D @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_COMBK ) ) @ ( E @ c_Product__Type_OSigma ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(90,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__ge1_0) ).
thf(791,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(208,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= B )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__iff__inf_0) ).
thf(1038,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= B )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(510,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( D @ c_Relation_Orefl__on ) ) )
| ~ ( B @ ( D @ ( A @ c_in ) ) )
| ( B @ ( B @ tc_prod ) @ ( C @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_refl__on__def_1) ).
thf(1679,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( D @ c_Relation_Orefl__on ) ) )
| ~ ( B @ ( D @ ( A @ c_in ) ) )
| ( B @ ( B @ tc_prod ) @ ( C @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).
thf(291,axiom,
! [B: $i,A: $i] :
( ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__absorb_0) ).
thf(1218,plain,
! [B: $i,A: $i] :
( ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(347,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( D @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( E @ c_Relation_OImage ) ) ) @ ( B @ c_in ) ) )
| ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Image__singleton__iff_0) ).
thf(1336,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( D @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( E @ c_Relation_OImage ) ) ) @ ( B @ c_in ) ) )
| ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(292,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( A = E )
| ( ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
!= ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ c_Set_Oinsert ) ) @ ( D @ c_Set_Oinsert ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_2) ).
thf(1220,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( A = E )
| ( ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
!= ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ c_Set_Oinsert ) ) @ ( D @ c_Set_Oinsert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(526,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ c_Relation_Oantisym ) )
| ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_antisymD_0) ).
thf(1711,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ c_Relation_Oantisym ) )
| ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).
thf(423,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ c_Relation_OId @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Relation_Oantisym ) )
| ( B @ ( A @ c_Relation_Oantisym ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_antisym__reflcl_0) ).
thf(1499,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ c_Relation_OId @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Relation_Oantisym ) )
| ( B @ ( A @ c_Relation_Oantisym ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(562,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( E @ c_Equiv__Relations_Oequiv ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( A @ ( C @ ( C @ ( D @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ( ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) )
= ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equiv__class__eq_0) ).
thf(1790,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( E @ c_Equiv__Relations_Oequiv ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( A @ ( C @ ( C @ ( D @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ( ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) )
= ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[562]) ).
thf(528,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( C @ ( B @ ( A @ c_in ) ) )
| ( C @ ( D @ ( A @ c_in ) ) )
| ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
!= ( C @ ( D @ ( A @ c_Set_Oinsert ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__ident_0) ).
thf(1716,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( C @ ( B @ ( A @ c_in ) ) )
| ( C @ ( D @ ( A @ c_in ) ) )
| ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
!= ( C @ ( D @ ( A @ c_Set_Oinsert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).
thf(571,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( D @ tc_prod ) @ ( B @ ( D @ ( D @ ( C @ ( F @ c_Pair ) ) ) @ c_in ) ) )
| ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Recdef_Ocut ) ) ) ) @ hAPP ) )
= ( F @ ( A @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cut__apply_0) ).
thf(1813,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( D @ tc_prod ) @ ( B @ ( D @ ( D @ ( C @ ( F @ c_Pair ) ) ) @ c_in ) ) )
| ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Recdef_Ocut ) ) ) ) @ hAPP ) )
= ( F @ ( A @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).
thf(330,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( D @ c_in ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( B @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert_0) ).
thf(1300,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( D @ c_in ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( B @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(403,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( B @ ( A @ c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1 ) @ ( B @ ( A @ c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1 ) @ c_Pair ) ) ) @ c_in ) ) )
| ( B @ ( A @ c_Nitpick_Orefl_H ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nitpick_Orefl_H__def_1) ).
thf(1452,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( B @ ( A @ c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1 ) @ ( B @ ( A @ c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1 ) @ c_Pair ) ) ) @ c_in ) ) )
| ( B @ ( A @ c_Nitpick_Orefl_H ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(442,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ c_Relation_Osym ) )
| ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_symD_0) ).
thf(1538,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ c_Relation_Osym ) )
| ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).
thf(168,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( E @ ( A @ c_Set_Oimage ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__mono_0) ).
thf(951,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( E @ ( A @ c_Set_Oimage ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(98,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__inf__iff_2) ).
thf(808,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(68,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Wellfounded_Owf ) )
| ( B @ ( B @ ( B @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_Relation_Oconverse ) ) @ c_Wellfounded_Owf ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__converse__trancl_0) ).
thf(744,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Wellfounded_Owf ) )
| ( B @ ( B @ ( B @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_Relation_Oconverse ) ) @ c_Wellfounded_Owf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(551,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( D @ ( B @ c_Relation_ORange ) ) @ ( A @ c_in ) ) )
| ( C @ ( D @ tc_prod ) @ ( B @ ( C @ ( D @ ( A @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__XRangeE__1__1 ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_RangeE_0) ).
thf(1766,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( D @ ( B @ c_Relation_ORange ) ) @ ( A @ c_in ) ) )
| ( C @ ( D @ tc_prod ) @ ( B @ ( C @ ( D @ ( A @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__XRangeE__1__1 ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).
thf(589,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( E @ c_Equiv__Relations_Oequiv ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( D @ c_Relation_OImage ) ) ) @ ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( D @ c_Relation_OImage ) ) ) @ c_lessequals ) ) )
| ~ ( C @ ( E @ ( B @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__equiv__class_0) ).
thf(1849,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( E @ c_Equiv__Relations_Oequiv ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( D @ c_Relation_OImage ) ) ) @ ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( D @ c_Relation_OImage ) ) ) @ c_lessequals ) ) )
| ~ ( C @ ( E @ ( B @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[589]) ).
thf(441,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ tc_prod ) @ ( E @ ( C @ ( D @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ( D @ ( C @ tc_prod ) @ ( C @ ( D @ ( E @ c_Relation_Oconverse ) ) @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_converseI_0) ).
thf(1536,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ tc_prod ) @ ( E @ ( C @ ( D @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ( D @ ( C @ tc_prod ) @ ( C @ ( D @ ( E @ c_Relation_Oconverse ) ) @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).
thf(521,axiom,
! [C: $i,B: $i,A: $i] : ( A @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__code_1) ).
thf(1702,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).
thf(8,negated_conjecture,
! [B: $i,A: $i] :
( ( B = A )
| ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( v_P @ v_F @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( v_P @ v_F @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_7) ).
thf(600,plain,
! [B: $i,A: $i] :
( ( B = A )
| ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( v_P @ v_F @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( v_P @ v_F @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(213,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_Orderings_Obot__class_Obot @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= B )
| ~ ( A @ class_Lattices_Obounded__lattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__bot__right_0) ).
thf(1052,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_Orderings_Obot__class_Obot @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= B )
| ~ ( A @ class_Lattices_Obounded__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(123,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( C @ ( C @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ c_COMBK ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Product__Type_OSigma ) ) ) )
= ( tc_bool @ ( E @ ( C @ tc_prod ) @ tc_fun ) @ ( E @ ( C @ ( C @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ c_COMBK ) ) @ ( B @ c_Product__Type_OSigma ) ) ) @ ( E @ ( C @ ( C @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ c_COMBK ) ) @ ( A @ c_Product__Type_OSigma ) ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Times__Int__distrib1_0) ).
thf(864,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( C @ ( C @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ c_COMBK ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Product__Type_OSigma ) ) ) )
= ( tc_bool @ ( E @ ( C @ tc_prod ) @ tc_fun ) @ ( E @ ( C @ ( C @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ c_COMBK ) ) @ ( B @ c_Product__Type_OSigma ) ) ) @ ( E @ ( C @ ( C @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ c_COMBK ) ) @ ( A @ c_Product__Type_OSigma ) ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(543,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( C @ ( C @ ( C @ ( D @ c_Relation_Oconverse ) ) @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__converseI_0) ).
thf(1749,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( C @ ( C @ ( C @ ( D @ c_Relation_Oconverse ) ) @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).
thf(6,negated_conjecture,
~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( v_i @ ( v_P @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( v_b @ ( v_a @ c_Pair ) ) ) @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_5) ).
thf(595,plain,
~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( v_i @ ( v_P @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( v_b @ ( v_a @ c_Pair ) ) ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(128,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( D @ ( A @ c_Set_Oinsert ) ) @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__inter__insert_0) ).
thf(876,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( D @ ( A @ c_Set_Oinsert ) ) @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Set_Oinsert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(380,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( A = B )
| ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtranclD_0) ).
thf(1404,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( A = B )
| ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(358,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( D @ ( C @ ( B @ c_Relation_ODomain ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_DomainI_0) ).
thf(1358,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( D @ ( C @ ( B @ c_Relation_ODomain ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(30,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__aci_I7_J_0) ).
thf(656,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(567,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( D @ ( C @ c_Wellfounded_Oacc ) @ ( B @ c_in ) ) )
| ~ ( D @ ( C @ ( A @ c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 ) ) @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acc__induct__rule_2) ).
thf(1802,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( D @ ( C @ c_Wellfounded_Oacc ) @ ( B @ c_in ) ) )
| ~ ( D @ ( C @ ( A @ c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 ) ) @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).
thf(200,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_Relation_Oantisym ) )
| ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_Oantisym ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_antisym__converse_1) ).
thf(1023,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_Relation_Oantisym ) )
| ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_Oantisym ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(180,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_lessequals ) ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__absorb2_0) ).
thf(978,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_lessequals ) ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(253,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( C @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Relation_Orel__comp ) ) ) ) @ c_Relation_Oconverse ) ) )
= ( C @ ( D @ ( E @ ( D @ ( C @ ( A @ c_Relation_Oconverse ) ) @ ( E @ ( D @ ( B @ c_Relation_Oconverse ) ) @ c_Relation_Orel__comp ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_converse__rel__comp_0) ).
thf(1140,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( C @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Relation_Orel__comp ) ) ) ) @ c_Relation_Oconverse ) ) )
= ( C @ ( D @ ( E @ ( D @ ( C @ ( A @ c_Relation_Oconverse ) ) @ ( E @ ( D @ ( B @ c_Relation_Oconverse ) ) @ c_Relation_Orel__comp ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(506,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( E @ c_Equiv__Relations_Oequiv ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( A @ ( C @ ( C @ ( D @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) @ ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equiv__class__subset_0) ).
thf(1670,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( E @ c_Equiv__Relations_Oequiv ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( A @ ( C @ ( C @ ( D @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) @ ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).
thf(565,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( D @ tc_prod ) @ ( D @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( A @ c_in ) ) )
| ( D @ ( D @ tc_prod ) @ ( D @ ( tc_bool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Transitive__Closure_Ortrancl ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__rtrancl__UnI_1) ).
thf(1797,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( D @ tc_prod ) @ ( D @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( A @ c_in ) ) )
| ( D @ ( D @ tc_prod ) @ ( D @ ( tc_bool @ ( D @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Transitive__Closure_Ortrancl ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).
thf(584,axiom,
! [C: $i,B: $i,A: $i] : ( B @ ( B @ tc_prod ) @ ( B @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__eq__or__trancl_1) ).
thf(1839,plain,
! [C: $i,B: $i,A: $i] : ( B @ ( B @ tc_prod ) @ ( B @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[584]) ).
thf(338,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( F @ tc_prod ) @ ( F @ ( D @ ( A @ ( E @ c_Relation_Oinv__image ) ) ) @ ( F @ ( F @ ( C @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ( D @ ( D @ tc_prod ) @ ( E @ ( D @ ( D @ ( C @ ( A @ hAPP ) @ ( B @ ( A @ hAPP ) @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__inv__image_0) ).
thf(1316,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( F @ tc_prod ) @ ( F @ ( D @ ( A @ ( E @ c_Relation_Oinv__image ) ) ) @ ( F @ ( F @ ( C @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ( D @ ( D @ tc_prod ) @ ( E @ ( D @ ( D @ ( C @ ( A @ hAPP ) @ ( B @ ( A @ hAPP ) @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(36,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( A @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__left__commute_0) ).
thf(671,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( A @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(340,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( E @ ( C @ ( B @ ( D @ c_Set_Oimage ) ) ) @ ( A @ ( D @ hAPP ) @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__iff_2) ).
thf(1321,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( E @ ( C @ ( B @ ( D @ c_Set_Oimage ) ) ) @ ( A @ ( D @ hAPP ) @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(384,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( D @ tc_prod ) @ ( D @ ( A @ c_Transitive__Closure_Otrancl ) @ ( D @ ( D @ ( C @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ( D @ ( D @ tc_prod ) @ ( A @ ( D @ ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1 ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_tranclD2_1) ).
thf(1412,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( D @ tc_prod ) @ ( D @ ( A @ c_Transitive__Closure_Otrancl ) @ ( D @ ( D @ ( C @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ( D @ ( D @ tc_prod ) @ ( A @ ( D @ ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1 ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(80,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__ord_I2_J_0) ).
thf(771,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(156,axiom,
! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_Relation_OId__on ) @ c_Relation_Osym ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sym__Id__on_0) ).
thf(931,plain,
! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_Relation_OId__on ) @ c_Relation_Osym ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(513,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( E @ ( D @ ( A @ ( C @ c_Relation_OImage ) ) ) @ ( B @ c_in ) ) )
| ( D @ ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__XImage__iff__1__1 ) ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Image__iff_0) ).
thf(1685,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( E @ ( D @ ( A @ ( C @ c_Relation_OImage ) ) ) @ ( B @ c_in ) ) )
| ( D @ ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__XImage__iff__1__1 ) ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).
thf(179,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ ( B @ c_in ) ) )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert_1) ).
thf(976,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ ( B @ c_in ) ) )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(42,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Transitive__Closure_Ortrancl ) )
= ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ c_Relation_OId @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nitpick_Ortrancl__def_0) ).
thf(688,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Transitive__Closure_Ortrancl ) )
= ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ c_Relation_OId @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(143,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_Orderings_Obot__class_Obot @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= B )
| ~ ( A @ class_Lattices_Obounded__lattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup__bot__left_0) ).
thf(903,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_Orderings_Obot__class_Obot @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= B )
| ~ ( A @ class_Lattices_Obounded__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(401,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup1CI_1) ).
thf(1448,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(276,axiom,
! [B: $i,A: $i] :
( ~ ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_lessequals ) ) )
| ( A
= ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__empty_0) ).
thf(1189,plain,
! [B: $i,A: $i] :
( ~ ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_lessequals ) ) )
| ( A
= ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(325,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Diff__cancel2_0) ).
thf(1289,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(114,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
| ~ ( D @ ( A @ ( B @ c_in ) ) )
| ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert__iff_3) ).
thf(844,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
| ~ ( D @ ( A @ ( B @ c_in ) ) )
| ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(308,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
!= ( A @ ( D @ ( C @ ( B @ c_Set_Oimage ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__is__image_0) ).
thf(1253,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
!= ( A @ ( D @ ( C @ ( B @ c_Set_Oimage ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(371,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( B @ c_in ) ) )
| ( E @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_imageI_0) ).
thf(1385,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( B @ c_in ) ) )
| ( E @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(173,axiom,
! [B: $i,A: $i] :
( ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ c_Relation_OId @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( B @ ( A @ c_Transitive__Closure_Ortrancl ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__reflcl__absorb_0) ).
thf(963,plain,
! [B: $i,A: $i] :
( ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ c_Relation_OId @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( B @ ( A @ c_Transitive__Closure_Ortrancl ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(508,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( C @ ( B @ c_Relation_ODomain ) ) @ ( A @ c_in ) ) )
| ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1 ) ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Domain__iff_0) ).
thf(1674,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( C @ ( B @ c_Relation_ODomain ) ) @ ( A @ c_in ) ) )
| ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1 ) ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).
thf(415,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( C @ ( D @ c_Relation_ODomain ) ) @ ( A @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Not__Domain__rtrancl_0) ).
thf(1481,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( C @ ( D @ c_Relation_ODomain ) ) @ ( A @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(28,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Lattices_Olattice )
| ( B @ ( A @ tc_fun ) @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_fun__Lattices_Oupper__semilattice) ).
thf(652,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Lattices_Olattice )
| ( B @ ( A @ tc_fun ) @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(575,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__XtransI__1__3 ) @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__XtransI__1__1 ) @ c_Pair ) ) ) @ c_in ) ) )
| ( B @ ( A @ c_Relation_Otrans ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_transI_2) ).
thf(1822,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__XtransI__1__3 ) @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__XtransI__1__1 ) @ c_Pair ) ) ) @ c_in ) ) )
| ( B @ ( A @ c_Relation_Otrans ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).
thf(62,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oimage ) ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__empty_0) ).
thf(731,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oimage ) ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(85,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__idemp_0) ).
thf(781,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(451,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( tc_bool @ ( D @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Relation_ORange ) ) )
= ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Relation_ORange ) ) @ ( D @ ( C @ ( A @ c_Relation_ORange ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Range__Un__eq_0) ).
thf(1558,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( tc_bool @ ( D @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Relation_ORange ) ) )
= ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Relation_ORange ) ) @ ( D @ ( C @ ( A @ c_Relation_ORange ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).
thf(319,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_Relation_Osym ) )
| ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_Osym ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sym__converse_1) ).
thf(1276,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_Relation_Osym ) )
| ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_Osym ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(467,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ c_Relation_Otrans ) )
| ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_transD_0) ).
thf(1590,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ c_Relation_Otrans ) )
| ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).
thf(140,axiom,
! [B: $i,A: $i] :
( ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__empty__right_0) ).
thf(896,plain,
! [B: $i,A: $i] :
( ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(70,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( B @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ ( C @ c_COMBK ) ) @ ( C @ c_Product__Type_OSigma ) ) ) @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( B @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ ( C @ c_COMBK ) ) @ ( C @ c_Product__Type_OSigma ) ) ) @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trancl__subset__Sigma_0) ).
thf(748,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( B @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ ( C @ c_COMBK ) ) @ ( C @ c_Product__Type_OSigma ) ) ) @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( B @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ ( C @ c_COMBK ) ) @ ( C @ c_Product__Type_OSigma ) ) ) @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(419,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ c_Wellfounded_Owf ) )
| ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_Set_Oinsert ) ) @ c_Wellfounded_Owf ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__insert_2) ).
thf(1491,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ c_Wellfounded_Owf ) )
| ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_Set_Oinsert ) ) @ c_Wellfounded_Owf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(515,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( t_a @ ( t_a @ ( D @ c_Wellfounded_Oacc ) @ ( B @ c_in ) ) )
| ~ ( t_a @ ( t_a @ tc_prod ) @ ( D @ ( t_a @ ( t_a @ ( D @ ( A @ v_sko__Wellfounded__Xacc__Xinducts__1 ) @ ( C @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acc_Oinducts_1) ).
thf(1689,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( t_a @ ( t_a @ ( D @ c_Wellfounded_Oacc ) @ ( B @ c_in ) ) )
| ~ ( t_a @ ( t_a @ tc_prod ) @ ( D @ ( t_a @ ( t_a @ ( D @ ( A @ v_sko__Wellfounded__Xacc__Xinducts__1 ) @ ( C @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).
thf(148,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Transitive__Closure_Ortrancl ) )
= ( B @ ( B @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_Relation_Oconverse ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__converse_0) ).
thf(914,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Transitive__Closure_Ortrancl ) )
= ( B @ ( B @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_Relation_Oconverse ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(556,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( E @ ( B @ c_Equiv__Relations_Oequiv ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( E @ ( C @ ( C @ ( A @ ( D @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equiv__class__eq__iff_2) ).
thf(1777,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( E @ ( B @ c_Equiv__Relations_Oequiv ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( E @ ( C @ ( C @ ( A @ ( D @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).
thf(327,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__left__commute_0) ).
thf(1294,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(334,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ ( A @ c_Relation_Orel__comp ) ) ) ) )
= ( B @ ( B @ ( B @ ( A @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_Relation_Orel__comp ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_r__comp__rtrancl__eq_0) ).
thf(1308,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ ( A @ c_Relation_Orel__comp ) ) ) ) )
= ( B @ ( B @ ( B @ ( A @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_Relation_Orel__comp ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(523,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ c_Relation_Osym ) )
| ~ ( C @ ( B @ c_Relation_Osym ) )
| ( C @ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Relation_Osym ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sym__Int_0) ).
thf(1706,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ c_Relation_Osym ) )
| ~ ( C @ ( B @ c_Relation_Osym ) )
| ( C @ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Relation_Osym ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).
thf(501,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( D @ ( C @ c_Wellfounded_Oacc ) @ ( B @ c_in ) ) )
| ~ ( D @ ( C @ ( A @ c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 ) ) @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acc__induct_2) ).
thf(1661,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( D @ ( C @ c_Wellfounded_Oacc ) @ ( B @ c_in ) ) )
| ~ ( D @ ( C @ ( A @ c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 ) ) @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).
thf(109,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( B = D )
| ( ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
!= ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ c_Set_Oinsert ) ) @ ( D @ c_Set_Oinsert ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_doubleton__eq__iff_1) ).
thf(832,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( B = D )
| ( ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
!= ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ c_Set_Oinsert ) ) @ ( D @ c_Set_Oinsert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(397,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_in ) ) )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntE_1) ).
thf(1440,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_in ) ) )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(155,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__insert__right_0) ).
thf(929,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Set_Oinsert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(399,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ c_Wellfounded_Owf ) )
| ~ ( C @ ( B @ ( E @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( C @ ( D @ ( B @ c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__eq__minimal_1) ).
thf(1444,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ c_Wellfounded_Owf ) )
| ~ ( C @ ( B @ ( E @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( C @ ( D @ ( B @ c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(398,axiom,
! [C: $i,B: $i,A: $i] :
~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( B @ ( C @ c_Arrow__Order__Mirabelle_Omkbot ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__mkbot_0) ).
thf(1442,plain,
! [C: $i,B: $i,A: $i] :
~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( B @ ( C @ c_Arrow__Order__Mirabelle_Omkbot ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(54,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_Transitive__Closure_Ortrancl ) )
= ( B @ ( A @ c_Transitive__Closure_Ortrancl ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__idemp_0) ).
thf(716,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_Transitive__Closure_Ortrancl ) )
= ( B @ ( A @ c_Transitive__Closure_Ortrancl ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(263,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( E @ ( E @ ( D @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_Osingle__valued ) ) )
| ( ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Relation_OImage ) ) ) )
= ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( D @ ( C @ ( A @ c_Relation_OImage ) ) ) @ ( E @ ( D @ ( B @ ( A @ c_Relation_OImage ) ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Image__Int__eq_0) ).
thf(1161,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( E @ ( E @ ( D @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_Osingle__valued ) ) )
| ( ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Relation_OImage ) ) ) )
= ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( D @ ( C @ ( A @ c_Relation_OImage ) ) ) @ ( E @ ( D @ ( B @ ( A @ c_Relation_OImage ) ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(479,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ c_Wellfounded_Owf ) )
| ( C @ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Wellfounded_Owf ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__Int1_0) ).
thf(1614,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ c_Wellfounded_Owf ) )
| ( C @ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Wellfounded_Owf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).
thf(94,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_distrib__sup__le_0) ).
thf(800,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(493,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( D @ ( A @ ( E @ c_Equiv__Relations_Ocongruent ) ) ) )
| ~ ( D @ ( D @ tc_prod ) @ ( E @ ( D @ ( D @ ( C @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ( ( B @ ( A @ hAPP ) )
= ( C @ ( A @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_congruent_Ocongruent_0) ).
thf(1642,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( D @ ( A @ ( E @ c_Equiv__Relations_Ocongruent ) ) ) )
| ~ ( D @ ( D @ tc_prod ) @ ( E @ ( D @ ( D @ ( C @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ( ( B @ ( A @ hAPP ) )
= ( C @ ( A @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).
thf(429,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( D @ ( C @ c_Pair ) ) ) @ c_Set_Oinsert ) ) @ c_Wellfounded_Owf ) )
| ( B @ ( A @ c_Wellfounded_Owf ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__insert_0) ).
thf(1512,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( D @ ( C @ c_Pair ) ) ) @ c_Set_Oinsert ) ) @ c_Wellfounded_Owf ) )
| ( B @ ( A @ c_Wellfounded_Owf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(321,axiom,
! [B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__empty__left_0) ).
thf(1280,plain,
! [B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(461,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ c_Relation_Otrans ) )
| ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__def_0) ).
thf(1578,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ c_Relation_Otrans ) )
| ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(175,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Wellfounded_Oacyclic ) )
| ( B @ ( A @ c_Wellfounded_Oacyclic ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acyclic__converse_0) ).
thf(967,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Wellfounded_Oacyclic ) )
| ( B @ ( A @ c_Wellfounded_Oacyclic ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(446,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( F @ ( E @ c_Pair ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_split ) ) ) @ hAPP ) )
= ( F @ ( E @ ( A @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Product__Type_Osplit_0) ).
thf(1546,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( F @ ( E @ c_Pair ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_split ) ) ) @ hAPP ) )
= ( F @ ( E @ ( A @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(102,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__Diff_0) ).
thf(818,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(119,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ c_Wellfounded_Owf ) )
| ~ ( tc_bool @ ( B @ tc_fun ) @ ( B @ ( B @ ( A @ ( C @ c_Relation_OImage ) ) ) @ ( A @ c_lessequals ) ) )
| ( A
= ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wfE__pf_0) ).
thf(854,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ c_Wellfounded_Owf ) )
| ~ ( tc_bool @ ( B @ tc_fun ) @ ( B @ ( B @ ( A @ ( C @ c_Relation_OImage ) ) ) @ ( A @ c_lessequals ) ) )
| ( A
= ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(306,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_lessequals ) ) )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_double__diff_0) ).
thf(1248,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_lessequals ) ) )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(547,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_prod ) @ ( A @ ( C @ ( C @ ( D @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( A @ ( E @ c_Equiv__Relations_Oequiv ) ) )
| ~ ( C @ ( E @ ( B @ c_in ) ) )
| ~ ( C @ ( E @ ( D @ c_in ) ) )
| ( ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) )
!= ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__equiv__class__iff_0) ).
thf(1757,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_prod ) @ ( A @ ( C @ ( C @ ( D @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( A @ ( E @ c_Equiv__Relations_Oequiv ) ) )
| ~ ( C @ ( E @ ( B @ c_in ) ) )
| ~ ( C @ ( E @ ( D @ c_in ) ) )
| ( ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) )
!= ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).
thf(189,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__infE_0) ).
thf(999,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(14,axiom,
tc_bool @ class_Orderings_Obot,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Orderings_Obot) ).
thf(620,plain,
tc_bool @ class_Orderings_Obot,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(233,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( B @ c_Relation_OId @ c_lessequals ) ) )
| ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( B @ ( B @ ( B @ ( A @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Relation_Orel__comp ) ) ) ) @ c_lessequals ) ) )
| ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__Int__subset_0) ).
thf(1097,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( B @ c_Relation_OId @ c_lessequals ) ) )
| ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( B @ ( B @ ( B @ ( A @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Relation_Orel__comp ) ) ) ) @ c_lessequals ) ) )
| ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(110,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_Wellfounded_Oacyclic ) )
| ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Wellfounded_Oacyclic ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acyclic__converse_1) ).
thf(835,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_Wellfounded_Oacyclic ) )
| ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Wellfounded_Oacyclic ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(376,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mem__def_1) ).
thf(1395,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(485,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( E @ c_Equiv__Relations_Oequiv ) ) )
| ~ ( C @ ( E @ ( B @ c_in ) ) )
| ~ ( C @ ( E @ ( D @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( A @ ( C @ ( C @ ( D @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ( ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) )
= ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_eq__equiv__class__iff_1) ).
thf(1625,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( E @ c_Equiv__Relations_Oequiv ) ) )
| ~ ( C @ ( E @ ( B @ c_in ) ) )
| ~ ( C @ ( E @ ( D @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( A @ ( C @ ( C @ ( D @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ( ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) )
= ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).
thf(436,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( A @ ( E @ c_Pair ) ) ) @ c_in ) ) )
| ( D @ ( D @ ( C @ ( B @ c_Relation_ORange ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Range__iff_1) ).
thf(1527,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( A @ ( E @ c_Pair ) ) ) @ c_in ) ) )
| ( D @ ( D @ ( C @ ( B @ c_Relation_ORange ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(257,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( C @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_Oconverse ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_converse__converse_0) ).
thf(1148,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( C @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_Oconverse ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(395,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( D @ c_in ) ) )
| ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acc__downwards__aux_0) ).
thf(1436,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( D @ c_in ) ) )
| ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(337,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ c_Relation_Osym ) )
| ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sym__def_0) ).
thf(1314,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ c_Relation_Osym ) )
| ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(499,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ c_in ) ) )
| ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UnCI_0) ).
thf(1657,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ c_in ) ) )
| ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).
thf(517,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( G @ ( F @ ( B @ hAPP ) @ hAPP ) @ ( A @ c_in ) ) )
| ( E @ ( D @ ( C @ ( G @ ( F @ c_Pair ) ) ) @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ ( C @ ( B @ c_split ) ) ) @ hAPP ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mem__splitI_0) ).
thf(1693,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( G @ ( F @ ( B @ hAPP ) @ hAPP ) @ ( A @ c_in ) ) )
| ( E @ ( D @ ( C @ ( G @ ( F @ c_Pair ) ) ) @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ ( C @ ( B @ c_split ) ) ) @ hAPP ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).
thf(107,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Odistrib__lattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__distrib2_0) ).
thf(828,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Odistrib__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(219,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= A )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
!= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Diff__triv_0) ).
thf(1065,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= A )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
!= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(170,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_Order__Relation_Ostrict__linear__order__on ) ) )
| ( B @ ( A @ c_Relation_Oirrefl ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_strict__linear__order__on__def_1) ).
thf(955,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_Order__Relation_Ostrict__linear__order__on ) ) )
| ( B @ ( A @ c_Relation_Oirrefl ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(477,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ tc_prod ) @ ( G @ ( E @ ( D @ ( C @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ( F @ ( F @ ( E @ ( D @ tc_prod ) @ ( G @ ( F @ ( E @ ( D @ ( A @ c_split ) ) ) @ c_Set_Oimage ) ) ) @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pair__imageI_0) ).
thf(1610,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ tc_prod ) @ ( G @ ( E @ ( D @ ( C @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ( F @ ( F @ ( E @ ( D @ tc_prod ) @ ( G @ ( F @ ( E @ ( D @ ( A @ c_split ) ) ) @ c_Set_Oimage ) ) ) @ ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).
thf(572,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ c_Relation_Otrans ) )
| ~ ( C @ ( B @ c_Relation_Otrans ) )
| ( C @ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Relation_Otrans ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__Int_0) ).
thf(1816,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ c_Relation_Otrans ) )
| ~ ( C @ ( B @ c_Relation_Otrans ) )
| ( C @ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Relation_Otrans ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).
thf(421,axiom,
! [B: $i,A: $i] :
~ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_bot1E_0) ).
thf(1495,plain,
! [B: $i,A: $i] :
~ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(383,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( D @ c_Relation_Orefl__on ) ) )
| ~ ( B @ ( D @ ( A @ c_in ) ) )
| ( B @ ( B @ tc_prod ) @ ( C @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_refl__onD_0) ).
thf(1410,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( D @ c_Relation_Orefl__on ) ) )
| ~ ( B @ ( D @ ( A @ c_in ) ) )
| ( B @ ( B @ tc_prod ) @ ( C @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(78,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
= ( D @ ( D @ ( C @ ( A @ c_Set_Oinsert ) ) @ ( B @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__commute_0) ).
thf(767,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
= ( D @ ( D @ ( C @ ( A @ c_Set_Oinsert ) ) @ ( B @ c_Set_Oinsert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(205,axiom,
! [A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__empty_2) ).
thf(1033,plain,
! [A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(525,axiom,
! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_Relation_Otrans ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__rtrancl_0) ).
thf(1710,plain,
! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_Relation_Otrans ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).
thf(172,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_lessequals ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__eq__subset_2) ).
thf(960,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_lessequals ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(411,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( D @ tc_prod ) @ ( D @ ( A @ c_Transitive__Closure_Otrancl ) @ ( D @ ( D @ ( C @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ( D @ ( D @ tc_prod ) @ ( D @ ( A @ c_Transitive__Closure_Ortrancl ) @ ( D @ ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1 ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_tranclD_1) ).
thf(1473,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( D @ tc_prod ) @ ( D @ ( A @ c_Transitive__Closure_Otrancl ) @ ( D @ ( D @ ( C @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ( D @ ( D @ tc_prod ) @ ( D @ ( A @ c_Transitive__Closure_Ortrancl ) @ ( D @ ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1 ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(133,axiom,
! [A: $i] : ( tc_bool @ ( A @ tc_fun ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__empty_1) ).
thf(886,plain,
! [A: $i] : ( tc_bool @ ( A @ tc_fun ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(540,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trancl_Or__into__trancl_0) ).
thf(1742,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).
thf(154,axiom,
! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__upper2_0) ).
thf(928,plain,
! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(184,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__subset__iff_0) ).
thf(987,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(355,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_in ) ) )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ball__empty_0) ).
thf(1352,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_in ) ) )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(312,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_Relation_Orefl__on ) ) )
| ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( B @ ( B @ ( A @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_Orel__comp ) ) ) ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_refl__on__comp__subset_0) ).
thf(1261,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_Relation_Orefl__on ) ) )
| ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( B @ ( B @ ( A @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_Orel__comp ) ) ) ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(9,negated_conjecture,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( v_i @ ( v_P @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( v_P @ v_F @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_8) ).
thf(596,plain,
! [B: $i,A: $i] :
( ( A = B )
| ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( v_i @ ( v_P @ hAPP ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( v_P @ v_F @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(448,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf1E_0) ).
thf(1550,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).
thf(58,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B
= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) )
!= ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__is__empty_0) ).
thf(723,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B
= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) )
!= ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(104,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__infI2_0) ).
thf(822,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(117,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__left__commute_0) ).
thf(850,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(126,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Int__crazy_0) ).
thf(871,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(231,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__subset__iff_2) ).
thf(1093,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(16,axiom,
tc_bool @ class_Lattices_Olattice,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olattice) ).
thf(624,plain,
tc_bool @ class_Lattices_Olattice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(112,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( A @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Odistrib__lattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__sup__distrib1_0) ).
thf(839,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( A @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Odistrib__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(60,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Relation_ORange ) ) @ ( D @ ( C @ ( A @ c_Relation_ORange ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( D @ ( C @ ( tc_bool @ ( D @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Relation_ORange ) ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Range__Int__subset_0) ).
thf(728,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Relation_ORange ) ) @ ( D @ ( C @ ( A @ c_Relation_ORange ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( D @ ( C @ ( tc_bool @ ( D @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Relation_ORange ) ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(66,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( C @ ( B @ ( D @ c_Set_Oimage ) ) ) @ ( E @ ( C @ ( A @ ( D @ c_Set_Oimage ) ) ) @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__image__iff_2) ).
thf(740,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( C @ ( B @ ( D @ c_Set_Oimage ) ) ) @ ( E @ ( C @ ( A @ ( D @ c_Set_Oimage ) ) ) @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(579,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_in ) ) )
| ( C @ ( D @ ( A @ c_in ) ) )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UnE_0) ).
thf(1829,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_in ) ) )
| ( C @ ( D @ ( A @ c_in ) ) )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).
thf(249,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( A @ ( C @ c_lessequals ) ) )
| ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( A @ c_lessequals ) ) )
| ( ( B @ ( A @ c_Transitive__Closure_Ortrancl ) )
= ( B @ ( C @ c_Transitive__Closure_Ortrancl ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__subset_0) ).
thf(1129,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( A @ ( C @ c_lessequals ) ) )
| ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( A @ c_lessequals ) ) )
| ( ( B @ ( A @ c_Transitive__Closure_Ortrancl ) )
= ( B @ ( C @ c_Transitive__Closure_Ortrancl ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(439,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( A @ c_Wellfounded_Oacc ) @ ( B @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( A @ ( C @ ( C @ ( B @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1 ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__acc__down_0) ).
thf(1532,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( A @ c_Wellfounded_Oacc ) @ ( B @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( A @ ( C @ ( C @ ( B @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1 ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(121,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( B @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__supE_1) ).
thf(860,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( B @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(463,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( D @ c_Relation_Osingle__valued ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( A @ ( E @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_single__valued__confluent_0) ).
thf(1582,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( D @ c_Relation_Osingle__valued ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( A @ ( E @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(198,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_Relation_Orefl__on ) ) )
| ( C @ ( C @ ( C @ ( B @ c_Relation_Oconverse ) ) @ ( A @ c_Relation_Orefl__on ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_refl__on__converse_1) ).
thf(1019,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_Relation_Orefl__on ) ) )
| ( C @ ( C @ ( C @ ( B @ c_Relation_Oconverse ) ) @ ( A @ c_Relation_Orefl__on ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(145,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_le__supI2_0) ).
thf(908,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(186,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__subset__iff_1) ).
thf(992,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(471,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trancl__rtrancl__trancl_0) ).
thf(1597,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
thf(393,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( E @ ( D @ ( A @ ( C @ c_Relation_OImage ) ) ) @ ( B @ c_in ) ) )
| ( E @ ( D @ tc_prod ) @ ( C @ ( E @ ( D @ ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__XImageE__1__1 ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ImageE_0) ).
thf(1431,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( E @ ( D @ ( A @ ( C @ c_Relation_OImage ) ) ) @ ( B @ c_in ) ) )
| ( E @ ( D @ tc_prod ) @ ( C @ ( E @ ( D @ ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__XImageE__1__1 ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(426,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( C @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ c_Relation_Oconverse ) ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( C @ ( C @ ( C @ ( D @ c_Relation_Oconverse ) ) @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trancl__converseI_0) ).
thf(1505,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( C @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ c_Relation_Oconverse ) ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( C @ ( C @ ( C @ ( D @ c_Relation_Oconverse ) ) @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(378,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( D @ tc_prod ) @ ( B @ ( D @ ( D @ ( C @ ( G @ c_Pair ) ) ) @ c_in ) ) )
| ( ( G @ ( A @ hAPP ) )
= ( G @ ( F @ hAPP ) ) )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Recdef_Ocut ) ) ) ) )
!= ( E @ ( D @ ( C @ ( B @ ( F @ c_Recdef_Ocut ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cuts__eq_0) ).
thf(1399,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( D @ tc_prod ) @ ( B @ ( D @ ( D @ ( C @ ( G @ c_Pair ) ) ) @ c_in ) ) )
| ( ( G @ ( A @ hAPP ) )
= ( G @ ( F @ hAPP ) ) )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Recdef_Ocut ) ) ) ) )
!= ( E @ ( D @ ( C @ ( B @ ( F @ c_Recdef_Ocut ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(483,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__into__trancl2_0) ).
thf(1621,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).
thf(475,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__Xtrans__def__1__3 ) @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__Xtrans__def__1__2 ) @ c_Pair ) ) ) @ c_in ) ) )
| ( B @ ( A @ c_Relation_Otrans ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__def_2) ).
thf(1606,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__Xtrans__def__1__3 ) @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__Xtrans__def__1__2 ) @ c_Pair ) ) ) @ c_in ) ) )
| ( B @ ( A @ c_Relation_Otrans ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).
thf(194,axiom,
! [B: $i,A: $i] :
( ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__absorb_0) ).
thf(1009,plain,
! [B: $i,A: $i] :
( ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(537,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ hAPP ) @ hBOOL )
| ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sup1CI_0) ).
thf(1737,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ hAPP ) @ hBOOL )
| ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).
thf(31,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= B )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__idem_0) ).
thf(659,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= B )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(386,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
| ~ ( B @ ( C @ c_Relation_Oantisym ) )
| ( B @ ( A @ c_Relation_Oantisym ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_antisym__subset_0) ).
thf(1416,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
| ~ ( B @ ( C @ c_Relation_Oantisym ) )
| ( B @ ( A @ c_Relation_Oantisym ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(22,axiom,
tc_bool @ class_Lattices_Olower__semilattice,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olower__semilattice) ).
thf(639,plain,
tc_bool @ class_Lattices_Olower__semilattice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(284,axiom,
! [B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_empty__Diff_0) ).
thf(1204,plain,
! [B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(221,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( E @ c_in ) ) )
| ( ( B @ ( C @ ( D @ ( C @ ( B @ ( A @ c_COMBK ) ) @ c_Set_Oimage ) ) ) )
= ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__constant_0) ).
thf(1069,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( E @ c_in ) ) )
| ( ( B @ ( C @ ( D @ ( C @ ( B @ ( A @ c_COMBK ) ) @ c_Set_Oimage ) ) ) )
= ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(50,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( B @ ( B @ ( B @ ( A @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Relation_Orel__comp ) ) ) ) @ c_lessequals ) ) )
| ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trancl__Int__subset_0) ).
thf(708,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( B @ ( B @ ( B @ ( A @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Relation_Orel__comp ) ) ) ) @ c_lessequals ) ) )
| ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(131,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( B @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) )
| ( C @ ( A @ ( D @ c_in ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert__iff_1) ).
thf(882,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( B @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) )
| ( C @ ( A @ ( D @ c_in ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(497,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ c_in ) ) )
| ( D @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insertCI_0) ).
thf(1653,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ c_in ) ) )
| ( D @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).
thf(162,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_inf__le2_0) ).
thf(940,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(511,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ c_Relation_Oirrefl ) )
| ~ ( B @ ( B @ tc_prod ) @ ( C @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_irrefl__def_0) ).
thf(1681,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ c_Relation_Oirrefl ) )
| ~ ( B @ ( B @ tc_prod ) @ ( C @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).
thf(273,axiom,
tc_bool @ class_HOL_Oord,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_bool__HOL_Oord) ).
thf(1184,plain,
tc_bool @ class_HOL_Oord,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(207,axiom,
! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__lower2_0) ).
thf(1037,plain,
! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(82,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( F @ ( tc_bool @ ( E @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Relation_Orel__comp ) ) ) ) )
= ( tc_bool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ ( E @ ( D @ ( F @ ( C @ ( A @ c_Relation_Orel__comp ) ) ) ) @ ( E @ ( D @ ( F @ ( B @ ( A @ c_Relation_Orel__comp ) ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__comp__distrib_0) ).
thf(775,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( F @ ( tc_bool @ ( E @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Relation_Orel__comp ) ) ) ) )
= ( tc_bool @ ( E @ ( F @ tc_prod ) @ tc_fun ) @ ( E @ ( D @ ( F @ ( C @ ( A @ c_Relation_Orel__comp ) ) ) ) @ ( E @ ( D @ ( F @ ( B @ ( A @ c_Relation_Orel__comp ) ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(196,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_lessequals ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equalityI_0) ).
thf(1014,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_lessequals ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(177,axiom,
! [B: $i,A: $i] :
( ( B @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ c_Relation_OId @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Transitive__Closure_Otrancl ) )
= ( B @ ( A @ c_Transitive__Closure_Ortrancl ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trancl__reflcl_0) ).
thf(972,plain,
! [B: $i,A: $i] :
( ( B @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ c_Relation_OId @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Transitive__Closure_Otrancl ) )
= ( B @ ( A @ c_Transitive__Closure_Ortrancl ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(2414,plain,
$false,
inference(e,[status(thm)],[1454,1105,1729,1083,1179,777,645,892,1586,1501,1168,760,1237,846,628,1031,893,1840,666,1818,1158,1005,683,1068,1618,994,1422,1544,873,878,1793,1041,1855,1200,1142,1269,614,677,1305,597,1497,1608,1655,1310,1735,1327,1640,945,1063,1354,1507,1458,1788,1426,1164,797,1260,698,1095,1196,1835,1001,1645,1601,1366,1529,1746,898,1243,1127,1782,1391,1576,1724,1475,1518,1265,1703,1228,1623,1628,719,785,1330,802,1826,934,949,1055,1409,1760,1298,1323,619,1462,1059,1132,1379,1514,1479,1115,1568,1362,1232,1847,969,1347,1572,1489,1714,789,1373,1418,1828,1151,1383,806,1283,1302,756,1664,1811,1450,1109,1632,1334,646,981,1843,1377,866,1072,1119,1351,1345,1433,1201,1521,1564,1215,634,1104,1697,1651,1206,942,1691,1438,793,925,810,1338,1636,1074,1604,1153,761,1470,1708,1768,714,1047,1057,1343,1021,1580,1666,1487,693,815,729,1560,1387,910,957,1223,746,1091,1123,862,1570,1174,1676,1217,598,1751,820,1824,1370,916,1837,625,1296,1687,889,1210,1407,1634,974,852,1555,1079,1027,1291,710,1740,842,1402,1360,1143,1762,1804,1672,1540,593,869,1755,989,1592,742,1089,1234,1541,1851,1772,1534,1017,1375,1121,1111,1227,1138,1719,783,1118,857,1397,884,1659,753,1182,1739,1424,642,1414,1446,1612,1744,706,1493,1683,637,1584,837,1263,701,1150,738,1831,654,1668,1552,1192,1050,984,721,1799,1429,779,1393,1525,1588,1099,1530,1456,1599,1246,1318,1202,1241,1779,1695,1663,1616,773,926,1086,938,1286,1035,1187,674,953,1185,662,718,906,1278,824,1273,1548,1595,733,601,1135,1648,965,750,1727,1510,1251,1764,1833,1007,1125,1620,826,1795,1520,1256,1784,1389,1503,1786,936,1271,1312,1733,1107,1239,1332,947,1638,1356,611,787,919,804,1258,704,764,1194,900,831,1853,1282,736,1349,996,1722,599,1307,1175,1574,1011,880,649,890,631,758,1630,726,621,848,1325,668,1820,1731,594,1029,895,769,1460,1177,1381,932,1061,1198,1213,986,1113,1775,1477,1364,1102,922,1562,912,685,1171,1594,1699,1044,695,1245,1076,1809,1166,1208,944,1467,663,1420,812,1081,617,1145,795,680,939,1340,1845,640,1025,1156,1225,887,1566,1368,712,1003,1770,690,1516,1753,1267,1230,1484,791,1038,1679,1218,1336,1220,1711,1499,1790,1716,1813,1300,1452,1538,951,808,744,1766,1849,1536,1702,600,1052,864,1749,595,876,1404,1358,656,1802,1023,978,1140,1670,1797,1839,1316,671,1321,1412,771,931,1685,976,688,903,1448,1189,1289,844,1253,1385,963,1674,1481,652,1822,731,781,1558,1276,1590,896,748,1491,1689,914,1777,1294,1308,1706,1661,832,1440,929,1444,1442,716,1161,1614,800,1642,1512,1280,1578,967,1546,818,854,1248,1757,999,620,1097,835,1395,1625,1527,1148,1436,1314,1657,1693,828,1065,955,1610,1816,1495,1410,767,1033,1710,960,1473,886,1742,928,987,1352,1261,596,1550,723,822,850,871,1093,624,839,728,740,1829,1129,1532,860,1582,1019,908,992,1597,1431,1505,1399,1621,1606,1009,1737,659,1416,639,1204,1069,708,882,1653,940,1681,1184,1037,775,1014,972]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SCT023-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.13 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.25/0.51 % Computer : n015.cluster.edu
% 0.25/0.51 % Model : x86_64 x86_64
% 0.25/0.51 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.25/0.51 % Memory : 8046.5625MB
% 0.25/0.51 % OS : Linux 6.8.0-71-generic
% 0.25/0.51 % CPULimit : 300
% 0.25/0.51 % WCLimit : 300
% 0.25/0.51 % DateTime : Sat Sep 26 06:22:59 UTC 2026
% 0.25/0.51 % CPUTime :
% 0.25/0.51 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 1.38/1.37 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 3.23/1.95 % [INFO] Parsing done (570ms).
% 3.23/1.97 % [INFO] Running in sequential loop mode.
% 4.49/2.55 % [INFO] eprover registered as external prover.
% 4.49/2.56 % [INFO] Scanning for conjecture ...
% 5.28/2.88 % [INFO] Found a conjecture (or negated_conjecture) and 596 axioms. Running axiom selection ...
% 7.01/3.29 % [INFO] Axiom selection finished. Selected 583 axioms (removed 13 axioms).
% 8.58/3.67 % [INFO] Problem is propositional (TPTP CNF).
% 8.99/3.70 % [INFO] Type checking passed.
% 8.99/3.71 % [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 ...
% 29.43/8.37 % External prover 'e' found a proof!
% 29.43/8.37 % [INFO] Killing All external provers ...
% 29.43/8.37 % Time passed: 7647ms (effective reasoning time: 6388ms)
% 29.43/8.38 % Axioms used in derivation (583): cls_inf__sup__absorb_0, cls_trancl__converseD_0, cls_inf__sup__aci_I2_J_0, cls_Diff__cancel_0, cls_in__mktop_1, cls_subset__insert_1, cls_Diff__iff_2, cls_rtrancl__idemp_0, cls_equiv__class__eq__iff_0, cls_sym__conv__converse__eq_1, cls_Int__Un__distrib_0, clsarity_fun__Lattices_Olower__semilattice, cls_Range__Un__eq_0, cls_Int__absorb2_0, cls_sym__Int__converse_0, cls_sup__ge1_0, cls_image__constant_0, cls_insertE_0, cls_rtrancl__converseD_0, cls_wf__subset_0, cls_equalityI_0, cls_insert__inter__insert_0, cls_Un__Diff_0, cls_congruent_Ocongruent_0, cls_Un__subset__iff_0, cls_splitD_H_0, cls_total__on__def_0, cls_converseI_0, cls_single__valuedD_0, cls_wf__acyclic_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_Un__empty__left_0, 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_trans__def_1, clsarity_bool__Lattices_Olower__semilattice, cls_Id__O__R_0, cls_le__iff__inf_1, cls_Un__upper1_0, 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, 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_Int__Un__distrib2_0, cls_rtrancl__trans_0, cls_inf1E_1, cls_Diff__triv_0, cls_insert__iff_1, cls_wf__union__compatible_0, cls_insert__subset_0, cls_inf__sup__distrib1_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_Image__Un_0, cls_in__mkbot_4, 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_congruent2_Ocongruent2_0, cls_inf__commute_0, cls_trans__converse_1, cls_DomainE_0, cls_subset__insert__iff_2, cls_Range__Id__on_0, cls_refl__on__Id__on_0, cls_Un__left__commute_0, cls_rtrancl__into__trancl1_0, cls_wf__converse__trancl_0, cls_single__valued__Id_0, cls_rtrancl__trancl__absorb_0, clsarity_bool__HOL_Oord, cls_set__mp_0, cls_cut__apply_0, cls_Un__Int__distrib2_0, cls_Int__empty__right_0, cls_trans__Int_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_rtrancl__mono_0, cls_Un__subset__iff_1, cls_rtrancl__unfold_0, cls_Un__empty_2, cls_le__iff__sup_1, cls_antisym__converse_0, cls_Image__subset_0, cls_wf__insert_0, cls_empty__is__image_0, cls_converse__rtrancl__into__rtrancl_0, cls_wfE__min_1, cls_Image__empty_0, clsarity_fun__Orderings_Obot, cls_Image__iff_1, cls_le__supE_1, cls_le__iff__sup_0, cls_rtrancl__reflcl_0, cls_rev__image__eqI_0, cls_in__mktop_3, cls_rel__comp__distrib2_0, cls_sym__trancl_0, cls_r__into__trancl_H_0, cls_cuts__eq_0, cls_SigmaI_0, cls_Un__absorb2_0, cls_trancl__into__trancl2_0, cls_bot__least_0, cls_inf__sup__aci_I8_J_0, cls_rtrancl__eq__or__trancl_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_Range__Int__subset_0, 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_wf__trancl_0, cls_rtrancl__converse_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_subset__iff_0, cls_insert__code_2, 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_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_tranclD_1, 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_Domain__Int__subset_0, cls_inf__absorb2_0, cls_wf__comp__self_1, clsarity_bool__Lattices_Oupper__semilattice, 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_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_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_rtrancl__reflcl__absorb_0, cls_DomainI_0, cls_transI_1, cls_Un__subset__iff_2, clsarity_fun__Lattices_Olattice, cls_wf__asym_0, cls_linorder__linear_0, cls_Un__empty_0, cls_in__mktop_5, cls_Int__assoc_0, cls_acc_Oinduct_1, cls_acc__downwards_0, cls_wf__eq__minimal_1, cls_sym__rtrancl_0, cls_subset__trans_0, cls_in__mktop_0, cls_inf__le2_0, cls_refl__onD2_0, cls_image__empty_0, cls_Times__subset__cancel2_0, cls_double__diff_0, cls_trans__converse_0, cls_acc_Ocases_0, cls_insert__is__Un_0, cls_DiffI_0, cls_transD_0, cls_SigmaD1_0, cls_Domain__Un__eq_0, cls_Image__iff_2, cls_le__supE_0, cls_rtrancl__eq__or__trancl_1, cls_trans__Id__on_0, cls_empty__not__insert_0, cls_sup__assoc_0, cls_Diff__Int__distrib2_0, cls_acc_Oinduct_0, cls_image__constant__conv_0, cls_total__on__diff__Id_0, cls_in__mkbot_2, cls_Id__on__subset__Times_0, cls_rtrancl__r__diff__Id_0, cls_insertI1_0, cls_split__case__cert_0, cls_le__sup__iff_1, clsarity_bool__Orderings_Obot, cls_mem__def_0, cls_inf__sup__aci_I7_J_0, cls_Un__Int__crazy_0, cls_trans__inv__image_0, cls_acyclic__def_0, cls_acyclic__insert_1, cls_insert__Diff1_0, cls_Image__Int__subset_0, cls_in__mktop_4, cls_Diff__insert2_0, cls_Int__commute_0, cls_wfE__pf_0, cls_sup__least_0, cls_subset__refl_0, cls_rev__ImageI_0, cls_Pair__eq_0, cls_Domain__converse_0, cls_trancl__converseI_0, cls_empty__subsetI_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_converse__iff_1, cls_refl__onD_0, cls_singletonE_0, cls_Nitpick_Ortrancl__def_0, cls_image__diff__subset_0, cls_Image__mono_0, cls_Int__Diff_0, cls_rtrancl__Int__subset_0, cls_image__iff_2, cls_insertCI_0, cls_le__infE_0, cls_image__Int__subset_0, cls_pair__in__Id__conv_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_DiffE_0, cls_R__O__Id_0, cls_trancl__into__rtrancl_0, cls_reflcl__trancl_0, cls_sup1CI_1, cls_Sigma__mono_1, cls_ImageE_1, cls_le__infI1_0, cls_bot1E_0, cls_trancl__unfold__left_0, cls_inf__assoc_0, cls_rtrancl__trancl__trancl_0, cls_Int__lower2_0, cls_rel__compI_0, cls_insert__mono_0, cls_le__supI2_0, cls_Un__assoc_0, cls_Un__Diff__cancel2_0, cls_antisym__reflcl_0, cls_bex__empty_0, cls_trancl__id_0, cls_in__rtrancl__UnI_1, cls_Sigma__Un__distrib1_0, cls_Int__absorb_0, cls_converse__Id_0, cls_in__rel__def_0, cls_refl__on__Un_0, cls_Int__left__absorb_0, cls_doubleton__eq__iff_3, cls_inf__sup__ord_I4_J_0, cls_total__on__converse_1, cls_acc__subset_0, cls_Diff__mono_0, cls_Un__absorb_0, cls_ImageE_0, cls_equiv_Osym_0, cls_UnE_0, cls_subset__insertI2_0, cls_wf__union__merge_0, cls_Diff__disjoint_0, cls_converseD_0, cls_acc_OaccI_0, cls_converse__inv__image_0, cls_Diff__Int__distrib_0, cls_antisym__Id_0, cls_trancl__rtrancl__absorb_0, cls_Int__lower1_0, cls_trancl__range_0, cls_eq__eqI_0, 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_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_single__valued__confluent_0, cls_acc_Oinducts_2, cls_inf__bot__left_0, cls_inf1I_0, cls_equiv_Orefl__on_0, cls_le__eqI_0, cls_insert__not__empty_0, cls_Image__Id_0, cls_Int__left__commute_0, cls_le__sup__iff_2, cls_inf__idem_0, cls_trancl__Int__subset_0, clsarity_fun__Lattices_Obounded__lattice, cls_equiv__class__subset_0, cls_pair__imageI_0, cls_IdI_0, cls_inf__sup__aci_I4_J_0, cls_subset__insert__iff_0, cls_acc__induct_1, cls_Un__Int__assoc__eq_1, cls_doubleton__eq__iff_1, cls_trans__reflclI_0, cls_eq__equiv__class__iff_0, cls_converse__converse_0, cls_insert__absorb2_0, cls_Product__Type_Osplit_0, cls_sup__inf__absorb_0, cls_irrefl__def_1, cls_acyclic__converse_0, cls_subset__singletonD_0, cls_RangeI_0, cls_Int__iff_2, cls_rtrancl_Ortrancl__refl_0, cls_Id__on__iff_1, cls_eq__equiv__class_0, cls_inf__greatest_0, cls_equiv__class__eq__iff_1, cls_in__mkbot_1, cls_Un__left__absorb_0, cls_in__mktop_2, cls_IntI_0, cls_in__inv__image_0, cls_Diff__empty_0, cls_Times__Un__distrib1_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_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_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, cls_IntE_1, cls_rtrancl__subset__rtrancl_0, cls_trancl__unfold__right_0, cls_Int__greatest_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_refl__on__Int_0, cls_wf__Int1_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_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_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_Sigma__Int__distrib1_0, cls_trancl__trans_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_Diff__insert__absorb_0, cls_converse__Int_0, cls_le__infI2_0, cls_insert__image_0, cls_disjoint__iff__not__equal_0, cls_Nitpick_Orefl_H__def_1, cls_refl__on__def_0, cls_insert__iff_2, cls_Diff__partition_0, cls_equiv__comp__eq_0, cls_Domain__iff_1, cls_sup__bot__left_0, cls_acc__induct__rule_0, cls_strict__linear__order__on__def_3, cls_Not__Domain__rtrancl_1, cls_wf__insert_1, cls_sup__inf__distrib1_0, cls_Un__Int__assoc__eq_0, cls_Sigma__mono_0, cls_insert__commute_0, cls_trancl__subset__Sigma_0, cls_equiv__class__eq__iff_2, cls_image__is__empty_0, cls_Un__insert__right_0, cls_acyclic__impl__antisym__rtrancl_0, cls_equalityE_0, cls_inf__sup__distrib2_0, cls_sym__Int_0, cls_trancl__converse_0, cls_imageI_0, cls_Times__Int__distrib1_0, cls_acyclic__converse_1, cls_wf__Un_0, cls_antisym__converse_1, cls_Pair__eq_1, cls_wf__Int2_0, 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_in__mkbot_0, 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, cls_Diff__subset_0, cls_predicate1D_0, cls_inf1E_0
% 29.43/8.38 % No. of inferences in proof: 1185
% 29.43/8.38 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 7647 ms resp. 6388 ms w/o parsing
% 31.63/8.88 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 32.03/8.90 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------