TSTP Solution File: LCL856-1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : LCL856-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n009.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 11:32:23 EDT 2023
% Result : Unsatisfiable 6.49s 2.45s
% Output : Refutation 6.96s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 235
% Syntax : Number of formulae : 423 ( 97 unt; 48 typ; 0 def)
% Number of atoms : 751 ( 194 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 5174 ( 370 ~; 376 |; 0 &;4428 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 89 ( 89 >; 0 *; 0 +; 0 <<)
% Number of symbols : 50 ( 48 usr; 12 con; 0-5 aty)
% Number of variables : 1228 ( 0 ^;1228 !; 0 ?;1228 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_Type_Otyping_type,type,
c_Type_Otyping: $i > $i > $i > $o ).
thf(v_e_type,type,
v_e: $i ).
thf(v_t_type,type,
v_t: $i ).
thf(v_T_type,type,
v_T: $i ).
thf(c_Wellfounded_Oaccp_type,type,
c_Wellfounded_Oaccp: $i > $i > $i > $o ).
thf(c_Predicate_Oconversep_type,type,
c_Predicate_Oconversep: $i > $i > $i > $i ).
thf(c_Lambda_Obeta_type,type,
c_Lambda_Obeta: $i ).
thf(tc_Lambda_OdB_type,type,
tc_Lambda_OdB: $i ).
thf(class_Lattices_Oupper__semilattice_type,type,
class_Lattices_Oupper__semilattice: $i > $o ).
thf(tc_fun_type,type,
tc_fun: $i > $i > $i ).
thf(class_Lattices_Olattice_type,type,
class_Lattices_Olattice: $i > $o ).
thf(class_Lattices_Olower__semilattice_type,type,
class_Lattices_Olower__semilattice: $i > $o ).
thf(c_Lambda_OdB_OVar_type,type,
c_Lambda_OdB_OVar: $i > $i ).
thf(c_Lattices_Oupper__semilattice__class_Osup_type,type,
c_Lattices_Oupper__semilattice__class_Osup: $i > $i > $i > $i ).
thf(c_Lattices_Olower__semilattice__class_Oinf_type,type,
c_Lattices_Olower__semilattice__class_Oinf: $i > $i > $i > $i ).
thf(c_Type_Otype_OFun_type,type,
c_Type_Otype_OFun: $i > $i > $i ).
thf(hAPP_type,type,
hAPP: $i > $i > $i ).
thf(c_Lambda_OdB_OApp_type,type,
c_Lambda_OdB_OApp: $i ).
thf(hBOOL_type,type,
hBOOL: $i > $o ).
thf(c_InductTermi_OIT_type,type,
c_InductTermi_OIT: $i ).
thf(c_Lambda_OdB_OAbs_type,type,
c_Lambda_OdB_OAbs: $i > $i ).
thf(c_Transitive__Closure_Ortranclp_type,type,
c_Transitive__Closure_Ortranclp: $i > $i > $i ).
thf(c_Transitive__Closure_Otranclp_type,type,
c_Transitive__Closure_Otranclp: $i > $i > $i ).
thf(c_Type_Oshift_type,type,
c_Type_Oshift: $i > $i > $i > $i > $i ).
thf(class_Lattices_Odistrib__lattice_type,type,
class_Lattices_Odistrib__lattice: $i > $o ).
thf(c_ListOrder_Ostep1_type,type,
c_ListOrder_Ostep1: $i > $i > $i > $i > $o ).
thf(c_List_Olist_ONil_type,type,
c_List_Olist_ONil: $i > $i ).
thf(c_Lambda_Osubst_type,type,
c_Lambda_Osubst: $i > $i > $i > $i ).
thf(tc_bool_type,type,
tc_bool: $i ).
thf(c_List_Ofoldl_type,type,
c_List_Ofoldl: $i > $i > $i > $i > $i > $i ).
thf(tc_nat_type,type,
tc_nat: $i ).
thf(c_fequal_type,type,
c_fequal: $i > $i ).
thf(c_Predicate_Opred__comp_type,type,
c_Predicate_Opred__comp: $i > $i > $i > $i > $i > $i ).
thf(c_Lambda_Olift_type,type,
c_Lambda_Olift: $i > $i > $i ).
thf(c_Wellfounded_OwfP_type,type,
c_Wellfounded_OwfP: $i > $i > $o ).
thf(c_List_Olistsp_type,type,
c_List_Olistsp: $i > $i > $i > $o ).
thf(c_ATP__Linkup_Osko__Wellfounded__Xnot__accp__down__1__1_type,type,
c_ATP__Linkup_Osko__Wellfounded__Xnot__accp__down__1__1: $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Wellfounded__Xaccp__Xintros__1__1_type,type,
c_ATP__Linkup_Osko__Wellfounded__Xaccp__Xintros__1__1: $i > $i > $i > $i ).
thf(tc_Type_Otype_type,type,
tc_Type_Otype: $i ).
thf(c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__rule__1__1_type,type,
c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__rule__1__1: $i > $i > $i > $i ).
thf(t_a_type,type,
t_a: $i ).
thf(v_sko__Wellfounded__Xaccp__Xinduct__1_type,type,
v_sko__Wellfounded__Xaccp__Xinduct__1: $i > $i > $i ).
thf(c_HOL_Ozero__class_Ozero_type,type,
c_HOL_Ozero__class_Ozero: $i > $i ).
thf(v_sko__Wellfounded__Xaccp__Xinducts__1_type,type,
v_sko__Wellfounded__Xaccp__Xinducts__1: $i > $i > $i ).
thf(c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1_type,type,
c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1: $i > $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Wellfounded__XaccpI__1__1_type,type,
c_ATP__Linkup_Osko__Wellfounded__XaccpI__1__1: $i > $i > $i > $i ).
thf(c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1_type,type,
c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1: $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__1__1_type,type,
c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__1__1: $i > $i > $i > $i ).
thf(77,axiom,
class_Lattices_Oupper__semilattice @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oupper__semilattice) ).
thf(365,plain,
class_Lattices_Oupper__semilattice @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(148,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Predicate_Oconversep @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ ( tc_fun @ D @ tc_bool ) ) ) @ C @ D )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Predicate_Oconversep @ A @ C @ D ) @ ( c_Predicate_Oconversep @ B @ C @ D ) @ ( tc_fun @ D @ ( tc_fun @ C @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__meet_0) ).
thf(518,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Predicate_Oconversep @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ ( tc_fun @ D @ tc_bool ) ) ) @ C @ D )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Predicate_Oconversep @ A @ C @ D ) @ ( c_Predicate_Oconversep @ B @ C @ D ) @ ( tc_fun @ D @ ( tc_fun @ C @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(125,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( c_Type_Otyping @ C @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ D ) @ E @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ B )
| ~ ( c_Type_Otyping @ C @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ D ) @ E @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_var__app__type__eq_0) ).
thf(468,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( c_Type_Otyping @ C @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ D ) @ E @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ B )
| ~ ( c_Type_Otyping @ C @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ D ) @ E @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(20,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__left__idem_0) ).
thf(234,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(164,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ A @ D @ E ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conversep_Ocases_0) ).
thf(555,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ A @ D @ E ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(72,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ A @ B ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ E ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ A @ B ) @ C ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtranclp_Ortrancl__into__rtrancl_0) ).
thf(352,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ A @ B ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ E ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ A @ B ) @ C ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(25,axiom,
class_Lattices_Odistrib__lattice @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Odistrib__lattice) ).
thf(247,plain,
class_Lattices_Odistrib__lattice @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(84,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ ( tc_fun @ D @ tc_bool ) ) ) @ E ) @ F ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ E ) @ F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup2CI_1) ).
thf(379,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ ( tc_fun @ D @ tc_bool ) ) ) @ E ) @ F ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ E ) @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(35,axiom,
! [B: $i,A: $i] :
( ( ( c_Lambda_OdB_OAbs @ A )
!= ( c_Lambda_OdB_OAbs @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I3_J_0) ).
thf(269,plain,
! [B: $i,A: $i] :
( ( ( c_Lambda_OdB_OAbs @ A )
!= ( c_Lambda_OdB_OAbs @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(7,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Type_Otype_OFun @ A @ B )
!= ( c_Type_Otype_OFun @ C @ D ) )
| ( B = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type_Osimps_I2_J_1) ).
thf(202,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Type_Otype_OFun @ A @ B )
!= ( c_Type_Otype_OFun @ C @ D ) )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(150,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ A @ B @ C ) ) @ ( c_Lambda_Osubst @ A @ D @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__preserves__beta2_H_0) ).
thf(523,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ A @ B @ C ) ) @ ( c_Lambda_Osubst @ A @ D @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(176,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__1__1 @ A @ C @ D ) ) )
| ~ ( c_Wellfounded_Oaccp @ C @ B @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_accp__induct_2) ).
thf(582,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__1__1 @ A @ C @ D ) ) )
| ~ ( c_Wellfounded_Oaccp @ C @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(112,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ ( c_Transitive__Closure_Otranclp @ A @ B ) @ B @ B ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ ( c_Predicate_Oconversep @ A @ B @ B ) @ B ) @ C ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tranclp__converseD_0) ).
thf(440,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ ( c_Transitive__Closure_Otranclp @ A @ B ) @ B @ B ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ ( c_Predicate_Oconversep @ A @ B @ B ) @ B ) @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(145,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ A @ B @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ C ) )
| ( B
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apps__eq__Abs__conv_1) ).
thf(511,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ A @ B @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ C ) )
| ( B
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(86,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__inf__distrib1_0) ).
thf(384,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(162,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ C @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_App__eq__foldl__conv_0) ).
thf(550,plain,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ C @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(140,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ A @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ B @ A @ C ) @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ B ) @ A @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_head__Var__reduction_0) ).
thf(500,plain,
! [C: $i,B: $i,A: $i] :
( ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ A @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ B @ A @ C ) @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ B ) @ A @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(47,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ A @ B @ C @ D @ E ) @ F ) @ G ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ B @ H ) @ G ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ F ) @ H ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pred__comp_Ointros_0) ).
thf(301,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Opred__comp @ A @ B @ C @ D @ E ) @ F ) @ G ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ B @ H ) @ G ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ F ) @ H ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(110,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( c_Wellfounded_Oaccp @ C @ D @ t_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ C @ D ) @ ( v_sko__Wellfounded__Xaccp__Xinducts__1 @ A @ C ) ) )
| ~ ( c_Wellfounded_Oaccp @ C @ B @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_accp_Oinducts_0) ).
thf(436,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( c_Wellfounded_Oaccp @ C @ D @ t_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ C @ D ) @ ( v_sko__Wellfounded__Xaccp__Xinducts__1 @ A @ C ) ) )
| ~ ( c_Wellfounded_Oaccp @ C @ B @ t_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(142,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ A ) ) @ B ) @ C @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ B ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ A @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ C @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Beta_0) ).
thf(504,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ A ) ) @ B ) @ C @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ B ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ A @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ C @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(67,axiom,
! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ A ) @ B ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Oequal__imp__fequal_0) ).
thf(344,plain,
! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ A ) @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(166,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Wellfounded_Oaccp @ A @ B @ C )
| ( hBOOL @ ( hAPP @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Wellfounded__XaccpI__1__1 @ A @ B @ C ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_accpI_0) ).
thf(559,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Wellfounded_Oaccp @ A @ B @ C )
| ( hBOOL @ ( hAPP @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Wellfounded__XaccpI__1__1 @ A @ B @ C ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(2,negated_conjecture,
~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ v_t @ tc_Lambda_OdB ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(189,plain,
~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ v_t @ tc_Lambda_OdB ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(42,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Transitive__Closure_Ortranclp @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Ortranclp @ A @ B ) @ ( c_Transitive__Closure_Ortranclp @ C @ B ) @ ( tc_fun @ B @ ( tc_fun @ B @ tc_bool ) ) ) @ B )
= ( c_Transitive__Closure_Ortranclp @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ B @ ( tc_fun @ B @ tc_bool ) ) ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtranclp__sup__rtranclp_0) ).
thf(289,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Transitive__Closure_Ortranclp @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Ortranclp @ A @ B ) @ ( c_Transitive__Closure_Ortranclp @ C @ B ) @ ( tc_fun @ B @ ( tc_fun @ B @ tc_bool ) ) ) @ B )
= ( c_Transitive__Closure_Ortranclp @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ B @ ( tc_fun @ B @ tc_bool ) ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(116,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ A @ B @ C ) @ D ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ E ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conversep_Ointros_0) ).
thf(448,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ A @ B @ C ) @ D ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ E ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(55,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__left__idem_0) ).
thf(316,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(12,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ A @ B ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ A @ B ) @ C ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nitpick_Ortranclp__def_2) ).
thf(216,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ A @ B ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ A @ B ) @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(128,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
= C )
| ~ ( c_Type_Otyping @ A @ ( c_Lambda_OdB_OVar @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_typing__elims_I1_J_0) ).
thf(475,plain,
! [C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ B )
= C )
| ~ ( c_Type_Otyping @ A @ ( c_Lambda_OdB_OVar @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(136,axiom,
! [A: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ A ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_Lambda_OdB_OAbs @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apps__eq__Abs__conv_2) ).
thf(492,plain,
! [A: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ A ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB )
= ( c_Lambda_OdB_OAbs @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(180,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_Olift @ A @ B ) ) @ ( c_Lambda_Olift @ C @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__preserves__beta_0) ).
thf(591,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_Olift @ A @ B ) ) @ ( c_Lambda_Olift @ C @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(57,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ D @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I2_J_0) ).
thf(321,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ D @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(82,axiom,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Ortranclp @ ( c_Transitive__Closure_Ortranclp @ A @ B ) @ B )
= ( c_Transitive__Closure_Ortranclp @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtranclp__idemp_0) ).
thf(376,plain,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Ortranclp @ ( c_Transitive__Closure_Ortranclp @ A @ B ) @ B )
= ( c_Transitive__Closure_Ortranclp @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(146,axiom,
! [A: $i] :
( ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ A @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IT__implies__termi_0) ).
thf(514,plain,
! [A: $i] :
( ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ A @ tc_Lambda_OdB )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(69,axiom,
class_Lattices_Olattice @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Olattice) ).
thf(348,plain,
class_Lattices_Olattice @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(130,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ A @ B @ B ) @ B ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ A @ B ) @ D ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtranclp__converseI_0) ).
thf(480,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ A @ B @ B ) @ B ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ A @ B ) @ D ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(186,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Predicate_Oconversep @ ( c_Predicate_Opred__comp @ A @ B @ C @ D @ E ) @ C @ E )
= ( c_Predicate_Opred__comp @ ( c_Predicate_Oconversep @ B @ D @ E ) @ ( c_Predicate_Oconversep @ A @ C @ D ) @ E @ D @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__pred__comp_0) ).
thf(602,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Predicate_Oconversep @ ( c_Predicate_Opred__comp @ A @ B @ C @ D @ E ) @ C @ E )
= ( c_Predicate_Opred__comp @ ( c_Predicate_Oconversep @ B @ D @ E ) @ ( c_Predicate_Oconversep @ A @ C @ D ) @ E @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(92,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ A @ B ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ C ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tranclp_Or__into__trancl_0) ).
thf(397,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ A @ B ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(39,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ D @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__inf__distrib2_0) ).
thf(280,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ D @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(91,axiom,
! [B: $i,A: $i] : ( c_List_Olistsp @ A @ ( c_List_Olist_ONil @ B ) @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_listsp_ONil_0) ).
thf(396,plain,
! [B: $i,A: $i] : ( c_List_Olistsp @ A @ ( c_List_Olist_ONil @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(98,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Wellfounded_Oaccp @ A @ B @ C )
| ( hBOOL @ ( hAPP @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__Xintros__1__1 @ A @ B @ C ) ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_accp_OaccI_0) ).
thf(411,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Wellfounded_Oaccp @ A @ B @ C )
| ( hBOOL @ ( hAPP @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__Xintros__1__1 @ A @ B @ C ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(106,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ D @ C ) @ ( v_sko__Wellfounded__Xaccp__Xinduct__1 @ A @ D ) ) )
| ~ ( c_Wellfounded_Oaccp @ D @ B @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_accp_Oinduct_1) ).
thf(428,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ D @ C ) @ ( v_sko__Wellfounded__Xaccp__Xinduct__1 @ A @ D ) ) )
| ~ ( c_Wellfounded_Oaccp @ D @ B @ t_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(152,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Type_Otyping @ A @ B @ C )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ A @ D @ C @ tc_Type_Otype ) @ E @ F )
| ( c_Type_Otyping @ A @ ( c_Lambda_Osubst @ E @ B @ D ) @ F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__lemma_0) ).
thf(527,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_Type_Otyping @ A @ B @ C )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ A @ D @ C @ tc_Type_Otype ) @ E @ F )
| ( c_Type_Otyping @ A @ ( c_Lambda_Osubst @ E @ B @ D ) @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(8,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ C ) @ D ) )
| ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I2_J_0) ).
thf(206,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ C ) @ D ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(50,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ A @ ( c_Lambda_OdB_OVar @ B ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__Var__IT_0) ).
thf(307,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ A @ ( c_Lambda_OdB_OVar @ B ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(118,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_appR_0) ).
thf(452,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(26,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Type_Otype_OFun @ A @ B )
!= ( c_Type_Otype_OFun @ C @ D ) )
| ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type_Osimps_I2_J_0) ).
thf(248,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Type_Otype_OFun @ A @ B )
!= ( c_Type_Otype_OFun @ C @ D ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(153,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ A ) @ B @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ C ) @ D @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__apps__neq__Abs__apps_0) ).
thf(529,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ A ) @ B @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ C ) @ D @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(160,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Type_Otyping @ A @ B @ C )
| ~ ( c_Type_Otyping @ A @ D @ C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ D ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subject__reduction_H_0) ).
thf(546,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Type_Otyping @ A @ B @ C )
| ~ ( c_Type_Otyping @ A @ D @ C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ D ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(85,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__assoc_0) ).
thf(381,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(155,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ A ) @ B @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ C ) @ D @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( B = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Abs__apps__eq__Abs__apps__conv_1) ).
thf(534,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ A ) @ B @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ C ) @ D @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(14,axiom,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ B @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__idem_0) ).
thf(220,plain,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(78,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ A @ ( tc_fun @ E @ ( tc_fun @ F @ tc_bool ) ) ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf2E_1) ).
thf(366,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ A @ ( tc_fun @ E @ ( tc_fun @ F @ tc_bool ) ) ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(62,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ A @ B ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ A @ B ) @ E ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ A @ B ) @ C ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tranclp__trans_0) ).
thf(334,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ A @ B ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ A @ B ) @ E ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ A @ B ) @ C ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(70,axiom,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ A @ B ) @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtranclp_Ortrancl__refl_0) ).
thf(349,plain,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ A @ B ) @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(184,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ A @ B @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ A @ C @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ B @ C @ tc_Lambda_OdB ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apps__preserves__betas_0) ).
thf(598,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ A @ B @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ A @ C @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( c_ListOrder_Ostep1 @ c_Lambda_Obeta @ B @ C @ tc_Lambda_OdB ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(167,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( c_Wellfounded_Oaccp @ C @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__rule__1__1 @ A @ C @ D ) @ D )
| ~ ( c_Wellfounded_Oaccp @ C @ B @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_accp__induct__rule_0) ).
thf(561,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( c_Wellfounded_Oaccp @ C @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__rule__1__1 @ A @ C @ D ) @ D )
| ~ ( c_Wellfounded_Oaccp @ C @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(45,axiom,
! [B: $i,A: $i] :
( ( class_Lattices_Odistrib__lattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Odistrib__lattice @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Odistrib__lattice) ).
thf(297,plain,
! [B: $i,A: $i] :
( ( class_Lattices_Odistrib__lattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Odistrib__lattice @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(104,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ A @ B @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ C @ B @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apps__preserves__beta_0) ).
thf(424,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ A @ B @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ C @ B @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(96,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_OdB_OAbs @ A ) ) @ ( c_Lambda_OdB_OAbs @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__beta__Abs_0) ).
thf(407,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_OdB_OAbs @ A ) ) @ ( c_Lambda_OdB_OAbs @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(27,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OAbs @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Lambda_0) ).
thf(252,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OAbs @ A ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(60,axiom,
! [B: $i,A: $i] :
( ( c_Wellfounded_OwfP @ ( c_Transitive__Closure_Otranclp @ A @ B ) @ B )
| ~ ( c_Wellfounded_OwfP @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wfP__trancl_0) ).
thf(329,plain,
! [B: $i,A: $i] :
( ( c_Wellfounded_OwfP @ ( c_Transitive__Closure_Otranclp @ A @ B ) @ B )
| ~ ( c_Wellfounded_OwfP @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(120,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ C @ D @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( A
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ C @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ A @ B @ C @ D ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( D
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_App__eq__foldl__conv_2) ).
thf(456,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ C @ D @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( A
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ C @ ( c_ListApplication_Osko__ListApplication__XApp__eq__foldl__conv__1__1 @ A @ B @ C @ D ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( D
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(58,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ A @ B ) @ C ) @ D ) )
| ( C = D )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ A @ B ) @ C ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtranclpD_0) ).
thf(324,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ A @ B ) @ C ) @ D ) )
| ( C = D )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ A @ B ) @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(169,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ B ) @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ B @ C @ A ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ B ) @ C @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_head__Var__reduction_1) ).
thf(566,plain,
! [C: $i,B: $i,A: $i] :
( ( A
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ B ) @ ( c_ListBeta_Osko__ListBeta__Xhead__Var__reduction__1__1 @ B @ C @ A ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ B ) @ C @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(132,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ ( c_Predicate_Oconversep @ A @ B @ B ) @ B ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ ( c_Transitive__Closure_Otranclp @ A @ B ) @ B @ B ) @ C ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tranclp__converseI_0) ).
thf(484,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ ( c_Predicate_Oconversep @ A @ B @ B ) @ B ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ ( c_Transitive__Closure_Otranclp @ A @ B ) @ B @ B ) @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(1,negated_conjecture,
c_Type_Otyping @ v_e @ v_t @ v_T,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(188,plain,
c_Type_Otyping @ v_e @ v_t @ v_T,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(74,axiom,
! [B: $i,A: $i] :
( ( c_Lambda_OdB_OAbs @ A )
!= ( c_Lambda_OdB_OVar @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I7_J_0) ).
thf(356,plain,
! [B: $i,A: $i] :
( ( c_Lambda_OdB_OAbs @ A )
!= ( c_Lambda_OdB_OVar @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(181,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( v_sko__Wellfounded__Xaccp__Xinduct__1 @ A @ C ) ) )
| ~ ( c_Wellfounded_Oaccp @ C @ B @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_accp_Oinduct_2) ).
thf(593,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( v_sko__Wellfounded__Xaccp__Xinduct__1 @ A @ C ) ) )
| ~ ( c_Wellfounded_Oaccp @ C @ B @ t_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(102,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ D @ C ) @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__rule__1__1 @ A @ D @ E ) ) )
| ~ ( c_Wellfounded_Oaccp @ D @ B @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_accp__induct__rule_1) ).
thf(420,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ D @ C ) @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__rule__1__1 @ A @ D @ E ) ) )
| ~ ( c_Wellfounded_Oaccp @ D @ B @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(134,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Type_Otyping @ ( c_Type_Oshift @ A @ B @ C @ tc_Type_Otype ) @ ( c_Lambda_Olift @ D @ B ) @ E )
| ~ ( c_Type_Otyping @ A @ D @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__type_0) ).
thf(488,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Type_Otyping @ ( c_Type_Oshift @ A @ B @ C @ tc_Type_Otype ) @ ( c_Lambda_Olift @ D @ B ) @ E )
| ~ ( c_Type_Otyping @ A @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(16,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ A @ B ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ A @ B ) @ E ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ C ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tranclp__into__tranclp2_0) ).
thf(225,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ A @ B ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ A @ B ) @ E ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ C ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(65,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ ( tc_fun @ D @ tc_bool ) ) ) @ E ) @ F ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ B @ E ) @ F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup2CI_0) ).
thf(339,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ ( tc_fun @ D @ tc_bool ) ) ) @ E ) @ F ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ B @ E ) @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(10,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OVar @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__IT_0) ).
thf(212,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_OdB_OVar @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(126,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_Osubst @ A @ B @ C ) ) @ ( c_Lambda_Osubst @ D @ B @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ A ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__preserves__beta_0) ).
thf(471,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_Osubst @ A @ B @ C ) ) @ ( c_Lambda_Osubst @ D @ B @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ A ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(29,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Ofoldl @ A @ B @ ( c_List_Olist_ONil @ C ) @ D @ C )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_foldl__Nil_0) ).
thf(256,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_List_Ofoldl @ A @ B @ ( c_List_Olist_ONil @ C ) @ D @ C )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( class_Lattices_Olower__semilattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Olattice @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olower__semilattice) ).
thf(193,plain,
! [B: $i,A: $i] :
( ( class_Lattices_Olower__semilattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Olattice @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(156,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ A @ B @ C ) @ D ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ E ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conversep__iff_1) ).
thf(537,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ A @ B @ C ) @ D ) @ E ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ E ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(89,axiom,
! [C: $i,B: $i,A: $i] :
~ ( c_ListOrder_Ostep1 @ A @ ( c_List_Olist_ONil @ B ) @ C @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__Nil__step1_0) ).
thf(393,plain,
! [C: $i,B: $i,A: $i] :
~ ( c_ListOrder_Ostep1 @ A @ ( c_List_Olist_ONil @ B ) @ C @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(170,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ A ) ) @ ( c_Lambda_OdB_OAbs @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_abs_0) ).
thf(569,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OAbs @ A ) ) @ ( c_Lambda_OdB_OAbs @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(80,axiom,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ B @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__idem_0) ).
thf(371,plain,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(21,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ D @ ( tc_fun @ E @ ( tc_fun @ F @ tc_bool ) ) ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf2E_0) ).
thf(237,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ D @ ( tc_fun @ E @ ( tc_fun @ F @ tc_bool ) ) ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(34,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ C @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I3_J_0) ).
thf(266,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ C @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(144,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lambda_OdB_OAbs @ A )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ B @ C @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( C
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Abs__eq__apps__conv_1) ).
thf(508,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lambda_OdB_OAbs @ A )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ B @ C @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( C
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(52,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ A @ B ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ A @ B ) @ E ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ A @ B ) @ C ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtranclp__tranclp__tranclp_0) ).
thf(311,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ A @ B ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ A @ B ) @ E ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ A @ B ) @ C ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(158,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ A ) ) @ B )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ C ) @ D @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Abs__App__neq__Var__apps_0) ).
thf(541,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ A ) ) @ B )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ C ) @ D @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(178,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ A @ D @ E ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conversepD_0) ).
thf(586,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Predicate_Oconversep @ A @ D @ E ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(107,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Olift @ A @ B ) ) @ ( c_Lambda_Olift @ C @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__preserves__beta_H_0) ).
thf(430,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Olift @ A @ B ) ) @ ( c_Lambda_Olift @ C @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(33,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ A @ B ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ E ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ A @ B ) @ C ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtranclp__into__tranclp1_0) ).
thf(264,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ A @ B ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ E ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ A @ B ) @ C ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(114,axiom,
! [B: $i,A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OVar @ A ) ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_beta__cases_I1_J_0) ).
thf(444,plain,
! [B: $i,A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( c_Lambda_OdB_OVar @ A ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(177,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Wellfounded_Oaccp @ A @ B @ C )
| ~ ( c_Wellfounded_OwfP @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_accp__wfPD_0) ).
thf(584,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Wellfounded_Oaccp @ A @ B @ C )
| ~ ( c_Wellfounded_OwfP @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(41,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I8_J_0) ).
thf(286,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(174,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lambda_OdB_OVar @ A )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ B @ C @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( C
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__eq__apps__conv_1) ).
thf(577,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lambda_OdB_OVar @ A )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ B @ C @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( C
= ( c_List_Olist_ONil @ tc_Lambda_OdB ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(43,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I6_J_0) ).
thf(291,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(31,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ C ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ATP__Linkup_Ofequal__imp__equal_0) ).
thf(259,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_fequal @ C ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(99,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ A @ B @ C ) ) )
| ~ ( c_Type_Otyping @ D @ B @ E )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ B ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ D @ C @ E @ tc_Type_Otype ) @ A @ F )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__type__IT_0) ).
thf(413,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Osubst @ A @ B @ C ) ) )
| ~ ( c_Type_Otyping @ D @ B @ E )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ B ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ D @ C @ E @ tc_Type_Otype ) @ A @ F )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(3,axiom,
! [B: $i,A: $i] :
( ( class_Lattices_Oupper__semilattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Olattice @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Oupper__semilattice) ).
thf(191,plain,
! [B: $i,A: $i] :
( ( class_Lattices_Oupper__semilattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Olattice @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(94,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ D @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__assoc_0) ).
thf(402,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ D @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(172,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ A ) @ B @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ C ) @ D @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( B = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__apps__eq__Var__apps__conv_1) ).
thf(572,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ A ) @ B @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ C ) @ D @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(53,axiom,
class_Lattices_Olower__semilattice @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olower__semilattice) ).
thf(313,plain,
class_Lattices_Olower__semilattice @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(139,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ A ) @ B @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( c_List_Olistsp @ c_InductTermi_OIT @ B @ tc_Lambda_OdB ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IT_OVar_0) ).
thf(498,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ A ) @ B @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( c_List_Olistsp @ c_InductTermi_OIT @ B @ tc_Lambda_OdB ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(124,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ D @ C ) @ ( v_sko__Wellfounded__Xaccp__Xinducts__1 @ A @ D ) ) )
| ~ ( c_Wellfounded_Oaccp @ D @ B @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_accp_Oinducts_1) ).
thf(466,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ D @ C ) @ ( v_sko__Wellfounded__Xaccp__Xinducts__1 @ A @ D ) ) )
| ~ ( c_Wellfounded_Oaccp @ D @ B @ t_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(71,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ A @ B ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ A @ B ) @ E ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ A @ B ) @ C ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tranclp__rtranclp__tranclp_0) ).
thf(350,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ A @ B ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ A @ B ) @ E ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ A @ B ) @ C ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(187,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ A @ B @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ C ) )
| ( A
= ( c_Lambda_OdB_OAbs @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apps__eq__Abs__conv_0) ).
thf(604,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ A @ B @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_Lambda_OdB_OAbs @ C ) )
| ( A
= ( c_Lambda_OdB_OAbs @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(37,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I5_J_0) ).
thf(274,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(18,axiom,
! [C: $i,B: $i,A: $i] :
~ ( c_ListOrder_Ostep1 @ A @ B @ ( c_List_Olist_ONil @ C ) @ C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__step1__Nil_0) ).
thf(230,plain,
! [C: $i,B: $i,A: $i] :
~ ( c_ListOrder_Ostep1 @ A @ B @ ( c_List_Olist_ONil @ C ) @ C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(76,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B )
!= ( c_Lambda_OdB_OAbs @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I8_J_0) ).
thf(362,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B )
!= ( c_Lambda_OdB_OAbs @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(24,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ ( tc_fun @ D @ tc_bool ) ) ) @ E ) @ F ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ B @ E ) @ F ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ E ) @ F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf2I_0) ).
thf(245,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ ( tc_fun @ D @ tc_bool ) ) ) @ E ) @ F ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ B @ E ) @ F ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ E ) @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(109,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ A @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ C @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB )
| ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ B @ tc_Lambda_OdB )
| ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ A ) ) @ B ) @ C @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__induction__lemma_0) ).
thf(434,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ A @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) @ C @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB )
| ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ B @ tc_Lambda_OdB )
| ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ A ) ) @ B ) @ C @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ tc_Lambda_OdB ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(48,axiom,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Ortranclp @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_fequal @ B ) @ ( tc_fun @ B @ ( tc_fun @ B @ tc_bool ) ) ) @ B )
= ( c_Transitive__Closure_Ortranclp @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtranclp__reflcl_0) ).
thf(303,plain,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Ortranclp @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_fequal @ B ) @ ( tc_fun @ B @ ( tc_fun @ B @ tc_bool ) ) ) @ B )
= ( c_Transitive__Closure_Ortranclp @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(87,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ C ) @ D ) )
| ( B = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I2_J_1) ).
thf(387,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ C ) @ D ) )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(137,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ A @ B @ C ) ) @ ( c_Lambda_Osubst @ A @ D @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__preserves__beta2_0) ).
thf(494,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ A @ B @ C ) ) @ ( c_Lambda_Osubst @ A @ D @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(68,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__absorb_0) ).
thf(345,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(11,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Lambda_OdB_OAbs @ A )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I9_J_0) ).
thf(213,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Lambda_OdB_OAbs @ A )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(149,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ A ) @ B @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ C ) @ D @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__apps__eq__Var__apps__conv_0) ).
thf(520,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ A ) @ B @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ C ) @ D @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(122,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Wellfounded__Xnot__accp__down__1__1 @ A @ B @ C ) ) @ B ) )
| ( c_Wellfounded_Oaccp @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__accp__down_0) ).
thf(462,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Wellfounded__Xnot__accp__down__1__1 @ A @ B @ C ) ) @ B ) )
| ( c_Wellfounded_Oaccp @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(93,axiom,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B )
!= ( c_Lambda_OdB_OVar @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I5_J_0) ).
thf(399,plain,
! [C: $i,B: $i,A: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B )
!= ( c_Lambda_OdB_OVar @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(15,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ A @ B ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ A @ B ) @ E ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ C ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtranclp__into__tranclp2_0) ).
thf(223,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ A @ B ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ A @ B ) @ E ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ C ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(168,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ A @ B @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ C @ B @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apps__eq__tail__conv_0) ).
thf(563,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ A @ B @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ C @ B @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(46,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ A @ B ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ A @ B ) @ E ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ A @ B ) @ C ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtranclp__trans_0) ).
thf(299,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ A @ B ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ A @ B ) @ E ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ A @ B ) @ C ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(111,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__beta__AppR_0) ).
thf(438,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(127,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__beta__App_0) ).
thf(473,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ C ) @ D ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ B ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(135,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ A ) )
| ~ ( c_Type_Otyping @ B @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_type__implies__IT_0) ).
thf(490,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ A ) )
| ~ ( c_Type_Otyping @ B @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(105,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( c_Wellfounded_Oaccp @ C @ D @ t_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ C @ D ) @ ( v_sko__Wellfounded__Xaccp__Xinduct__1 @ A @ C ) ) )
| ~ ( c_Wellfounded_Oaccp @ C @ B @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_accp_Oinduct_0) ).
thf(426,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( c_Wellfounded_Oaccp @ C @ D @ t_a )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ C @ D ) @ ( v_sko__Wellfounded__Xaccp__Xinduct__1 @ A @ C ) ) )
| ~ ( c_Wellfounded_Oaccp @ C @ B @ t_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(161,axiom,
! [A: $i] :
( ( c_Lambda_OdB_OAbs @ A )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ A ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Abs__eq__apps__conv_2) ).
thf(548,plain,
! [A: $i] :
( ( c_Lambda_OdB_OAbs @ A )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ A ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(81,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_Olift @ A @ B ) @ C @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__lift_0) ).
thf(374,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_Olift @ A @ B ) @ C @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(9,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ C @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I7_J_0) ).
thf(209,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ C @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(147,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Wellfounded_Oaccp @ A @ B @ C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ A @ C ) @ B ) @ D ) )
| ~ ( c_Wellfounded_Oaccp @ A @ D @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_accp__downwards_0) ).
thf(516,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Wellfounded_Oaccp @ A @ B @ C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ A @ C ) @ B ) @ D ) )
| ~ ( c_Wellfounded_Oaccp @ A @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(163,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Predicate_Oconversep @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ ( tc_fun @ D @ tc_bool ) ) ) @ C @ D )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Predicate_Oconversep @ A @ C @ D ) @ ( c_Predicate_Oconversep @ B @ C @ D ) @ ( tc_fun @ D @ ( tc_fun @ C @ tc_bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__join_0) ).
thf(553,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Predicate_Oconversep @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ ( tc_fun @ D @ tc_bool ) ) ) @ C @ D )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Predicate_Oconversep @ A @ C @ D ) @ ( c_Predicate_Oconversep @ B @ C @ D ) @ ( tc_fun @ D @ ( tc_fun @ C @ tc_bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(151,axiom,
! [A: $i] :
( ( c_Lambda_OdB_OVar @ A )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ A ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__eq__apps__conv_2) ).
thf(525,plain,
! [A: $i] :
( ( c_Lambda_OdB_OVar @ A )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OVar @ A ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(165,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Wellfounded_Oaccp @ A @ B @ C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ D ) )
| ~ ( c_Wellfounded_Oaccp @ A @ D @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_accp__downward_0) ).
thf(557,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Wellfounded_Oaccp @ A @ B @ C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ D ) )
| ~ ( c_Wellfounded_Oaccp @ A @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(175,axiom,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_App__eq__foldl__conv_4) ).
thf(580,plain,
! [B: $i,A: $i] :
( ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B )
= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B ) @ ( c_List_Olist_ONil @ tc_Lambda_OdB ) @ tc_Lambda_OdB @ tc_Lambda_OdB ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(59,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Olift @ A @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift__IT_0) ).
thf(327,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( c_Lambda_Olift @ A @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(97,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_Wellfounded_Oaccp @ A @ ( c_ATP__Linkup_Osko__Wellfounded__Xnot__accp__down__1__1 @ A @ B @ C ) @ C )
| ( c_Wellfounded_Oaccp @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__accp__down_1) ).
thf(409,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_Wellfounded_Oaccp @ A @ ( c_ATP__Linkup_Osko__Wellfounded__Xnot__accp__down__1__1 @ A @ B @ C ) @ C )
| ( c_Wellfounded_Oaccp @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(6,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__inf__absorb_0) ).
thf(199,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(61,axiom,
! [B: $i,A: $i] :
( ( c_Lambda_OdB_OVar @ A )
!= ( c_Lambda_OdB_OAbs @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I6_J_0) ).
thf(331,plain,
! [B: $i,A: $i] :
( ( c_Lambda_OdB_OVar @ A )
!= ( c_Lambda_OdB_OAbs @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(141,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Wellfounded_Oaccp @ A @ B @ C )
| ~ ( c_Wellfounded_Oaccp @ A @ D @ C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ A @ C ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_accp__downwards__aux_0) ).
thf(502,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Wellfounded_Oaccp @ A @ B @ C )
| ~ ( c_Wellfounded_Oaccp @ A @ D @ C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ A @ C ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(75,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ C @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__left__commute_0) ).
thf(359,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ C @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(159,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ D @ C ) @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__1__1 @ A @ D @ E ) ) )
| ~ ( c_Wellfounded_Oaccp @ D @ B @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_accp__induct_1) ).
thf(544,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( hBOOL @ ( hAPP @ A @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ D @ C ) @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__1__1 @ A @ D @ E ) ) )
| ~ ( c_Wellfounded_Oaccp @ D @ B @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(63,axiom,
class_Lattices_Oupper__semilattice @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Oupper__semilattice) ).
thf(336,plain,
class_Lattices_Oupper__semilattice @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(185,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( c_Wellfounded_Oaccp @ C @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__1__1 @ A @ C @ D ) @ D )
| ~ ( c_Wellfounded_Oaccp @ C @ B @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_accp__induct_0) ).
thf(600,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ( c_Wellfounded_Oaccp @ C @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__1__1 @ A @ C @ D ) @ D )
| ~ ( c_Wellfounded_Oaccp @ C @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(54,axiom,
! [B: $i,A: $i] :
( ( class_Lattices_Olattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Olattice @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olattice) ).
thf(314,plain,
! [B: $i,A: $i] :
( ( class_Lattices_Olattice @ ( tc_fun @ A @ B ) )
| ~ ( class_Lattices_Olattice @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(182,axiom,
! [B: $i,A: $i] : ( c_Type_Otyping @ A @ ( c_Lambda_OdB_OVar @ B ) @ ( hAPP @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_typing_OVar_0) ).
thf(595,plain,
! [B: $i,A: $i] : ( c_Type_Otyping @ A @ ( c_Lambda_OdB_OVar @ B ) @ ( hAPP @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(115,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Wellfounded_Oaccp @ A @ B @ C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ D ) )
| ~ ( c_Wellfounded_Oaccp @ A @ D @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_accp_Ocases_0) ).
thf(446,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Wellfounded_Oaccp @ A @ B @ C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ D ) )
| ~ ( c_Wellfounded_Oaccp @ A @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(171,axiom,
! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ A ) ) @ B ) ) @ ( c_Lambda_Osubst @ A @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_beta_0) ).
thf(571,plain,
! [B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ A ) ) @ B ) ) @ ( c_Lambda_Osubst @ A @ B @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(117,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ A ) )
| ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ A @ tc_Lambda_OdB ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_termi__implies__IT_0) ).
thf(450,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ A ) )
| ~ ( c_Wellfounded_Oaccp @ ( c_Predicate_Oconversep @ c_Lambda_Obeta @ tc_Lambda_OdB @ tc_Lambda_OdB ) @ A @ tc_Lambda_OdB ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(157,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ A @ B @ C ) ) @ ( c_Lambda_Osubst @ D @ B @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ A ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__preserves__beta_H_0) ).
thf(539,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_Lambda_Osubst @ A @ B @ C ) ) @ ( c_Lambda_Osubst @ D @ B @ C ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ A ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(131,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__rule__1__1 @ A @ C @ D ) ) )
| ~ ( c_Wellfounded_Oaccp @ C @ B @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_accp__induct__rule_2) ).
thf(482,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__induct__rule__1__1 @ A @ C @ D ) ) )
| ~ ( c_Wellfounded_Oaccp @ C @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(13,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Type_Oshift @ A @ B @ C @ D ) @ B )
= C ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_shift__eq_0) ).
thf(218,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_Type_Oshift @ A @ B @ C @ D ) @ B )
= C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(79,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ C @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I1_J_0) ).
thf(368,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(179,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lambda_OdB_OVar @ A )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ B @ C @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OVar @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Var__eq__apps__conv_0) ).
thf(588,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lambda_OdB_OVar @ A )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ B @ C @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OVar @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(56,axiom,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ ( c_Lambda_OdB_OVar @ B ) ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_app__Var__IT_0) ).
thf(319,plain,
! [B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ ( c_Lambda_OdB_OVar @ B ) ) ) )
| ~ ( hBOOL @ ( hAPP @ c_InductTermi_OIT @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(30,axiom,
class_Lattices_Odistrib__lattice @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Odistrib__lattice) ).
thf(258,plain,
class_Lattices_Odistrib__lattice @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(88,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I4_J_0) ).
thf(390,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(101,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ A @ B ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ A @ B @ B ) @ B ) @ D ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtranclp__converseD_0) ).
thf(418,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ A @ B ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ ( c_Predicate_Oconversep @ A @ B @ B ) @ B ) @ D ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(83,axiom,
class_Lattices_Olower__semilattice @ tc_nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Olower__semilattice) ).
thf(378,plain,
class_Lattices_Olower__semilattice @ tc_nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(129,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Wellfounded_Oaccp @ A @ B @ C )
| ~ ( c_Wellfounded_Oaccp @ A @ ( c_ATP__Linkup_Osko__Wellfounded__XaccpI__1__1 @ A @ B @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_accpI_1) ).
thf(478,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Wellfounded_Oaccp @ A @ B @ C )
| ~ ( c_Wellfounded_Oaccp @ A @ ( c_ATP__Linkup_Osko__Wellfounded__XaccpI__1__1 @ A @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(108,axiom,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Otranclp @ ( c_Predicate_Oconversep @ A @ B @ B ) @ B )
= ( c_Predicate_Oconversep @ ( c_Transitive__Closure_Otranclp @ A @ B ) @ B @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tranclp__converse_0) ).
thf(432,plain,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Otranclp @ ( c_Predicate_Oconversep @ A @ B @ B ) @ B )
= ( c_Predicate_Oconversep @ ( c_Transitive__Closure_Otranclp @ A @ B ) @ B @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(32,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ D @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ A @ ( tc_fun @ E @ ( tc_fun @ F @ tc_bool ) ) ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup2E_0) ).
thf(262,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ D @ B ) @ C ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ A @ ( tc_fun @ E @ ( tc_fun @ F @ tc_bool ) ) ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(95,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Lambda_Olift @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B ) @ C )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Olift @ A @ C ) ) @ ( c_Lambda_Olift @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lift_Osimps_I2_J_0) ).
thf(405,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Lambda_Olift @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B ) @ C )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Olift @ A @ C ) ) @ ( c_Lambda_Olift @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(103,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ A @ B @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ C @ B @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_apps__preserves__beta2_0) ).
thf(422,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ A @ B @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) @ ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ C @ B @ tc_Lambda_OdB @ tc_Lambda_OdB ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(36,axiom,
class_Lattices_Olattice @ tc_bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olattice) ).
thf(273,plain,
class_Lattices_Olattice @ tc_bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(49,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ A @ B ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ E ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ A @ B ) @ C ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tranclp_Otrancl__into__trancl_0) ).
thf(305,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ A @ B ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ E ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ A @ B ) @ C ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(44,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ A @ B ) @ C ) @ D ) )
| ( C = D )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ A @ B ) @ C ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nitpick_Ortranclp__def_0) ).
thf(294,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Otranclp @ A @ B ) @ C ) @ D ) )
| ( C = D )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ A @ B ) @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(66,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ C @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__commute_0) ).
thf(341,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Olower__semilattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A )
= ( c_Lattices_Olower__semilattice__class_Oinf @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(143,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Type_Otyping @ A @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ B ) @ C ) @ D )
| ~ ( c_Type_Otyping @ A @ C @ E )
| ~ ( c_Type_Otyping @ A @ B @ ( c_Type_Otype_OFun @ E @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_App_0) ).
thf(506,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Type_Otyping @ A @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ B ) @ C ) @ D )
| ~ ( c_Type_Otyping @ A @ C @ E )
| ~ ( c_Type_Otyping @ A @ B @ ( c_Type_Otype_OFun @ E @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ( ( c_Lambda_OdB_OVar @ A )
!= ( c_Lambda_OdB_OVar @ B ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I1_J_0) ).
thf(195,plain,
! [B: $i,A: $i] :
( ( ( c_Lambda_OdB_OVar @ A )
!= ( c_Lambda_OdB_OVar @ B ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(154,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Predicate_Oconversep @ ( c_Predicate_Oconversep @ A @ B @ C ) @ C @ B )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conversep__conversep_0) ).
thf(532,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Predicate_Oconversep @ ( c_Predicate_Oconversep @ A @ B @ C ) @ C @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(40,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ C @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__left__commute_0) ).
thf(283,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ C @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(100,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ A ) @ B @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ C ) @ D @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Abs__apps__eq__Abs__apps__conv_0) ).
thf(415,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ A ) @ B @ tc_Lambda_OdB @ tc_Lambda_OdB )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ ( c_Lambda_OdB_OAbs @ C ) @ D @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(22,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__distrib1_0) ).
thf(239,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ D @ A ) @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(23,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__commute_0) ).
thf(242,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Oupper__semilattice @ A )
| ( ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(90,axiom,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ A @ B ) @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nitpick_Ortranclp__def_1) ).
thf(395,plain,
! [C: $i,B: $i,A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ A @ B ) @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(123,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ C ) @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_appL_0) ).
thf(464,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ C ) @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(173,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ C ) @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__beta__AppL_0) ).
thf(575,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B ) ) @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ C ) @ B ) ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ c_Lambda_Obeta @ tc_Lambda_OdB ) @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(183,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Wellfounded_Oaccp @ A @ B @ C )
| ~ ( c_Wellfounded_Oaccp @ A @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__Xintros__1__1 @ A @ B @ C ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_accp_OaccI_1) ).
thf(596,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Wellfounded_Oaccp @ A @ B @ C )
| ~ ( c_Wellfounded_Oaccp @ A @ ( c_ATP__Linkup_Osko__Wellfounded__Xaccp__Xintros__1__1 @ A @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(121,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lambda_OdB_OAbs @ A )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ B @ C @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OAbs @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Abs__eq__apps__conv_0) ).
thf(459,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lambda_OdB_OAbs @ A )
!= ( c_List_Ofoldl @ c_Lambda_OdB_OApp @ B @ C @ tc_Lambda_OdB @ tc_Lambda_OdB ) )
| ( ( c_Lambda_OdB_OAbs @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(38,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Lambda_OdB_OVar @ A )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_dB_Osimps_I4_J_0) ).
thf(277,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Lambda_OdB_OVar @ A )
!= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(113,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Type_Otyping @ A @ ( c_Lambda_OdB_OAbs @ B ) @ ( c_Type_Otype_OFun @ C @ D ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C @ tc_Type_Otype ) @ B @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Abs_0) ).
thf(442,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Type_Otyping @ A @ ( c_Lambda_OdB_OAbs @ B ) @ ( c_Type_Otype_OFun @ C @ D ) )
| ~ ( c_Type_Otyping @ ( c_Type_Oshift @ A @ ( c_HOL_Ozero__class_Ozero @ tc_nat ) @ C @ tc_Type_Otype ) @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(133,axiom,
! [A: $i] :
( ( c_Predicate_Oconversep @ ( c_fequal @ A ) @ A @ A )
= ( c_fequal @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conversep__eq_0) ).
thf(486,plain,
! [A: $i] :
( ( c_Predicate_Oconversep @ ( c_fequal @ A ) @ A @ A )
= ( c_fequal @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(64,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ A @ B ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ C ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_r__into__rtranclp_0) ).
thf(337,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ A @ B ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ C ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(73,axiom,
! [B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Otranclp @ A @ B ) @ ( c_fequal @ B ) @ ( tc_fun @ B @ ( tc_fun @ B @ tc_bool ) ) )
= ( c_Transitive__Closure_Ortranclp @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_reflcl__tranclp_0) ).
thf(354,plain,
! [B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Otranclp @ A @ B ) @ ( c_fequal @ B ) @ ( tc_fun @ B @ ( tc_fun @ B @ tc_bool ) ) )
= ( c_Transitive__Closure_Ortranclp @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(51,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ A @ B ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ A @ B ) @ E ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ C ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__rtranclp__into__rtranclp_0) ).
thf(309,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ A @ B ) @ C ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Transitive__Closure_Ortranclp @ A @ B ) @ E ) @ D ) )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ A @ C ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(19,axiom,
! [B: $i,A: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ A ) @ B @ A )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__eq_0) ).
thf(232,plain,
! [B: $i,A: $i] :
( ( c_Lambda_Osubst @ ( c_Lambda_OdB_OVar @ A ) @ B @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(28,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B ) @ C @ D )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ A @ C @ D ) ) @ ( c_Lambda_Osubst @ B @ C @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subst__App_0) ).
thf(254,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lambda_Osubst @ ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ A ) @ B ) @ C @ D )
= ( hAPP @ ( hAPP @ c_Lambda_OdB_OApp @ ( c_Lambda_Osubst @ A @ C @ D ) ) @ ( c_Lambda_Osubst @ B @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(17,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__distrib2_0) ).
thf(227,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Odistrib__lattice @ A )
| ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ A ) @ D @ A )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ A ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ C @ D @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(138,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Type_Otyping @ A @ B @ C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ D ) @ B ) )
| ~ ( c_Type_Otyping @ A @ D @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subject__reduction_0) ).
thf(496,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Type_Otyping @ A @ B @ C )
| ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_Lambda_Obeta @ D ) @ B ) )
| ~ ( c_Type_Otyping @ A @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(119,axiom,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( v_sko__Wellfounded__Xaccp__Xinducts__1 @ A @ C ) ) )
| ~ ( c_Wellfounded_Oaccp @ C @ B @ t_a ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_accp_Oinducts_2) ).
thf(454,plain,
! [C: $i,B: $i,A: $i] :
( ( hBOOL @ ( hAPP @ A @ B ) )
| ~ ( hBOOL @ ( hAPP @ A @ ( v_sko__Wellfounded__Xaccp__Xinducts__1 @ A @ C ) ) )
| ~ ( c_Wellfounded_Oaccp @ C @ B @ t_a ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(607,plain,
$false,
inference(e,[status(thm)],[365,518,468,234,555,352,247,379,269,202,523,582,440,511,384,550,500,301,436,504,344,559,189,289,448,316,216,475,492,591,321,376,514,348,480,602,397,280,396,411,428,527,206,307,452,248,529,546,381,534,220,366,334,349,598,561,297,424,407,252,329,456,324,566,484,188,356,593,420,488,225,339,212,471,256,193,537,393,569,371,237,266,508,311,541,586,430,264,444,584,286,577,291,259,413,191,402,572,313,498,466,350,604,274,230,362,245,434,303,387,494,345,213,520,462,399,223,563,299,438,473,490,426,548,374,209,516,553,525,557,580,327,409,199,331,502,359,544,336,600,314,595,446,571,450,539,482,218,368,588,319,258,390,418,378,478,432,262,405,422,273,305,294,341,506,195,532,283,415,239,242,395,464,575,596,459,277,442,486,337,354,309,232,254,227,496,454]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : LCL856-1 : TPTP v8.1.2. Released v4.1.0.
% 0.07/0.15 % Command : run_Leo-III %s %d
% 0.16/0.36 % Computer : n009.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Thu May 18 15:57:34 EDT 2023
% 0.16/0.36 % CPUTime :
% 0.93/0.88 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.68/1.09 % [INFO] Parsing done (204ms).
% 1.68/1.10 % [INFO] Running in sequential loop mode.
% 2.21/1.30 % [INFO] eprover registered as external prover.
% 2.21/1.30 % [INFO] cvc4 registered as external prover.
% 2.21/1.30 % [INFO] Scanning for conjecture ...
% 2.52/1.39 % [INFO] Found a conjecture and 185 axioms. Running axiom selection ...
% 2.82/1.47 % [INFO] Axiom selection finished. Selected 185 axioms (removed 0 axioms).
% 3.14/1.56 % [INFO] Problem is propositional (TPTP CNF).
% 3.28/1.57 % [INFO] Type checking passed.
% 3.28/1.57 % [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 ...
% 6.49/2.45 % External prover 'e' found a proof!
% 6.49/2.45 % [INFO] Killing All external provers ...
% 6.49/2.45 % Time passed: 1925ms (effective reasoning time: 1350ms)
% 6.49/2.45 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 6.49/2.45 % Axioms used in derivation (185): cls_inf__sup__absorb_0, cls_inf__sup__aci_I2_J_0, cls_accp__induct__rule_1, cls_dB_Osimps_I6_J_0, cls_apps__eq__Abs__conv_0, cls_converse__meet_0, clsarity_fun__Lattices_Olower__semilattice, cls_lift_Osimps_I2_J_0, cls_subst__App_0, cls_Var__eq__apps__conv_1, cls_subst__eq_0, cls_dB_Osimps_I8_J_0, cls_subject__reduction_0, cls_accp_Oinduct_0, cls_termi__implies__IT_0, cls_accp__wfPD_0, clsarity_nat__Lattices_Odistrib__lattice, cls_conversepD_0, cls_inf__sup__aci_I6_J_0, cls_accp__downwards_0, cls_converse__pred__comp_0, clsarity_bool__Lattices_Olower__semilattice, cls_rtranclp__sup__rtranclp_0, cls_rtrancl__beta__Abs_0, cls_app__Var__IT_0, cls_not__step1__Nil_0, cls_appR_0, cls_listsp_ONil_0, cls_inf__sup__distrib1_0, cls_sup__inf__distrib2_0, cls_rtranclp__trans_0, clsarity_fun__Lattices_Oupper__semilattice, cls_inf__left__commute_0, cls_head__Var__reduction_1, cls_beta_0, cls_tranclp__converse_0, cls_dB_Osimps_I7_J_0, cls_accp__induct_1, cls_subst__preserves__beta_0, cls_Abs_0, cls_rtranclp__tranclp__tranclp_0, cls_lift__type_0, cls_inf__commute_0, cls_Abs__apps__eq__Abs__apps__conv_1, cls_rtranclp__into__tranclp1_0, cls_wfP__trancl_0, cls_type__implies__IT_0, cls_accp_Oinducts_2, cls_inf2E_0, cls_Var__apps__eq__Var__apps__conv_0, cls_tranclp__converseI_0, cls_accp__induct_0, cls_Nitpick_Ortranclp__def_0, cls_shift__eq_0, cls_dB_Osimps_I3_J_0, cls_inf__sup__aci_I8_J_0, cls_Var__eq__apps__conv_2, cls_accpI_0, cls_Var__apps__eq__Var__apps__conv_1, cls_sup2CI_0, cls_App__eq__foldl__conv_0, cls_accp_OaccI_0, cls_type_Osimps_I2_J_1, cls_inf2I_0, cls_dB_Osimps_I4_J_0, cls_typing__elims_I1_J_0, cls_subject__reduction_H_0, clsarity_bool__Lattices_Oupper__semilattice, cls_Var__IT_0, cls_accpI_1, cls_converse__rtranclp__into__rtranclp_0, clsarity_nat__Lattices_Olower__semilattice, cls_App_0, cls_inf__sup__aci_I3_J_0, cls_ATP__Linkup_Ofequal__imp__equal_0, cls_apps__preserves__betas_0, cls_sup__commute_0, cls_head__Var__reduction_0, cls_IT__implies__termi_0, cls_sup2CI_1, clsarity_fun__Lattices_Olattice, cls_apps__eq__Abs__conv_2, cls_conversep__conversep_0, cls_dB_Osimps_I1_J_0, cls_Abs__App__neq__Var__apps_0, cls_rtrancl__beta__App_0, cls_inf__sup__aci_I7_J_0, cls_rtrancl__beta__AppL_0, cls_sup__assoc_0, cls_Nitpick_Ortranclp__def_1, cls_type_Osimps_I2_J_0, cls_inf2E_1, cls_pred__comp_Ointros_0, cls_inf__sup__aci_I1_J_0, cls_not__Nil__step1_0, cls_apps__eq__Abs__conv_1, cls_lift__preserves__beta_0, clsarity_nat__Lattices_Olattice, cls_Var__apps__neq__Abs__apps_0, cls_accp_Oinducts_0, cls_subst__lemma_0, cls_tranclp__rtranclp__tranclp_0, cls_conversep_Ointros_0, cls_inf__assoc_0, cls_dB_Osimps_I2_J_1, cls_accp__downwards__aux_0, cls_not__accp__down_0, cls_not__accp__down_1, cls_lift__preserves__beta_H_0, cls_accp_OaccI_1, cls_tranclp__trans_0, clsarity_bool__Lattices_Olattice, cls_tranclp_Otrancl__into__trancl_0, cls_rtranclp_Ortrancl__refl_0, cls_App__eq__foldl__conv_2, cls_sup__left__idem_0, cls_tranclp_Or__into__trancl_0, cls_inf__idem_0, cls_accp__induct_2, cls_abs_0, cls_accp__downward_0, cls_apps__eq__tail__conv_0, cls_Abs__eq__apps__conv_2, cls_sup__inf__absorb_0, cls_rtranclp__idemp_0, cls_typing_OVar_0, cls_IT_OVar_0, cls_inf__sup__aci_I4_J_0, cls_Nitpick_Ortranclp__def_2, cls_lift__IT_0, cls_tranclp__converseD_0, cls_accp_Ocases_0, cls_apps__preserves__beta2_0, cls_converse__join_0, cls_rtranclp__reflcl_0, cls_apps__preserves__beta_0, clsarity_nat__Lattices_Oupper__semilattice, cls_ATP__Linkup_Oequal__imp__fequal_0, cls_inf__sup__aci_I5_J_0, cls_Abs__eq__apps__conv_0, cls_accp__induct__rule_2, cls_sup__idem_0, cls_App__eq__foldl__conv_4, cls_rtranclpD_0, cls_sup__left__commute_0, clsarity_bool__Lattices_Odistrib__lattice, cls_tranclp__into__tranclp2_0, cls_dB_Osimps_I5_J_0, cls_subst__type__IT_0, cls_accp_Oinducts_1, cls_beta__cases_I1_J_0, cls_Var__eq__apps__conv_0, cls_dB_Osimps_I2_J_0, cls_var__app__type__eq_0, cls_conversep__eq_0, cls_accp_Oinduct_2, cls_subst__Var__IT_0, cls_inf__left__idem_0, cls_foldl__Nil_0, cls_Lambda_0, cls_rtranclp_Ortrancl__into__rtrancl_0, cls_accp_Oinduct_1, cls_sup__inf__distrib1_0, cls_Abs__eq__apps__conv_1, cls_subst__preserves__beta2_0, cls_subst__lift_0, cls_sup2E_0, cls_conversep__iff_1, cls_appL_0, cls_Beta_0, cls_accp__induct__rule_0, clsarity_fun__Lattices_Odistrib__lattice, cls_rtranclp__converseD_0, cls_conversep_Ocases_0, cls_dB_Osimps_I9_J_0, cls_rtranclp__into__tranclp2_0, cls_subst__preserves__beta2_H_0, cls_inf__sup__distrib2_0, cls_rtranclp__converseI_0, cls_double__induction__lemma_0, cls_reflcl__tranclp_0, cls_rtrancl__beta__AppR_0, cls_Abs__apps__eq__Abs__apps__conv_0, cls_r__into__rtranclp_0, cls_subst__preserves__beta_H_0
% 6.49/2.45 % No. of inferences in proof: 375
% 6.49/2.45 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1925 ms resp. 1350 ms w/o parsing
% 6.96/2.56 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 6.96/2.57 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------