TSTP Solution File: SCT158+1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SCT158+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 11:50:49 EDT 2023
% Result : Theorem 95.72s 22.38s
% Output : Refutation 96.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 594
% Syntax : Number of formulae : 1142 ( 284 unt; 84 typ; 0 def)
% Number of atoms : 2870 ( 763 equ; 0 cnn)
% Maximal formula atoms : 22 ( 2 avg)
% Number of connectives : 20845 ( 339 ~; 88 |; 244 &;18702 @)
% ( 105 <=>;1367 =>; 0 <=; 0 <~>)
% Maximal formula depth : 26 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 189 ( 189 >; 0 *; 0 +; 0 <<)
% Number of symbols : 86 ( 84 usr; 14 con; 0-6 aty)
% Number of variables : 3724 ( 0 ^;3678 !; 46 ?;3724 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_member_type,type,
c_member: $i > $i > $i > $o ).
thf(tc_prod_type,type,
tc_prod: $i > $i > $i ).
thf(tc_Arrow__Order__Mirabelle_Oalt_type,type,
tc_Arrow__Order__Mirabelle_Oalt: $i ).
thf(c_Product__Type_OPair_type,type,
c_Product__Type_OPair: $i > $i > $i > $i > $i ).
thf(v_a_____type,type,
v_a____: $i ).
thf(v_b_____type,type,
v_b____: $i ).
thf(hAPP_type,type,
hAPP: $i > $i > $i ).
thf(v_F_type,type,
v_F: $i ).
thf(v_P_____type,type,
v_P____: $i ).
thf(v_a_H_____type,type,
v_a_H____: $i ).
thf(v_b_H_____type,type,
v_b_H____: $i ).
thf(v_P_H_____type,type,
v_P_H____: $i ).
thf(class_Lattices_Osemilattice__sup_type,type,
class_Lattices_Osemilattice__sup: $i > $o ).
thf(c_Lattices_Osemilattice__sup__class_Osup_type,type,
c_Lattices_Osemilattice__sup__class_Osup: $i > $i > $i > $i ).
thf(tc_HOL_Obool_type,type,
tc_HOL_Obool: $i ).
thf(class_Lattices_Osemilattice__inf_type,type,
class_Lattices_Osemilattice__inf: $i > $o ).
thf(tc_Nat_Onat_type,type,
tc_Nat_Onat: $i ).
thf(c_Lattices_Osemilattice__inf__class_Oinf_type,type,
c_Lattices_Osemilattice__inf__class_Oinf: $i > $i > $i > $i ).
thf(class_Lattices_Odistrib__lattice_type,type,
class_Lattices_Odistrib__lattice: $i > $o ).
thf(tc_fun_type,type,
tc_fun: $i > $i > $i ).
thf(class_Lattices_Obounded__lattice__bot_type,type,
class_Lattices_Obounded__lattice__bot: $i > $o ).
thf(c_Transitive__Closure_Ortrancl_type,type,
c_Transitive__Closure_Ortrancl: $i > $i > $i ).
thf(c_Relation_OId_type,type,
c_Relation_OId: $i > $i ).
thf(c_Orderings_Oord__class_Oless__eq_type,type,
c_Orderings_Oord__class_Oless__eq: $i > $i > $i > $o ).
thf(c_Groups_Ominus__class_Ominus_type,type,
c_Groups_Ominus__class_Ominus: $i > $i > $i > $i ).
thf(class_Orderings_Oord_type,type,
class_Orderings_Oord: $i > $o ).
thf(class_Lattices_Olattice_type,type,
class_Lattices_Olattice: $i > $o ).
thf(c_Relation_ORange_type,type,
c_Relation_ORange: $i > $i > $i > $i ).
thf(c_Relation_Osingle__valued_type,type,
c_Relation_Osingle__valued: $i > $i > $i > $o ).
thf(c_Relation_Oconverse_type,type,
c_Relation_Oconverse: $i > $i > $i > $i ).
thf(c_Relation_OImage_type,type,
c_Relation_OImage: $i > $i > $i > $i > $i ).
thf(c_Set_Oinsert_type,type,
c_Set_Oinsert: $i > $i > $i > $i ).
thf(class_Groups_Ominus_type,type,
class_Groups_Ominus: $i > $o ).
thf(c_Relation_Orefl__on_type,type,
c_Relation_Orefl__on: $i > $i > $i > $o ).
thf(c_Relation_OField_type,type,
c_Relation_OField: $i > $i > $i ).
thf(c_Relation_Oantisym_type,type,
c_Relation_Oantisym: $i > $i > $o ).
thf(c_Orderings_Obot__class_Obot_type,type,
c_Orderings_Obot__class_Obot: $i > $i ).
thf(c_Transitive__Closure_Otrancl_type,type,
c_Transitive__Closure_Otrancl: $i > $i > $i ).
thf(c_Wellfounded_Owf_type,type,
c_Wellfounded_Owf: $i > $i > $o ).
thf(c_Wellfounded_Omlex__prod_type,type,
c_Wellfounded_Omlex__prod: $i > $i > $i > $i ).
thf(c_Relation_OId__on_type,type,
c_Relation_OId__on: $i > $i > $i ).
thf(c_Relation_ODomain_type,type,
c_Relation_ODomain: $i > $i > $i > $i ).
thf(class_Orderings_Olinorder_type,type,
class_Orderings_Olinorder: $i > $o ).
thf(c_Set_Othe__elem_type,type,
c_Set_Othe__elem: $i > $i > $i ).
thf(c_Relation_Ototal__on_type,type,
c_Relation_Ototal__on: $i > $i > $i > $o ).
thf(c_Wellfounded_Oacyclic_type,type,
c_Wellfounded_Oacyclic: $i > $i > $o ).
thf(c_Order__Relation_Opartial__order__on_type,type,
c_Order__Relation_Opartial__order__on: $i > $i > $i > $o ).
thf(c_Order__Relation_Opreorder__on_type,type,
c_Order__Relation_Opreorder__on: $i > $i > $i > $o ).
thf(c_Relation_Oinv__image_type,type,
c_Relation_Oinv__image: $i > $i > $i > $i > $i ).
thf(c_Equiv__Relations_Oquotient_type,type,
c_Equiv__Relations_Oquotient: $i > $i > $i > $i ).
thf(c_Wellfounded_Omeasure_type,type,
c_Wellfounded_Omeasure: $i > $i > $i ).
thf(c_Order__Relation_Olinear__order__on_type,type,
c_Order__Relation_Olinear__order__on: $i > $i > $i > $o ).
thf(class_Orderings_Obot_type,type,
class_Orderings_Obot: $i > $o ).
thf(c_Wellfounded_OwfP_type,type,
c_Wellfounded_OwfP: $i > $i > $o ).
thf(c_Equiv__Relations_Oequiv_type,type,
c_Equiv__Relations_Oequiv: $i > $i > $i > $o ).
thf(c_FunDef_Oin__rel_type,type,
c_FunDef_Oin__rel: $i > $i > $i > $i ).
thf(hBOOL_type,type,
hBOOL: $i > $o ).
thf(c_fequal_type,type,
c_fequal: $i > $i ).
thf(tc_Arrow__Order__Mirabelle_Oindi_type,type,
tc_Arrow__Order__Mirabelle_Oindi: $i ).
thf(c_Arrow__Order__Mirabelle_OProf_type,type,
c_Arrow__Order__Mirabelle_OProf: $i ).
thf(c_Recdef_Owfrec__rel_type,type,
c_Recdef_Owfrec__rel: $i > $i > $i > $i > $i > $i > $o ).
thf(c_Nitpick_Owf__wfrec_H_type,type,
c_Nitpick_Owf__wfrec_H: $i > $i > $i > $i > $i > $i ).
thf(c_Recdef_Ocut_type,type,
c_Recdef_Ocut: $i > $i > $i > $i > $i > $i ).
thf(c_Nitpick_Owf__wfrec_type,type,
c_Nitpick_Owf__wfrec: $i > $i > $i > $i > $i ).
thf(c_Arrow__Order__Mirabelle_OLin_type,type,
c_Arrow__Order__Mirabelle_OLin: $i ).
thf(c_Arrow__Order__Mirabelle_Obelow_type,type,
c_Arrow__Order__Mirabelle_Obelow: $i > $i > $i > $i ).
thf(c_Recdef_Osame__fst_type,type,
c_Recdef_Osame__fst: $i > $i > $i > $i > $i ).
thf(c_Order__Relation_Owell__order__on_type,type,
c_Order__Relation_Owell__order__on: $i > $i > $i > $o ).
thf(c_Recdef_Owfrec_type,type,
c_Recdef_Owfrec: $i > $i > $i > $i > $i ).
thf(c_Product__Type_Ocurry_type,type,
c_Product__Type_Ocurry: $i > $i > $i > $i > $i > $i > $i ).
thf(c_Equiv__Relations_Ocongruent_type,type,
c_Equiv__Relations_Ocongruent: $i > $i > $i > $i > $o ).
thf(c_Wellfounded_Olex__prod_type,type,
c_Wellfounded_Olex__prod: $i > $i > $i > $i > $i ).
thf(c_Arrow__Order__Mirabelle_Omktop_type,type,
c_Arrow__Order__Mirabelle_Omktop: $i > $i > $i ).
thf(c_Arrow__Order__Mirabelle_Odictator_type,type,
c_Arrow__Order__Mirabelle_Odictator: $i > $i > $o ).
thf(c_Relation_Oirrefl_type,type,
c_Relation_Oirrefl: $i > $i > $o ).
thf(c_Arrow__Order__Mirabelle_Oabove_type,type,
c_Arrow__Order__Mirabelle_Oabove: $i > $i > $i > $i ).
thf(c_Wellfounded_Oacc_type,type,
c_Wellfounded_Oacc: $i > $i > $i ).
thf(c_Product__Type_Oprod_Oprod__rec_type,type,
c_Product__Type_Oprod_Oprod__rec: $i > $i > $i > $i > $i > $i ).
thf(c_Arrow__Order__Mirabelle_OIIA_type,type,
c_Arrow__Order__Mirabelle_OIIA: $i > $o ).
thf(c_Equiv__Relations_Ocongruent2_type,type,
c_Equiv__Relations_Ocongruent2: $i > $i > $i > $i > $i > $i > $o ).
thf(c_Product__Type_Ointernal__split_type,type,
c_Product__Type_Ointernal__split: $i > $i > $i > $i > $i > $i ).
thf(c_Arrow__Order__Mirabelle_Omkbot_type,type,
c_Arrow__Order__Mirabelle_Omkbot: $i > $i > $i ).
thf(c_Nitpick_Orefl_H_type,type,
c_Nitpick_Orefl_H: $i > $i > $o ).
thf(c_Arrow__Order__Mirabelle_Ounanimity_type,type,
c_Arrow__Order__Mirabelle_Ounanimity: $i > $o ).
thf(447,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ D @ C @ ( c_Wellfounded_Oacc @ D @ B ) )
=> ( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ A @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ B ) )
=> ( c_member @ D @ A @ ( c_Wellfounded_Oacc @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acc__downwards) ).
thf(2163,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ D @ C @ ( c_Wellfounded_Oacc @ D @ B ) )
=> ( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ A @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ B ) )
=> ( c_member @ D @ A @ ( c_Wellfounded_Oacc @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(288,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ C ) @ B )
=> ( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ C @ A ) @ B )
=> ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ A ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_r__r__into__trancl) ).
thf(1469,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ C ) @ B )
=> ( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ C @ A ) @ B )
=> ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ A ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(228,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__sup @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Lattices_Osemilattice__sup__class_Osup @ D @ C @ B ) @ A )
=> ~ ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ A )
=> ~ ( c_Orderings_Oord__class_Oless__eq @ D @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__supE) ).
thf(1190,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__sup @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Lattices_Osemilattice__sup__class_Osup @ D @ C @ B ) @ A )
=> ~ ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ A )
=> ~ ( c_Orderings_Oord__class_Oless__eq @ D @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(491,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ B ) @ A )
=> ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ B ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl_Or__into__trancl) ).
thf(2341,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ B ) @ A )
=> ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ B ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).
thf(329,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( c_member @ B @ C @ A )
=> ( c_member @ B @ D @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__mem__trans) ).
thf(1633,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( c_member @ B @ C @ A )
=> ( c_member @ B @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(476,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ D @ C @ ( c_Set_Oinsert @ D @ B @ A ) )
<=> ( ( C = B )
| ( c_member @ D @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__iff) ).
thf(2263,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_member @ D @ C @ ( c_Set_Oinsert @ D @ B @ A ) )
=> ( ( C = B )
| ( c_member @ D @ C @ A ) ) )
& ( ( ( C = B )
| ( c_member @ D @ C @ A ) )
=> ( c_member @ D @ C @ ( c_Set_Oinsert @ D @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).
thf(356,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( c_Equiv__Relations_Oequiv @ G @ F @ E )
=> ( ( c_member @ ( tc_fun @ G @ tc_HOL_Obool ) @ D @ ( c_Equiv__Relations_Oquotient @ G @ F @ E ) )
=> ( ( c_member @ ( tc_fun @ G @ tc_HOL_Obool ) @ C @ ( c_Equiv__Relations_Oquotient @ G @ F @ E ) )
=> ( ( c_member @ G @ B @ D )
=> ( ( c_member @ G @ A @ C )
=> ( ( c_member @ ( tc_prod @ G @ G ) @ ( c_Product__Type_OPair @ G @ G @ B @ A ) @ E )
=> ( D = C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_quotient__eqI) ).
thf(1729,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( c_Equiv__Relations_Oequiv @ G @ F @ E )
=> ( ( c_member @ ( tc_fun @ G @ tc_HOL_Obool ) @ D @ ( c_Equiv__Relations_Oquotient @ G @ F @ E ) )
=> ( ( c_member @ ( tc_fun @ G @ tc_HOL_Obool ) @ C @ ( c_Equiv__Relations_Oquotient @ G @ F @ E ) )
=> ( ( c_member @ G @ B @ D )
=> ( ( c_member @ G @ A @ C )
=> ( ( c_member @ ( tc_prod @ G @ G ) @ ( c_Product__Type_OPair @ G @ G @ B @ A ) @ E )
=> ( D = C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(47,axiom,
! [A: $i,B: $i] :
( ( c_Relation_ORange @ B @ B @ ( c_Transitive__Closure_Otrancl @ B @ A ) )
= ( c_Relation_ORange @ B @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__range) ).
thf(628,plain,
! [A: $i,B: $i] :
( ( c_Relation_ORange @ B @ B @ ( c_Transitive__Closure_Otrancl @ B @ A ) )
= ( c_Relation_ORange @ B @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(389,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( c_Product__Type_Ocurry @ E @ D @ tc_HOL_Obool @ C @ B @ A ) )
=> ( hBOOL @ ( hAPP @ C @ ( c_Product__Type_OPair @ E @ D @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_curryD) ).
thf(1899,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( c_Product__Type_Ocurry @ E @ D @ tc_HOL_Obool @ C @ B @ A ) )
=> ( hBOOL @ ( hAPP @ C @ ( c_Product__Type_OPair @ E @ D @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(131,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Relation_Oconverse @ C @ B @ ( c_Relation_Oconverse @ B @ C @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converse__converse) ).
thf(893,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Relation_Oconverse @ C @ B @ ( c_Relation_Oconverse @ B @ C @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(197,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Wellfounded_Owf @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ A @ ( c_Relation_OImage @ C @ C @ B @ A ) )
=> ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wfE__pf) ).
thf(1083,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Wellfounded_Owf @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ A @ ( c_Relation_OImage @ C @ C @ B @ A ) )
=> ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(149,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Odistrib__lattice @ D )
=> ( ( c_Lattices_Osemilattice__sup__class_Osup @ D @ C @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D @ B @ A ) )
= ( c_Lattices_Osemilattice__inf__class_Oinf @ D @ ( c_Lattices_Osemilattice__sup__class_Osup @ D @ C @ B ) @ ( c_Lattices_Osemilattice__sup__class_Osup @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__inf__distrib1) ).
thf(941,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Odistrib__lattice @ D )
=> ( ( c_Lattices_Osemilattice__sup__class_Osup @ D @ C @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D @ B @ A ) )
= ( c_Lattices_Osemilattice__inf__class_Oinf @ D @ ( c_Lattices_Osemilattice__sup__class_Osup @ D @ C @ B ) @ ( c_Lattices_Osemilattice__sup__class_Osup @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(396,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( c_member @ ( tc_prod @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) @ ( c_Product__Type_OPair @ H @ G @ F @ E ) @ ( c_Product__Type_OPair @ H @ G @ D @ C ) ) @ ( c_Wellfounded_Olex__prod @ H @ G @ B @ A ) )
<=> ( ( c_member @ ( tc_prod @ H @ H ) @ ( c_Product__Type_OPair @ H @ H @ F @ D ) @ B )
| ( ( F = D )
& ( c_member @ ( tc_prod @ G @ G ) @ ( c_Product__Type_OPair @ G @ G @ E @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__lex__prod) ).
thf(1950,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( ( c_member @ ( tc_prod @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) @ ( c_Product__Type_OPair @ H @ G @ F @ E ) @ ( c_Product__Type_OPair @ H @ G @ D @ C ) ) @ ( c_Wellfounded_Olex__prod @ H @ G @ B @ A ) )
=> ( ( c_member @ ( tc_prod @ H @ H ) @ ( c_Product__Type_OPair @ H @ H @ F @ D ) @ B )
| ( ( F = D )
& ( c_member @ ( tc_prod @ G @ G ) @ ( c_Product__Type_OPair @ G @ G @ E @ C ) @ A ) ) ) )
& ( ( ( c_member @ ( tc_prod @ H @ H ) @ ( c_Product__Type_OPair @ H @ H @ F @ D ) @ B )
| ( ( F = D )
& ( c_member @ ( tc_prod @ G @ G ) @ ( c_Product__Type_OPair @ G @ G @ E @ C ) @ A ) ) )
=> ( c_member @ ( tc_prod @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) @ ( c_Product__Type_OPair @ H @ G @ F @ E ) @ ( c_Product__Type_OPair @ H @ G @ D @ C ) ) @ ( c_Wellfounded_Olex__prod @ H @ G @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(307,axiom,
! [A: $i,B: $i,C: $i,D: $i] : ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Relation_ODomain @ D @ C @ B ) @ ( c_Relation_ODomain @ D @ C @ A ) ) @ ( c_Relation_ODomain @ D @ C @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Domain__Diff__subset) ).
thf(1554,plain,
! [A: $i,B: $i,C: $i,D: $i] : ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Relation_ODomain @ D @ C @ B ) @ ( c_Relation_ODomain @ D @ C @ A ) ) @ ( c_Relation_ODomain @ D @ C @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(344,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ D @ C ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) @ D @ A )
=> ( hBOOL @ ( hAPP @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__predicate1D) ).
thf(1686,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ D @ C ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) @ D @ A )
=> ( hBOOL @ ( hAPP @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(309,axiom,
! [A: $i,B: $i] :
( ( c_Wellfounded_Oacyclic @ B @ A )
<=> ! [C: $i] :
~ ( c_member @ ( tc_prod @ B @ B ) @ ( c_Product__Type_OPair @ B @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acyclic__def) ).
thf(1559,plain,
! [A: $i,B: $i] :
( ( ( c_Wellfounded_Oacyclic @ B @ A )
=> ! [C: $i] :
~ ( c_member @ ( tc_prod @ B @ B ) @ ( c_Product__Type_OPair @ B @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ B @ A ) ) )
& ( ! [C: $i] :
~ ( c_member @ ( tc_prod @ B @ B ) @ ( c_Product__Type_OPair @ B @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ B @ A ) )
=> ( c_Wellfounded_Oacyclic @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(204,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( c_member @ D @ C @ B )
=> ( ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ ( c_Set_Oinsert @ D @ C @ A ) )
= ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__insert__right__if0) ).
thf(1105,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( c_member @ D @ C @ B )
=> ( ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ ( c_Set_Oinsert @ D @ C @ A ) )
= ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(218,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ A @ C ) )
= ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B ) @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) ) @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__Int__crazy) ).
thf(1158,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ A @ C ) )
= ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B ) @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) ) @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(394,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Wellfounded_Owf @ C @ B )
=> ~ ( c_member @ ( tc_prod @ C @ C ) @ ( c_Product__Type_OPair @ C @ C @ A @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__not__refl) ).
thf(1924,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Wellfounded_Owf @ C @ B )
=> ~ ( c_member @ ( tc_prod @ C @ C ) @ ( c_Product__Type_OPair @ C @ C @ A @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(81,axiom,
! [A: $i,B: $i] :
( ( class_Lattices_Olattice @ B )
=> ( class_Lattices_Osemilattice__sup @ ( tc_fun @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Lattices_Osemilattice__sup) ).
thf(730,plain,
! [A: $i,B: $i] :
( ( class_Lattices_Olattice @ B )
=> ( class_Lattices_Osemilattice__sup @ ( tc_fun @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(300,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ C ) @ B )
=> ( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ C @ A ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) )
=> ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ A ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__into__trancl2) ).
thf(1522,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ C ) @ B )
=> ( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ C @ A ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) )
=> ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ A ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(504,axiom,
! [A: $i,B: $i] :
( ( c_Wellfounded_Owf @ B @ A )
<=> ! [C: $i] : ( c_member @ B @ C @ ( c_Wellfounded_Oacc @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__acc__iff) ).
thf(2395,plain,
! [A: $i,B: $i] :
( ( ( c_Wellfounded_Owf @ B @ A )
=> ! [C: $i] : ( c_member @ B @ C @ ( c_Wellfounded_Oacc @ B @ A ) ) )
& ( ! [C: $i] : ( c_member @ B @ C @ ( c_Wellfounded_Oacc @ B @ A ) )
=> ( c_Wellfounded_Owf @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).
thf(325,axiom,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] : ( hBOOL @ ( hAPP @ C @ D ) )
<=> ! [D: $i,E: $i] : ( hBOOL @ ( hAPP @ C @ ( c_Product__Type_OPair @ B @ A @ D @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__paired__All) ).
thf(1618,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] : ( hBOOL @ ( hAPP @ C @ D ) )
=> ! [D: $i,E: $i] : ( hBOOL @ ( hAPP @ C @ ( c_Product__Type_OPair @ B @ A @ D @ E ) ) ) )
& ( ! [D: $i,E: $i] : ( hBOOL @ ( hAPP @ C @ ( c_Product__Type_OPair @ B @ A @ D @ E ) ) )
=> ! [D: $i] : ( hBOOL @ ( hAPP @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(233,axiom,
! [A: $i,B: $i] : ( c_Relation_Orefl__on @ B @ A @ ( c_Relation_OId__on @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_refl__on__Id__on) ).
thf(1205,plain,
! [A: $i,B: $i] : ( c_Relation_Orefl__on @ B @ A @ ( c_Relation_OId__on @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(436,axiom,
( ( v_a____ = v_b_H____ )
& ( v_b____ = v_a_H____ ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__096a_A_061_Ab_H_A_G_Ab_A_061_Aa_H_096) ).
thf(2114,plain,
( ( v_a____ = v_b_H____ )
& ( v_b____ = v_a_H____ ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(364,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_member @ E @ D @ ( c_Relation_OImage @ C @ E @ B @ ( c_Set_Oinsert @ C @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) )
<=> ( c_member @ ( tc_prod @ C @ E ) @ ( c_Product__Type_OPair @ C @ E @ A @ D ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__singleton__iff) ).
thf(1793,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( c_member @ E @ D @ ( c_Relation_OImage @ C @ E @ B @ ( c_Set_Oinsert @ C @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) )
=> ( c_member @ ( tc_prod @ C @ E ) @ ( c_Product__Type_OPair @ C @ E @ A @ D ) @ B ) )
& ( ( c_member @ ( tc_prod @ C @ E ) @ ( c_Product__Type_OPair @ C @ E @ A @ D ) @ B )
=> ( c_member @ E @ D @ ( c_Relation_OImage @ C @ E @ B @ ( c_Set_Oinsert @ C @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(62,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__inf @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__infI1) ).
thf(677,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__inf @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(36,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Olattice @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C @ B @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__ord_I1_J) ).
thf(597,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Olattice @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C @ B @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(183,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] : ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( c_Relation_OImage @ D @ E @ C @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( c_Relation_OImage @ D @ E @ C @ B ) @ ( c_Relation_OImage @ D @ E @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__Int__subset) ).
thf(1041,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] : ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( c_Relation_OImage @ D @ E @ C @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( c_Relation_OImage @ D @ E @ C @ B ) @ ( c_Relation_OImage @ D @ E @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(2115,plain,
v_b____ = v_a_H____,
inference(cnf,[status(esa)],[2114]) ).
thf(2117,plain,
v_a_H____ = v_b____,
inference(lifteq,[status(thm)],[2115]) ).
thf(434,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ B ) @ ( c_Transitive__Closure_Ortrancl @ D @ ( c_Relation_Oconverse @ D @ D @ A ) ) )
=> ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ B @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__converseD) ).
thf(2104,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ B ) @ ( c_Transitive__Closure_Ortrancl @ D @ ( c_Relation_Oconverse @ D @ D @ A ) ) )
=> ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ B @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(125,axiom,
! [A: $i,B: $i] :
( ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ B @ tc_HOL_Obool ) @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__absorb) ).
thf(878,plain,
! [A: $i,B: $i] :
( ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ B @ tc_HOL_Obool ) @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(55,axiom,
class_Orderings_Oord @ tc_HOL_Obool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Oord) ).
thf(655,plain,
class_Orderings_Oord @ tc_HOL_Obool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(10,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__sup @ D )
=> ( ( c_Lattices_Osemilattice__sup__class_Osup @ D @ ( c_Lattices_Osemilattice__sup__class_Osup @ D @ C @ B ) @ A )
= ( c_Lattices_Osemilattice__sup__class_Osup @ D @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ D @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__assoc) ).
thf(533,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__sup @ D )
=> ( ( c_Lattices_Osemilattice__sup__class_Osup @ D @ ( c_Lattices_Osemilattice__sup__class_Osup @ D @ C @ B ) @ A )
= ( c_Lattices_Osemilattice__sup__class_Osup @ D @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ D @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(17,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__inf @ C )
=> ( ( c_Lattices_Osemilattice__inf__class_Oinf @ C @ B @ A )
= ( c_Lattices_Osemilattice__inf__class_Oinf @ C @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf_Ocommute) ).
thf(550,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__inf @ C )
=> ( ( c_Lattices_Osemilattice__inf__class_Oinf @ C @ B @ A )
= ( c_Lattices_Osemilattice__inf__class_Oinf @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(220,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ A @ ( c_Transitive__Closure_Ortrancl @ C @ B ) )
=> ( ( c_Transitive__Closure_Ortrancl @ C @ A )
= ( c_Transitive__Closure_Ortrancl @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__subset) ).
thf(1164,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ A @ ( c_Transitive__Closure_Ortrancl @ C @ B ) )
=> ( ( c_Transitive__Closure_Ortrancl @ C @ A )
= ( c_Transitive__Closure_Ortrancl @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(248,axiom,
! [A: $i,B: $i] :
( ( c_Wellfounded_Oacyclic @ B @ A )
=> ( c_Relation_Oantisym @ B @ ( c_Transitive__Closure_Ortrancl @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acyclic__impl__antisym__rtrancl) ).
thf(1275,plain,
! [A: $i,B: $i] :
( ( c_Wellfounded_Oacyclic @ B @ A )
=> ( c_Relation_Oantisym @ B @ ( c_Transitive__Closure_Ortrancl @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(382,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Order__Relation_Owell__order__on @ C @ B @ A )
<=> ( ( c_Order__Relation_Olinear__order__on @ C @ B @ A )
& ( c_Wellfounded_Owf @ C @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ A @ ( c_Relation_OId @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_well__order__on__def) ).
thf(1872,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Order__Relation_Owell__order__on @ C @ B @ A )
=> ( ( c_Order__Relation_Olinear__order__on @ C @ B @ A )
& ( c_Wellfounded_Owf @ C @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ A @ ( c_Relation_OId @ C ) ) ) ) )
& ( ( ( c_Order__Relation_Olinear__order__on @ C @ B @ A )
& ( c_Wellfounded_Owf @ C @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ A @ ( c_Relation_OId @ C ) ) ) )
=> ( c_Order__Relation_Owell__order__on @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(106,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Olattice @ C )
=> ( ( c_Lattices_Osemilattice__inf__class_Oinf @ C @ B @ A )
= ( c_Lattices_Osemilattice__inf__class_Oinf @ C @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__aci_I1_J) ).
thf(814,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Olattice @ C )
=> ( ( c_Lattices_Osemilattice__inf__class_Oinf @ C @ B @ A )
= ( c_Lattices_Osemilattice__inf__class_Oinf @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(405,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( c_Equiv__Relations_Oequiv @ H @ G @ F )
=> ( ( c_Equiv__Relations_Ocongruent2 @ H @ E @ D @ F @ C @ B )
=> ( ( c_member @ H @ A @ G )
=> ( c_Equiv__Relations_Ocongruent @ E @ D @ C @ ( hAPP @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_congruent2__implies__congruent) ).
thf(1988,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( c_Equiv__Relations_Oequiv @ H @ G @ F )
=> ( ( c_Equiv__Relations_Ocongruent2 @ H @ E @ D @ F @ C @ B )
=> ( ( c_member @ H @ A @ G )
=> ( c_Equiv__Relations_Ocongruent @ E @ D @ C @ ( hAPP @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(87,axiom,
! [A: $i,B: $i] :
( ( c_Transitive__Closure_Ortrancl @ B @ ( c_Transitive__Closure_Otrancl @ B @ A ) )
= ( c_Transitive__Closure_Ortrancl @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__rtrancl__absorb) ).
thf(747,plain,
! [A: $i,B: $i] :
( ( c_Transitive__Closure_Ortrancl @ B @ ( c_Transitive__Closure_Otrancl @ B @ A ) )
= ( c_Transitive__Closure_Ortrancl @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(268,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( c_member @ B @ D @ A )
<=> ( c_member @ B @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eqelem__imp__iff) ).
thf(1354,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( ( c_member @ B @ D @ A )
=> ( c_member @ B @ C @ A ) )
& ( ( c_member @ B @ C @ A )
=> ( c_member @ B @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(146,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oord @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( ( B = A )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ord__le__eq__trans) ).
thf(930,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oord @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( ( B = A )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(61,axiom,
! [A: $i,B: $i,C: $i] :
( ( C = B )
=> ~ ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ A @ tc_HOL_Obool ) @ C @ B )
=> ~ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ A @ tc_HOL_Obool ) @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equalityE) ).
thf(670,plain,
! [A: $i,B: $i,C: $i] :
( ( C = B )
=> ~ ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ A @ tc_HOL_Obool ) @ C @ B )
=> ~ ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ A @ tc_HOL_Obool ) @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(296,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_member @ ( tc_prod @ E @ D ) @ ( c_Product__Type_OPair @ E @ D @ C @ B ) @ ( c_Relation_Oconverse @ D @ E @ A ) )
<=> ( c_member @ ( tc_prod @ D @ E ) @ ( c_Product__Type_OPair @ D @ E @ B @ C ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converse__iff) ).
thf(1497,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( c_member @ ( tc_prod @ E @ D ) @ ( c_Product__Type_OPair @ E @ D @ C @ B ) @ ( c_Relation_Oconverse @ D @ E @ A ) )
=> ( c_member @ ( tc_prod @ D @ E ) @ ( c_Product__Type_OPair @ D @ E @ B @ C ) @ A ) )
& ( ( c_member @ ( tc_prod @ D @ E ) @ ( c_Product__Type_OPair @ D @ E @ B @ C ) @ A )
=> ( c_member @ ( tc_prod @ E @ D ) @ ( c_Product__Type_OPair @ E @ D @ C @ B ) @ ( c_Relation_Oconverse @ D @ E @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(352,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D != C )
=> ( ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ B @ c_Arrow__Order__Mirabelle_OProf )
=> ( ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ A @ c_Arrow__Order__Mirabelle_OProf )
=> ( ! [E: $i] :
( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ D @ C ) @ ( hAPP @ B @ E ) )
<=> ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ C @ D ) @ ( hAPP @ A @ E ) ) )
=> ( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ D @ C ) @ ( hAPP @ v_F @ B ) )
<=> ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ C @ D ) @ ( hAPP @ v_F @ A ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__C3_C) ).
thf(1705,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D != C )
=> ( ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ B @ c_Arrow__Order__Mirabelle_OProf )
=> ( ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ A @ c_Arrow__Order__Mirabelle_OProf )
=> ( ! [E: $i] :
( ( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ D @ C ) @ ( hAPP @ B @ E ) )
=> ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ C @ D ) @ ( hAPP @ A @ E ) ) )
& ( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ C @ D ) @ ( hAPP @ A @ E ) )
=> ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ D @ C ) @ ( hAPP @ B @ E ) ) ) )
=> ( ( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ D @ C ) @ ( hAPP @ v_F @ B ) )
=> ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ C @ D ) @ ( hAPP @ v_F @ A ) ) )
& ( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ C @ D ) @ ( hAPP @ v_F @ A ) )
=> ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ D @ C ) @ ( hAPP @ v_F @ B ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(196,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B ) @ A )
<=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__subset__conv) ).
thf(1078,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B ) @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(284,axiom,
! [A: $i,B: $i,C: $i,D: $i] : ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Relation_ORange @ C @ D @ B ) @ ( c_Relation_ORange @ C @ D @ A ) ) @ ( c_Relation_ORange @ C @ D @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_HOL_Obool ) @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Range__Diff__subset) ).
thf(1426,plain,
! [A: $i,B: $i,C: $i,D: $i] : ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Relation_ORange @ C @ D @ B ) @ ( c_Relation_ORange @ C @ D @ A ) ) @ ( c_Relation_ORange @ C @ D @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_HOL_Obool ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(230,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Relation_ODomain @ C @ B @ ( c_Relation_Oconverse @ B @ C @ A ) )
= ( c_Relation_ORange @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Domain__converse) ).
thf(1196,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Relation_ODomain @ C @ B @ ( c_Relation_Oconverse @ B @ C @ A ) )
= ( c_Relation_ORange @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(133,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ D @ C @ B )
=> ( c_member @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Relation_OImage @ D @ D @ A @ ( c_Set_Oinsert @ D @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) @ ( c_Equiv__Relations_Oquotient @ D @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_quotientI) ).
thf(898,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ D @ C @ B )
=> ( c_member @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Relation_OImage @ D @ D @ A @ ( c_Set_Oinsert @ D @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) @ ( c_Equiv__Relations_Oquotient @ D @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(494,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E != D )
=> ( ( D != C )
=> ( ( E != C )
=> ( ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ B @ c_Arrow__Order__Mirabelle_OProf )
=> ( ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ A @ c_Arrow__Order__Mirabelle_OProf )
=> ( ! [F: $i] :
( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ E @ D ) @ ( hAPP @ B @ F ) )
<=> ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ D @ C ) @ ( hAPP @ A @ F ) ) )
=> ( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ E @ D ) @ ( hAPP @ v_F @ B ) )
<=> ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ D @ C ) @ ( hAPP @ v_F @ A ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__C4_C) ).
thf(2348,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E != D )
=> ( ( D != C )
=> ( ( E != C )
=> ( ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ B @ c_Arrow__Order__Mirabelle_OProf )
=> ( ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ A @ c_Arrow__Order__Mirabelle_OProf )
=> ( ! [F: $i] :
( ( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ E @ D ) @ ( hAPP @ B @ F ) )
=> ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ D @ C ) @ ( hAPP @ A @ F ) ) )
& ( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ D @ C ) @ ( hAPP @ A @ F ) )
=> ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ E @ D ) @ ( hAPP @ B @ F ) ) ) )
=> ( ( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ E @ D ) @ ( hAPP @ v_F @ B ) )
=> ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ D @ C ) @ ( hAPP @ v_F @ A ) ) )
& ( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ D @ C ) @ ( hAPP @ v_F @ A ) )
=> ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ E @ D ) @ ( hAPP @ v_F @ B ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).
thf(425,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Wellfounded_Owf @ C @ B )
=> ( c_Wellfounded_Owf @ C @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__Int2) ).
thf(2046,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Wellfounded_Owf @ C @ B )
=> ( c_Wellfounded_Owf @ C @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(393,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( c_Recdef_Ocut @ F @ E @ D @ C @ B )
= ( c_Recdef_Ocut @ F @ E @ A @ C @ B ) )
<=> ! [G: $i] :
( ( c_member @ ( tc_prod @ F @ F ) @ ( c_Product__Type_OPair @ F @ F @ G @ B ) @ C )
=> ( ( hAPP @ D @ G )
= ( hAPP @ A @ G ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_cuts__eq) ).
thf(1914,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ( c_Recdef_Ocut @ F @ E @ D @ C @ B )
= ( c_Recdef_Ocut @ F @ E @ A @ C @ B ) )
=> ! [G: $i] :
( ( c_member @ ( tc_prod @ F @ F ) @ ( c_Product__Type_OPair @ F @ F @ G @ B ) @ C )
=> ( ( hAPP @ D @ G )
= ( hAPP @ A @ G ) ) ) )
& ( ! [G: $i] :
( ( c_member @ ( tc_prod @ F @ F ) @ ( c_Product__Type_OPair @ F @ F @ G @ B ) @ C )
=> ( ( hAPP @ D @ G )
= ( hAPP @ A @ G ) ) )
=> ( ( c_Recdef_Ocut @ F @ E @ D @ C @ B )
= ( c_Recdef_Ocut @ F @ E @ A @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(361,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ D @ C @ ( c_Relation_ODomain @ D @ B @ A ) )
=> ~ ! [E: $i] :
~ ( c_member @ ( tc_prod @ D @ B ) @ ( c_Product__Type_OPair @ D @ B @ C @ E ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_DomainE) ).
thf(1782,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ D @ C @ ( c_Relation_ODomain @ D @ B @ A ) )
=> ~ ! [E: $i] :
~ ( c_member @ ( tc_prod @ D @ B ) @ ( c_Product__Type_OPair @ D @ B @ C @ E ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(98,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Order__Relation_Opartial__order__on @ C @ B @ A )
<=> ( ( c_Order__Relation_Opreorder__on @ C @ B @ A )
& ( c_Relation_Oantisym @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_partial__order__on__def) ).
thf(782,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Order__Relation_Opartial__order__on @ C @ B @ A )
=> ( ( c_Order__Relation_Opreorder__on @ C @ B @ A )
& ( c_Relation_Oantisym @ C @ A ) ) )
& ( ( ( c_Order__Relation_Opreorder__on @ C @ B @ A )
& ( c_Relation_Oantisym @ C @ A ) )
=> ( c_Order__Relation_Opartial__order__on @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(74,axiom,
! [A: $i,B: $i] :
( ( c_Wellfounded_Owf @ B @ A )
=> ( c_Wellfounded_Owf @ B @ ( c_Transitive__Closure_Otrancl @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__trancl) ).
thf(709,plain,
! [A: $i,B: $i] :
( ( c_Wellfounded_Owf @ B @ A )
=> ( c_Wellfounded_Owf @ B @ ( c_Transitive__Closure_Otrancl @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(416,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ B ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) )
=> ( ( C != B )
=> ~ ! [E: $i] :
( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ E ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) )
=> ~ ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ E @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtranclE) ).
thf(2020,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ B ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) )
=> ( ( C != B )
=> ~ ! [E: $i] :
( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ E ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) )
=> ~ ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ E @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(323,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ B ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) )
=> ? [E: $i] :
( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ E ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) )
& ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ E @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_tranclD2) ).
thf(1613,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ B ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) )
=> ? [E: $i] :
( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ E ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) )
& ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ E @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(354,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( c_Relation_OImage @ E @ E @ D @ ( c_Set_Oinsert @ E @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) )
= ( c_Relation_OImage @ E @ E @ D @ ( c_Set_Oinsert @ E @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) ) )
=> ( ( c_Equiv__Relations_Oequiv @ E @ A @ D )
=> ( ( c_member @ E @ B @ A )
=> ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ C @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__equiv__class) ).
thf(1724,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( c_Relation_OImage @ E @ E @ D @ ( c_Set_Oinsert @ E @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) )
= ( c_Relation_OImage @ E @ E @ D @ ( c_Set_Oinsert @ E @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) ) )
=> ( ( c_Equiv__Relations_Oequiv @ E @ A @ D )
=> ( ( c_member @ E @ B @ A )
=> ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ C @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(22,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__sup @ D )
=> ( ( c_Lattices_Osemilattice__sup__class_Osup @ D @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ D @ B @ A ) )
= ( c_Lattices_Osemilattice__sup__class_Osup @ D @ B @ ( c_Lattices_Osemilattice__sup__class_Osup @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup_Oleft__commute) ).
thf(565,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__sup @ D )
=> ( ( c_Lattices_Osemilattice__sup__class_Osup @ D @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ D @ B @ A ) )
= ( c_Lattices_Osemilattice__sup__class_Osup @ D @ B @ ( c_Lattices_Osemilattice__sup__class_Osup @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(326,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Wellfounded_Owf @ B @ D )
=> ! [E: $i] :
( ( hAPP @ ( c_Recdef_Owfrec @ B @ A @ D @ C ) @ E )
= ( hAPP @ ( hAPP @ C @ ( c_Recdef_Ocut @ B @ A @ ( c_Recdef_Owfrec @ B @ A @ D @ C ) @ D @ E ) ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_tfl__wfrec) ).
thf(1623,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Wellfounded_Owf @ B @ D )
=> ! [E: $i] :
( ( hAPP @ ( c_Recdef_Owfrec @ B @ A @ D @ C ) @ E )
= ( hAPP @ ( hAPP @ C @ ( c_Recdef_Ocut @ B @ A @ ( c_Recdef_Owfrec @ B @ A @ D @ C ) @ D @ E ) ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(110,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__sup @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Lattices_Osemilattice__sup__class_Osup @ C @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__ge2) ).
thf(829,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__sup @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Lattices_Osemilattice__sup__class_Osup @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(202,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A )
<=> ( ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__Un__eq) ).
thf(1095,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A )
=> ( ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A )
= A ) )
& ( ( ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A )
= A )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(159,axiom,
! [A: $i,B: $i] :
( ( c_Transitive__Closure_Otrancl @ B @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ A @ ( c_Relation_OId @ B ) ) )
= ( c_Transitive__Closure_Ortrancl @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__reflcl) ).
thf(973,plain,
! [A: $i,B: $i] :
( ( c_Transitive__Closure_Otrancl @ B @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ A @ ( c_Relation_OId @ B ) ) )
= ( c_Transitive__Closure_Ortrancl @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(185,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) )
= ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__Un) ).
thf(1046,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) )
= ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(505,axiom,
! [A: $i,B: $i] :
~ ( c_member @ B @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_empty__iff) ).
thf(2400,plain,
! [A: $i,B: $i] :
~ ( c_member @ B @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).
thf(432,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_member @ ( tc_prod @ E @ D ) @ ( c_Product__Type_OPair @ E @ D @ C @ B ) @ A )
=> ( c_member @ ( tc_prod @ D @ E ) @ ( c_Product__Type_OPair @ D @ E @ B @ C ) @ ( c_Relation_Oconverse @ E @ D @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converseI) ).
thf(2067,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_member @ ( tc_prod @ E @ D ) @ ( c_Product__Type_OPair @ E @ D @ C @ B ) @ A )
=> ( c_member @ ( tc_prod @ D @ E ) @ ( c_Product__Type_OPair @ D @ E @ B @ C ) @ ( c_Relation_Oconverse @ E @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(244,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Set_Oinsert @ D @ C @ B ) @ ( c_Set_Oinsert @ D @ C @ A ) )
= ( c_Set_Oinsert @ D @ C @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__inter__insert) ).
thf(1265,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Set_Oinsert @ D @ C @ B ) @ ( c_Set_Oinsert @ D @ C @ A ) )
= ( c_Set_Oinsert @ D @ C @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(351,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_member @ ( tc_prod @ C @ C ) @ B @ A )
=> ( c_member @ ( tc_prod @ C @ C ) @ B @ ( c_Transitive__Closure_Ortrancl @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_r__into__rtrancl) ).
thf(1703,plain,
! [A: $i,B: $i,C: $i] :
( ( c_member @ ( tc_prod @ C @ C ) @ B @ A )
=> ( c_member @ ( tc_prod @ C @ C ) @ B @ ( c_Transitive__Closure_Ortrancl @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(25,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__inf @ C )
=> ( ( c_Lattices_Osemilattice__inf__class_Oinf @ C @ B @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C @ B @ A ) )
= ( c_Lattices_Osemilattice__inf__class_Oinf @ C @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__left__idem) ).
thf(570,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__inf @ C )
=> ( ( c_Lattices_Osemilattice__inf__class_Oinf @ C @ B @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C @ B @ A ) )
= ( c_Lattices_Osemilattice__inf__class_Oinf @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(404,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Order__Relation_Opreorder__on @ D @ ( c_Relation_OField @ D @ C ) @ C )
=> ( ( c_member @ D @ B @ ( c_Relation_OField @ D @ C ) )
=> ( ( c_member @ D @ A @ ( c_Relation_OField @ D @ C ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Relation_OImage @ D @ D @ C @ ( c_Set_Oinsert @ D @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) @ ( c_Relation_OImage @ D @ D @ C @ ( c_Set_Oinsert @ D @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) )
<=> ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ A @ B ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__Image1__Image1__iff) ).
thf(1985,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Order__Relation_Opreorder__on @ D @ ( c_Relation_OField @ D @ C ) @ C )
=> ( ( c_member @ D @ B @ ( c_Relation_OField @ D @ C ) )
=> ( ( c_member @ D @ A @ ( c_Relation_OField @ D @ C ) )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Relation_OImage @ D @ D @ C @ ( c_Set_Oinsert @ D @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) @ ( c_Relation_OImage @ D @ D @ C @ ( c_Set_Oinsert @ D @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) )
=> ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ A @ B ) @ C ) )
& ( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ A @ B ) @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Relation_OImage @ D @ D @ C @ ( c_Set_Oinsert @ D @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) @ ( c_Relation_OImage @ D @ D @ C @ ( c_Set_Oinsert @ D @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(422,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ ( tc_prod @ D @ D ) @ C @ ( c_Transitive__Closure_Otrancl @ D @ B ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ B @ A )
=> ( c_member @ ( tc_prod @ D @ D ) @ C @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__mono) ).
thf(2039,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ ( tc_prod @ D @ D ) @ C @ ( c_Transitive__Closure_Otrancl @ D @ B ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ B @ A )
=> ( c_member @ ( tc_prod @ D @ D ) @ C @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(336,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Relation_ORange @ E @ D @ ( c_Set_Oinsert @ ( tc_prod @ E @ D ) @ ( c_Product__Type_OPair @ E @ D @ C @ B ) @ A ) )
= ( c_Set_Oinsert @ D @ B @ ( c_Relation_ORange @ E @ D @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Range__insert) ).
thf(1660,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Relation_ORange @ E @ D @ ( c_Set_Oinsert @ ( tc_prod @ E @ D ) @ ( c_Product__Type_OPair @ E @ D @ C @ B ) @ A ) )
= ( c_Set_Oinsert @ D @ B @ ( c_Relation_ORange @ E @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(407,axiom,
c_Arrow__Order__Mirabelle_OIIA @ v_F,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_assms_I3_J) ).
thf(1992,plain,
c_Arrow__Order__Mirabelle_OIIA @ v_F,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(1,conjecture,
( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a____ @ v_b____ ) @ ( hAPP @ v_F @ v_P____ ) )
<=> ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a_H____ @ v_b_H____ ) @ ( hAPP @ v_F @ v_P_H____ ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a____ @ v_b____ ) @ ( hAPP @ v_F @ v_P____ ) )
<=> ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a_H____ @ v_b_H____ ) @ ( hAPP @ v_F @ v_P_H____ ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(512,plain,
~ ( ( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a____ @ v_b____ ) @ ( hAPP @ v_F @ v_P____ ) )
=> ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a_H____ @ v_b_H____ ) @ ( hAPP @ v_F @ v_P_H____ ) ) )
& ( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a_H____ @ v_b_H____ ) @ ( hAPP @ v_F @ v_P_H____ ) )
=> ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a____ @ v_b____ ) @ ( hAPP @ v_F @ v_P____ ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(513,plain,
( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a____ @ v_b____ ) @ ( hAPP @ v_F @ v_P____ ) )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a_H____ @ v_b_H____ ) @ ( hAPP @ v_F @ v_P_H____ ) ) ),
inference(cnf,[status(esa)],[512]) ).
thf(265,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
~ ( c_member @ B @ C @ A )
<=> ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_all__not__in__conv) ).
thf(1343,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
~ ( c_member @ B @ C @ A )
=> ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
& ( ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ! [C: $i] :
~ ( c_member @ B @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(1344,plain,
( ! [A: $i,B: $i] :
( ~ ? [C: $i] : ( c_member @ B @ C @ A )
=> ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
& ! [A: $i,B: $i] :
( ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ~ ? [C: $i] : ( c_member @ B @ C @ A ) ) ),
inference(miniscope,[status(thm)],[1343]) ).
thf(1345,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
| ~ ( c_member @ B @ C @ A ) ),
inference(cnf,[status(esa)],[1344]) ).
thf(1347,plain,
! [C: $i,B: $i,A: $i] :
( ( A
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
| ~ ( c_member @ B @ C @ A ) ),
inference(lifteq,[status(thm)],[1345]) ).
thf(1348,plain,
! [B: $i,A: $i] :
~ ( c_member @ A @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) ),
inference(simp,[status(thm)],[1347]) ).
thf(2455,plain,
! [B: $i,A: $i] :
( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a____ @ v_b____ ) @ ( hAPP @ v_F @ v_P____ ) )
| ( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a_H____ @ v_b_H____ ) @ ( hAPP @ v_F @ v_P_H____ ) )
!= ( c_member @ A @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[513,1348]) ).
thf(2456,plain,
! [B: $i,A: $i] :
( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a____ @ v_b____ ) @ ( hAPP @ v_F @ v_P____ ) )
| ( ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt )
!= A )
| ( ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a_H____ @ v_b_H____ )
!= B )
| ( ( hAPP @ v_F @ v_P_H____ )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) ),
inference(simp,[status(thm)],[2455]) ).
thf(2457,plain,
( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a____ @ v_b____ ) @ ( hAPP @ v_F @ v_P____ ) )
| ( ( hAPP @ v_F @ v_P_H____ )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) ),
inference(simp,[status(thm)],[2456]) ).
thf(2459,plain,
! [B: $i,A: $i] :
( ( ( hAPP @ v_F @ v_P_H____ )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) )
| ( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a____ @ v_b____ ) @ ( hAPP @ v_F @ v_P____ ) )
!= ( c_member @ A @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[2457,1348]) ).
thf(2463,plain,
! [B: $i,A: $i] :
( ( ( hAPP @ v_F @ v_P_H____ )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) )
| ( ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt )
!= A )
| ( ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a____ @ v_b____ )
!= B )
| ( ( hAPP @ v_F @ v_P____ )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) ) ),
inference(simp,[status(thm)],[2459]) ).
thf(2466,plain,
( ( ( hAPP @ v_F @ v_P_H____ )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) )
| ( ( hAPP @ v_F @ v_P____ )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) ),
inference(simp,[status(thm)],[2463]) ).
thf(151,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__inf @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C @ B @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__le2) ).
thf(949,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__inf @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__inf @ D )
=> ( ( c_Lattices_Osemilattice__inf__class_Oinf @ D @ C @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D @ B @ A ) )
= ( c_Lattices_Osemilattice__inf__class_Oinf @ D @ B @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf_Oleft__commute) ).
thf(542,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__inf @ D )
=> ( ( c_Lattices_Osemilattice__inf__class_Oinf @ D @ C @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D @ B @ A ) )
= ( c_Lattices_Osemilattice__inf__class_Oinf @ D @ B @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(263,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Relation_Osingle__valued @ C @ B @ A )
<=> ! [D: $i,E: $i] :
( ( c_member @ ( tc_prod @ C @ B ) @ ( c_Product__Type_OPair @ C @ B @ D @ E ) @ A )
=> ! [F: $i] :
( ( c_member @ ( tc_prod @ C @ B ) @ ( c_Product__Type_OPair @ C @ B @ D @ F ) @ A )
=> ( E = F ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_single__valued__def) ).
thf(1330,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Relation_Osingle__valued @ C @ B @ A )
=> ! [D: $i,E: $i] :
( ( c_member @ ( tc_prod @ C @ B ) @ ( c_Product__Type_OPair @ C @ B @ D @ E ) @ A )
=> ! [F: $i] :
( ( c_member @ ( tc_prod @ C @ B ) @ ( c_Product__Type_OPair @ C @ B @ D @ F ) @ A )
=> ( E = F ) ) ) )
& ( ! [D: $i,E: $i] :
( ( c_member @ ( tc_prod @ C @ B ) @ ( c_Product__Type_OPair @ C @ B @ D @ E ) @ A )
=> ! [F: $i] :
( ( c_member @ ( tc_prod @ C @ B ) @ ( c_Product__Type_OPair @ C @ B @ D @ F ) @ A )
=> ( E = F ) ) )
=> ( c_Relation_Osingle__valued @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(378,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_member @ ( tc_prod @ E @ D ) @ ( c_Product__Type_OPair @ E @ D @ C @ B ) @ A )
=> ( c_member @ E @ C @ ( c_Relation_ODomain @ E @ D @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_DomainI) ).
thf(1860,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_member @ ( tc_prod @ E @ D ) @ ( c_Product__Type_OPair @ E @ D @ C @ B ) @ A )
=> ( c_member @ E @ C @ ( c_Relation_ODomain @ E @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(478,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Relation_ORange @ D @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ B @ A ) )
= ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( c_Relation_ORange @ D @ C @ B ) @ ( c_Relation_ORange @ D @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Range__Un__eq) ).
thf(2274,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Relation_ORange @ D @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ B @ A ) )
= ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( c_Relation_ORange @ D @ C @ B ) @ ( c_Relation_ORange @ D @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).
thf(141,axiom,
! [A: $i,B: $i] :
( ( c_Relation_OField @ B @ A )
= ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( c_Relation_ODomain @ B @ B @ A ) @ ( c_Relation_ORange @ B @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Field__def) ).
thf(917,plain,
! [A: $i,B: $i] :
( ( c_Relation_OField @ B @ A )
= ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( c_Relation_ODomain @ B @ B @ A ) @ ( c_Relation_ORange @ B @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(372,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Recdef_Owfrec__rel @ F @ E @ D @ C @ B @ ( hAPP @ ( hAPP @ C @ A ) @ B ) )
<=> ? [G: $i] :
( ( ( hAPP @ ( hAPP @ C @ A ) @ B )
= ( hAPP @ ( hAPP @ C @ G ) @ B ) )
& ! [H: $i] :
( ( c_member @ ( tc_prod @ F @ F ) @ ( c_Product__Type_OPair @ F @ F @ H @ B ) @ D )
=> ( c_Recdef_Owfrec__rel @ F @ E @ D @ C @ H @ ( hAPP @ G @ H ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wfrec__rel_Oequations) ).
thf(1832,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( c_Recdef_Owfrec__rel @ F @ E @ D @ C @ B @ ( hAPP @ ( hAPP @ C @ A ) @ B ) )
=> ? [G: $i] :
( ( ( hAPP @ ( hAPP @ C @ A ) @ B )
= ( hAPP @ ( hAPP @ C @ G ) @ B ) )
& ! [H: $i] :
( ( c_member @ ( tc_prod @ F @ F ) @ ( c_Product__Type_OPair @ F @ F @ H @ B ) @ D )
=> ( c_Recdef_Owfrec__rel @ F @ E @ D @ C @ H @ ( hAPP @ G @ H ) ) ) ) )
& ( ? [G: $i] :
( ( ( hAPP @ ( hAPP @ C @ A ) @ B )
= ( hAPP @ ( hAPP @ C @ G ) @ B ) )
& ! [H: $i] :
( ( c_member @ ( tc_prod @ F @ F ) @ ( c_Product__Type_OPair @ F @ F @ H @ B ) @ D )
=> ( c_Recdef_Owfrec__rel @ F @ E @ D @ C @ H @ ( hAPP @ G @ H ) ) ) )
=> ( c_Recdef_Owfrec__rel @ F @ E @ D @ C @ B @ ( hAPP @ ( hAPP @ C @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(147,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Olattice @ C )
=> ( ( c_Lattices_Osemilattice__sup__class_Osup @ C @ B @ ( c_Lattices_Osemilattice__sup__class_Osup @ C @ B @ A ) )
= ( c_Lattices_Osemilattice__sup__class_Osup @ C @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__aci_I8_J) ).
thf(934,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Olattice @ C )
=> ( ( c_Lattices_Osemilattice__sup__class_Osup @ C @ B @ ( c_Lattices_Osemilattice__sup__class_Osup @ C @ B @ A ) )
= ( c_Lattices_Osemilattice__sup__class_Osup @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(189,axiom,
! [A: $i,B: $i] :
( ( class_Lattices_Olattice @ B )
=> ( class_Lattices_Osemilattice__inf @ ( tc_fun @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Lattices_Osemilattice__inf) ).
thf(1059,plain,
! [A: $i,B: $i] :
( ( class_Lattices_Olattice @ B )
=> ( class_Lattices_Osemilattice__inf @ ( tc_fun @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(213,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Obounded__lattice__bot @ C )
=> ( ( ( c_Lattices_Osemilattice__sup__class_Osup @ C @ B @ A )
= ( c_Orderings_Obot__class_Obot @ C ) )
<=> ( ( B
= ( c_Orderings_Obot__class_Obot @ C ) )
& ( A
= ( c_Orderings_Obot__class_Obot @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__eq__bot__iff) ).
thf(1132,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Obounded__lattice__bot @ C )
=> ( ( ( ( c_Lattices_Osemilattice__sup__class_Osup @ C @ B @ A )
= ( c_Orderings_Obot__class_Obot @ C ) )
=> ( ( B
= ( c_Orderings_Obot__class_Obot @ C ) )
& ( A
= ( c_Orderings_Obot__class_Obot @ C ) ) ) )
& ( ( ( B
= ( c_Orderings_Obot__class_Obot @ C ) )
& ( A
= ( c_Orderings_Obot__class_Obot @ C ) ) )
=> ( ( c_Lattices_Osemilattice__sup__class_Osup @ C @ B @ A )
= ( c_Orderings_Obot__class_Obot @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(509,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Relation_OField @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ B @ A ) )
= ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( c_Relation_OField @ C @ B ) @ ( c_Relation_OField @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Field__Un) ).
thf(2420,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Relation_OField @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ B @ A ) )
= ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( c_Relation_OField @ C @ B ) @ ( c_Relation_OField @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).
thf(107,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_member @ D @ C @ B )
=> ( ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Set_Oinsert @ D @ C @ A ) @ B )
= ( c_Set_Oinsert @ D @ C @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ A @ B ) ) ) )
& ( ~ ( c_member @ D @ C @ B )
=> ( ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Set_Oinsert @ D @ C @ A ) @ B )
= ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__insert__left) ).
thf(817,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_member @ D @ C @ B )
=> ( ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Set_Oinsert @ D @ C @ A ) @ B )
= ( c_Set_Oinsert @ D @ C @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ A @ B ) ) ) )
& ( ~ ( c_member @ D @ C @ B )
=> ( ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Set_Oinsert @ D @ C @ A ) @ B )
= ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(20,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__sup @ C )
=> ( ( c_Lattices_Osemilattice__sup__class_Osup @ C @ B @ A )
= ( c_Lattices_Osemilattice__sup__class_Osup @ C @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup_Ocommute) ).
thf(559,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__sup @ C )
=> ( ( c_Lattices_Osemilattice__sup__class_Osup @ C @ B @ A )
= ( c_Lattices_Osemilattice__sup__class_Osup @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(51,axiom,
! [A: $i,B: $i,C: $i] :
( ( C = B )
<=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ A @ tc_HOL_Obool ) @ C @ B )
& ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ A @ tc_HOL_Obool ) @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__eq__subset) ).
thf(638,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C = B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ A @ tc_HOL_Obool ) @ C @ B )
& ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ A @ tc_HOL_Obool ) @ B @ C ) ) )
& ( ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ A @ tc_HOL_Obool ) @ C @ B )
& ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ A @ tc_HOL_Obool ) @ B @ C ) )
=> ( C = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(386,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ B @ A )
=> ( ( c_Relation_Oantisym @ C @ A )
=> ( c_Relation_Oantisym @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_antisym__subset) ).
thf(1892,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ B @ A )
=> ( ( c_Relation_Oantisym @ C @ A )
=> ( c_Relation_Oantisym @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(215,axiom,
! [A: $i,B: $i] :
( ( c_Transitive__Closure_Ortrancl @ B @ ( c_Relation_Oconverse @ B @ B @ A ) )
= ( c_Relation_Oconverse @ B @ B @ ( c_Transitive__Closure_Ortrancl @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__converse) ).
thf(1147,plain,
! [A: $i,B: $i] :
( ( c_Transitive__Closure_Ortrancl @ B @ ( c_Relation_Oconverse @ B @ B @ A ) )
= ( c_Relation_Oconverse @ B @ B @ ( c_Transitive__Closure_Ortrancl @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(123,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__inf @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
<=> ( ( c_Lattices_Osemilattice__inf__class_Oinf @ C @ B @ A )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__iff__inf) ).
thf(870,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__inf @ C )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( ( c_Lattices_Osemilattice__inf__class_Oinf @ C @ B @ A )
= B ) )
& ( ( ( c_Lattices_Osemilattice__inf__class_Oinf @ C @ B @ A )
= B )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(126,axiom,
! [A: $i,B: $i] :
( ( class_Lattices_Obounded__lattice__bot @ B )
=> ( ( c_Lattices_Osemilattice__sup__class_Osup @ B @ A @ ( c_Orderings_Obot__class_Obot @ B ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__bot__right) ).
thf(881,plain,
! [A: $i,B: $i] :
( ( class_Lattices_Obounded__lattice__bot @ B )
=> ( ( c_Lattices_Osemilattice__sup__class_Osup @ B @ A @ ( c_Orderings_Obot__class_Obot @ B ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(207,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B ) @ A )
= ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ A ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__Un__distrib2) ).
thf(1115,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B ) @ A )
= ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ A ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(360,axiom,
! [A: $i,B: $i] :
( ( c_Arrow__Order__Mirabelle_Odictator @ B @ A )
<=> ! [C: $i] :
( ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ C @ c_Arrow__Order__Mirabelle_OProf )
=> ( ( hAPP @ B @ C )
= ( hAPP @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_dictator__def) ).
thf(1773,plain,
! [A: $i,B: $i] :
( ( ( c_Arrow__Order__Mirabelle_Odictator @ B @ A )
=> ! [C: $i] :
( ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ C @ c_Arrow__Order__Mirabelle_OProf )
=> ( ( hAPP @ B @ C )
= ( hAPP @ C @ A ) ) ) )
& ( ! [C: $i] :
( ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ C @ c_Arrow__Order__Mirabelle_OProf )
=> ( ( hAPP @ B @ C )
= ( hAPP @ C @ A ) ) )
=> ( c_Arrow__Order__Mirabelle_Odictator @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(369,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( c_Relation_ORange @ C @ B @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
<=> ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ C @ B ) @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Range__empty__iff) ).
thf(1815,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( c_Relation_ORange @ C @ B @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ C @ B ) @ tc_HOL_Obool ) ) ) )
& ( ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ C @ B ) @ tc_HOL_Obool ) ) )
=> ( ( c_Relation_ORange @ C @ B @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(238,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( c_Set_Oinsert @ C @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
= ( c_Set_Oinsert @ C @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) )
=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_singleton__inject) ).
thf(1232,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Set_Oinsert @ C @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
= ( c_Set_Oinsert @ C @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(374,axiom,
! [A: $i,B: $i] : ( c_member @ ( tc_prod @ B @ B ) @ ( c_Product__Type_OPair @ B @ B @ A @ A ) @ ( c_Relation_OId @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_IdI) ).
thf(1847,plain,
! [A: $i,B: $i] : ( c_member @ ( tc_prod @ B @ B ) @ ( c_Product__Type_OPair @ B @ B @ A @ A ) @ ( c_Relation_OId @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(450,axiom,
v_a____ != v_b____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_A_I1_J) ).
thf(2169,plain,
v_a____ != v_b____,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(506,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( c_Product__Type_OPair @ F @ E @ D @ C )
= ( c_Product__Type_OPair @ F @ E @ B @ A ) )
=> ~ ( ( D = B )
=> ( C != A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pair__inject) ).
thf(2403,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( c_Product__Type_OPair @ F @ E @ D @ C )
= ( c_Product__Type_OPair @ F @ E @ B @ A ) )
=> ~ ( ( D = B )
=> ( C != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).
thf(291,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_member @ ( tc_prod @ C @ C ) @ B @ A )
=> ( c_member @ ( tc_prod @ C @ C ) @ B @ ( c_Transitive__Closure_Otrancl @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_r__into__trancl_H) ).
thf(1479,plain,
! [A: $i,B: $i,C: $i] :
( ( c_member @ ( tc_prod @ C @ C ) @ B @ A )
=> ( c_member @ ( tc_prod @ C @ C ) @ B @ ( c_Transitive__Closure_Otrancl @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(321,axiom,
! [A: $i] : ( c_Order__Relation_Owell__order__on @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_well__order__on__empty) ).
thf(1609,plain,
! [A: $i] : ( c_Order__Relation_Owell__order__on @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(144,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A )
=> ( ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) @ A @ B ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__partition) ).
thf(924,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A )
=> ( ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) @ A @ B ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(90,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Order__Relation_Opartial__order__on @ C @ B @ ( c_Relation_Oconverse @ C @ C @ A ) )
<=> ( c_Order__Relation_Opartial__order__on @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_partial__order__on__converse) ).
thf(756,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Order__Relation_Opartial__order__on @ C @ B @ ( c_Relation_Oconverse @ C @ C @ A ) )
=> ( c_Order__Relation_Opartial__order__on @ C @ B @ A ) )
& ( ( c_Order__Relation_Opartial__order__on @ C @ B @ A )
=> ( c_Order__Relation_Opartial__order__on @ C @ B @ ( c_Relation_Oconverse @ C @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(474,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B ) @ A ) )
=> ( ~ ( hBOOL @ ( hAPP @ C @ A ) )
=> ( hBOOL @ ( hAPP @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup1E) ).
thf(2259,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B ) @ A ) )
=> ( ~ ( hBOOL @ ( hAPP @ C @ A ) )
=> ( hBOOL @ ( hAPP @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(112,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__inf @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( ( c_Lattices_Osemilattice__inf__class_Oinf @ C @ A @ B )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__absorb2) ).
thf(834,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__inf @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( ( c_Lattices_Osemilattice__inf__class_Oinf @ C @ A @ B )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(148,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Set_Oinsert @ C @ B @ A )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__not__empty) ).
thf(937,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Set_Oinsert @ C @ B @ A )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(397,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ D @ C @ B )
=> ( c_member @ D @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UnI2) ).
thf(1960,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ D @ C @ B )
=> ( c_member @ D @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(251,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A )
=> ( ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) @ A @ B )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__absorb2) ).
thf(1283,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A )
=> ( ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) @ A @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(136,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Odistrib__lattice @ D )
=> ( ( c_Lattices_Osemilattice__sup__class_Osup @ D @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D @ C @ B ) @ A )
= ( c_Lattices_Osemilattice__inf__class_Oinf @ D @ ( c_Lattices_Osemilattice__sup__class_Osup @ D @ C @ A ) @ ( c_Lattices_Osemilattice__sup__class_Osup @ D @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__inf__distrib2) ).
thf(905,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Odistrib__lattice @ D )
=> ( ( c_Lattices_Osemilattice__sup__class_Osup @ D @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D @ C @ B ) @ A )
= ( c_Lattices_Osemilattice__inf__class_Oinf @ D @ ( c_Lattices_Osemilattice__sup__class_Osup @ D @ C @ A ) @ ( c_Lattices_Osemilattice__sup__class_Osup @ D @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(380,axiom,
( ( ( v_a____ = v_b_H____ )
& ( v_b____ != v_a_H____ ) )
=> ( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a____ @ v_b____ ) @ ( hAPP @ v_F @ v_P____ ) )
<=> ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a_H____ @ v_b_H____ ) @ ( hAPP @ v_F @ v_P_H____ ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_calculation_I2_J) ).
thf(1864,plain,
( ( ( v_a____ = v_b_H____ )
& ( v_b____ != v_a_H____ ) )
=> ( ( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a____ @ v_b____ ) @ ( hAPP @ v_F @ v_P____ ) )
=> ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a_H____ @ v_b_H____ ) @ ( hAPP @ v_F @ v_P_H____ ) ) )
& ( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a_H____ @ v_b_H____ ) @ ( hAPP @ v_F @ v_P_H____ ) )
=> ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a____ @ v_b____ ) @ ( hAPP @ v_F @ v_P____ ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(438,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_member @ C @ B @ A )
<=> ( hBOOL @ ( hAPP @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mem__def) ).
thf(2122,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_member @ C @ B @ A )
=> ( hBOOL @ ( hAPP @ A @ B ) ) )
& ( ( hBOOL @ ( hAPP @ A @ B ) )
=> ( c_member @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).
thf(175,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A )
=> ( ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) @ A @ C ) )
= C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_double__diff) ).
thf(1020,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A )
=> ( ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) @ A @ C ) )
= C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(27,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__sup @ C )
=> ( ( c_Lattices_Osemilattice__sup__class_Osup @ C @ B @ A )
= ( c_Lattices_Osemilattice__sup__class_Osup @ C @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__commute) ).
thf(574,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__sup @ C )
=> ( ( c_Lattices_Osemilattice__sup__class_Osup @ C @ B @ A )
= ( c_Lattices_Osemilattice__sup__class_Osup @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(93,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ B @ ( c_Transitive__Closure_Ortrancl @ C @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__subset__rtrancl) ).
thf(766,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ B @ ( c_Transitive__Closure_Ortrancl @ C @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(373,axiom,
! [A: $i,B: $i] :
( ( B != A )
| ( hBOOL @ ( hAPP @ ( c_fequal @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fequal__2) ).
thf(1843,plain,
! [A: $i,B: $i] :
( ( B != A )
| ( hBOOL @ ( hAPP @ ( c_fequal @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(497,axiom,
! [A: $i] :
( ( c_Arrow__Order__Mirabelle_Ounanimity @ A )
<=> ! [B: $i] :
( ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ B @ c_Arrow__Order__Mirabelle_OProf )
=> ! [C: $i,D: $i] :
( ! [E: $i] : ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ C @ D ) @ ( hAPP @ B @ E ) )
=> ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ C @ D ) @ ( hAPP @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_unanimity__def) ).
thf(2367,plain,
! [A: $i] :
( ( ( c_Arrow__Order__Mirabelle_Ounanimity @ A )
=> ! [B: $i] :
( ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ B @ c_Arrow__Order__Mirabelle_OProf )
=> ! [C: $i,D: $i] :
( ! [E: $i] : ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ C @ D ) @ ( hAPP @ B @ E ) )
=> ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ C @ D ) @ ( hAPP @ A @ B ) ) ) ) )
& ( ! [B: $i] :
( ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ B @ c_Arrow__Order__Mirabelle_OProf )
=> ! [C: $i,D: $i] :
( ! [E: $i] : ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ C @ D ) @ ( hAPP @ B @ E ) )
=> ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ C @ D ) @ ( hAPP @ A @ B ) ) ) )
=> ( c_Arrow__Order__Mirabelle_Ounanimity @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).
thf(278,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ C ) @ ( c_Transitive__Closure_Ortrancl @ E @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ E @ E ) @ tc_HOL_Obool ) @ B @ A ) ) )
=> ( ! [F: $i] :
( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ F @ C ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) )
=> ! [G: $i] :
( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ G @ F ) @ A )
=> ( G = F ) ) )
=> ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ C ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__Un__separator__converseE) ).
thf(1394,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ C ) @ ( c_Transitive__Closure_Ortrancl @ E @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ E @ E ) @ tc_HOL_Obool ) @ B @ A ) ) )
=> ( ! [F: $i] :
( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ F @ C ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) )
=> ! [G: $i] :
( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ G @ F ) @ A )
=> ( G = F ) ) )
=> ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ C ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(166,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__inf @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C @ B @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__le1) ).
thf(998,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__inf @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C @ B @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(116,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__inf @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D @ A @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__infI2) ).
thf(849,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__inf @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D @ A @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( class_Lattices_Osemilattice__inf @ B )
=> ( ( c_Lattices_Osemilattice__inf__class_Oinf @ B @ A @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__idem) ).
thf(525,plain,
! [A: $i,B: $i] :
( ( class_Lattices_Osemilattice__inf @ B )
=> ( ( c_Lattices_Osemilattice__inf__class_Oinf @ B @ A @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(526,plain,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Osemilattice__inf @ B )
| ( ( c_Lattices_Osemilattice__inf__class_Oinf @ B @ A @ A )
= A ) ),
inference(cnf,[status(esa)],[525]) ).
thf(527,plain,
! [B: $i,A: $i] :
( ( ( c_Lattices_Osemilattice__inf__class_Oinf @ B @ A @ A )
= A )
| ~ ( class_Lattices_Osemilattice__inf @ B ) ),
inference(lifteq,[status(thm)],[526]) ).
thf(349,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Relation_ODomain @ D @ C @ B ) @ ( c_Relation_ODomain @ D @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Domain__mono) ).
thf(1696,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Relation_ODomain @ D @ C @ B ) @ ( c_Relation_ODomain @ D @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(310,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Relation_Orefl__on @ D @ C @ B )
=> ( ( c_member @ D @ A @ C )
=> ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ A @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_refl__onD) ).
thf(1564,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Relation_Orefl__on @ D @ C @ B )
=> ( ( c_member @ D @ A @ C )
=> ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ A @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(388,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Relation_OImage @ E @ D @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ C @ B ) @ A )
= ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Relation_OImage @ E @ D @ C @ A ) @ ( c_Relation_OImage @ E @ D @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__Image) ).
thf(1896,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Relation_OImage @ E @ D @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ E @ D ) @ tc_HOL_Obool ) @ C @ B ) @ A )
= ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Relation_OImage @ E @ D @ C @ A ) @ ( c_Relation_OImage @ E @ D @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(67,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Set_Oinsert @ D @ C @ B ) @ A )
= ( c_Set_Oinsert @ D @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__insert__left) ).
thf(692,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Set_Oinsert @ D @ C @ B ) @ A )
= ( c_Set_Oinsert @ D @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(503,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_member @ C @ B @ A )
=> ( ( c_Set_Oinsert @ C @ B @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__absorb) ).
thf(2392,plain,
! [A: $i,B: $i,C: $i] :
( ( c_member @ C @ B @ A )
=> ( ( c_Set_Oinsert @ C @ B @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).
thf(445,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( hBOOL @ ( hAPP @ D @ C ) )
=> ( hBOOL @ ( hAPP @ B @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ A @ tc_HOL_Obool ) @ B @ D ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup1CI) ).
thf(2154,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( hBOOL @ ( hAPP @ D @ C ) )
=> ( hBOOL @ ( hAPP @ B @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ A @ tc_HOL_Obool ) @ B @ D ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(333,axiom,
! [A: $i,B: $i,C: $i] :
( ( C != B )
=> ( ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ A @ c_Arrow__Order__Mirabelle_OLin )
=> ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( c_Arrow__Order__Mirabelle_Obelow @ A @ C @ B ) @ c_Arrow__Order__Mirabelle_OLin ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_below__Lin) ).
thf(1651,plain,
! [A: $i,B: $i,C: $i] :
( ( C != B )
=> ( ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ A @ c_Arrow__Order__Mirabelle_OLin )
=> ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( c_Arrow__Order__Mirabelle_Obelow @ A @ C @ B ) @ c_Arrow__Order__Mirabelle_OLin ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(194,axiom,
! [A: $i,B: $i] :
( ( c_Relation_ORange @ B @ B @ ( c_Relation_OId__on @ B @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Range__Id__on) ).
thf(1074,plain,
! [A: $i,B: $i] :
( ( c_Relation_ORange @ B @ B @ ( c_Relation_OId__on @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(412,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_member @ ( tc_prod @ E @ D ) @ ( c_Product__Type_OPair @ E @ D @ C @ B ) @ A )
=> ( c_member @ D @ B @ ( c_Relation_ORange @ E @ D @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_RangeI) ).
thf(2011,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_member @ ( tc_prod @ E @ D ) @ ( c_Product__Type_OPair @ E @ D @ C @ B ) @ A )
=> ( c_member @ D @ B @ ( c_Relation_ORange @ E @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(142,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__trans) ).
thf(920,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(347,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Lattices_Olattice @ E )
=> ( ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ E ) @ C @ B ) @ A )
= ( c_Lattices_Osemilattice__inf__class_Oinf @ E @ ( hAPP @ C @ A ) @ ( hAPP @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__apply) ).
thf(1691,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Lattices_Olattice @ E )
=> ( ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ E ) @ C @ B ) @ A )
= ( c_Lattices_Osemilattice__inf__class_Oinf @ E @ ( hAPP @ C @ A ) @ ( hAPP @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(15,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__inf @ D )
=> ( ( c_Lattices_Osemilattice__inf__class_Oinf @ D @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D @ C @ B ) @ A )
= ( c_Lattices_Osemilattice__inf__class_Oinf @ D @ C @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__assoc) ).
thf(546,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__inf @ D )
=> ( ( c_Lattices_Osemilattice__inf__class_Oinf @ D @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D @ C @ B ) @ A )
= ( c_Lattices_Osemilattice__inf__class_Oinf @ D @ C @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(259,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oord @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ D ) @ B @ A )
<=> ! [E: $i] : ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ B @ E ) @ ( hAPP @ A @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__fun__def) ).
thf(1306,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oord @ D )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ D ) @ B @ A )
=> ! [E: $i] : ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ B @ E ) @ ( hAPP @ A @ E ) ) )
& ( ! [E: $i] : ( c_Orderings_Oord__class_Oless__eq @ D @ ( hAPP @ B @ E ) @ ( hAPP @ A @ E ) )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ D ) @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(91,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__sup @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ A @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Lattices_Osemilattice__sup__class_Osup @ D @ C @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__supI) ).
thf(761,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__sup @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ A @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Lattices_Osemilattice__sup__class_Osup @ D @ C @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(2116,plain,
v_a____ = v_b_H____,
inference(cnf,[status(esa)],[2114]) ).
thf(2118,plain,
v_b_H____ = v_a____,
inference(lifteq,[status(thm)],[2116]) ).
thf(101,axiom,
! [A: $i,B: $i] :
( ( class_Lattices_Obounded__lattice__bot @ B )
=> ( ( c_Lattices_Osemilattice__inf__class_Oinf @ B @ A @ ( c_Orderings_Obot__class_Obot @ B ) )
= ( c_Orderings_Obot__class_Obot @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__bot__right) ).
thf(798,plain,
! [A: $i,B: $i] :
( ( class_Lattices_Obounded__lattice__bot @ B )
=> ( ( c_Lattices_Osemilattice__inf__class_Oinf @ B @ A @ ( c_Orderings_Obot__class_Obot @ B ) )
= ( c_Orderings_Obot__class_Obot @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(231,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A )
= ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__commute) ).
thf(1199,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A )
= ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(496,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Relation_Oconverse @ D @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ B @ A ) )
= ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_HOL_Obool ) @ ( c_Relation_Oconverse @ D @ C @ B ) @ ( c_Relation_Oconverse @ D @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converse__Un) ).
thf(2364,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Relation_Oconverse @ D @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ B @ A ) )
= ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_HOL_Obool ) @ ( c_Relation_Oconverse @ D @ C @ B ) @ ( c_Relation_Oconverse @ D @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).
thf(261,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F != E )
=> ( ( D != C )
=> ( ( F != C )
=> ( ( E != D )
=> ( ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ B @ c_Arrow__Order__Mirabelle_OProf )
=> ( ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ A @ c_Arrow__Order__Mirabelle_OProf )
=> ( ! [G: $i] :
( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ F @ E ) @ ( hAPP @ B @ G ) )
<=> ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ D @ C ) @ ( hAPP @ A @ G ) ) )
=> ( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ F @ E ) @ ( hAPP @ v_F @ B ) )
<=> ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ D @ C ) @ ( hAPP @ v_F @ A ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__C2_C) ).
thf(1311,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F != E )
=> ( ( D != C )
=> ( ( F != C )
=> ( ( E != D )
=> ( ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ B @ c_Arrow__Order__Mirabelle_OProf )
=> ( ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ A @ c_Arrow__Order__Mirabelle_OProf )
=> ( ! [G: $i] :
( ( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ F @ E ) @ ( hAPP @ B @ G ) )
=> ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ D @ C ) @ ( hAPP @ A @ G ) ) )
& ( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ D @ C ) @ ( hAPP @ A @ G ) )
=> ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ F @ E ) @ ( hAPP @ B @ G ) ) ) )
=> ( ( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ F @ E ) @ ( hAPP @ v_F @ B ) )
=> ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ D @ C ) @ ( hAPP @ v_F @ A ) ) )
& ( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ D @ C ) @ ( hAPP @ v_F @ A ) )
=> ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ F @ E ) @ ( hAPP @ v_F @ B ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(468,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_member @ C @ B @ ( c_Wellfounded_Oacc @ C @ A ) )
<=> ! [D: $i] :
( ( c_member @ ( tc_prod @ C @ C ) @ ( c_Product__Type_OPair @ C @ C @ D @ B ) @ A )
=> ( c_member @ C @ D @ ( c_Wellfounded_Oacc @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acc_Osimps) ).
thf(2232,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_member @ C @ B @ ( c_Wellfounded_Oacc @ C @ A ) )
=> ! [D: $i] :
( ( c_member @ ( tc_prod @ C @ C ) @ ( c_Product__Type_OPair @ C @ C @ D @ B ) @ A )
=> ( c_member @ C @ D @ ( c_Wellfounded_Oacc @ C @ A ) ) ) )
& ( ! [D: $i] :
( ( c_member @ ( tc_prod @ C @ C ) @ ( c_Product__Type_OPair @ C @ C @ D @ B ) @ A )
=> ( c_member @ C @ D @ ( c_Wellfounded_Oacc @ C @ A ) ) )
=> ( c_member @ C @ B @ ( c_Wellfounded_Oacc @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
thf(482,axiom,
! [A: $i,B: $i] :
( ( c_Relation_Oantisym @ B @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ A @ ( c_Relation_OId @ B ) ) )
<=> ( c_Relation_Oantisym @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_antisym__reflcl) ).
thf(2307,plain,
! [A: $i,B: $i] :
( ( ( c_Relation_Oantisym @ B @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ A @ ( c_Relation_OId @ B ) ) )
=> ( c_Relation_Oantisym @ B @ A ) )
& ( ( c_Relation_Oantisym @ B @ A )
=> ( c_Relation_Oantisym @ B @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ A @ ( c_Relation_OId @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).
thf(430,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Ominus @ E )
=> ( ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ E ) @ C @ B ) @ A )
= ( c_Groups_Ominus__class_Ominus @ E @ ( hAPP @ C @ A ) @ ( hAPP @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_minus__apply) ).
thf(2061,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Groups_Ominus @ E )
=> ( ( hAPP @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ E ) @ C @ B ) @ A )
= ( c_Groups_Ominus__class_Ominus @ E @ ( hAPP @ C @ A ) @ ( hAPP @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(411,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( c_Product__Type_OPair @ F @ E @ D @ C )
= ( c_Product__Type_OPair @ F @ E @ B @ A ) )
<=> ( ( D = B )
& ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pair__eq) ).
thf(2000,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ( c_Product__Type_OPair @ F @ E @ D @ C )
= ( c_Product__Type_OPair @ F @ E @ B @ A ) )
=> ( ( D = B )
& ( C = A ) ) )
& ( ( ( D = B )
& ( C = A ) )
=> ( ( c_Product__Type_OPair @ F @ E @ D @ C )
= ( c_Product__Type_OPair @ F @ E @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(138,axiom,
! [A: $i,B: $i] : ( c_Relation_Ototal__on @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_total__on__empty) ).
thf(910,plain,
! [A: $i,B: $i] : ( c_Relation_Ototal__on @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(442,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ D @ C @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) )
=> ~ ( ( c_member @ D @ C @ B )
=> ( c_member @ D @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_DiffE) ).
thf(2147,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ D @ C @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) )
=> ~ ( ( c_member @ D @ C @ B )
=> ( c_member @ D @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).
thf(338,axiom,
! [A: $i] :
( ( c_Relation_OField @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Field__empty) ).
thf(1666,plain,
! [A: $i] :
( ( c_Relation_OField @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(315,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_FunDef_Oin__rel @ E @ D @ C ) @ B ) @ A ) )
<=> ( c_member @ ( tc_prod @ E @ D ) @ ( c_Product__Type_OPair @ E @ D @ B @ A ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__rel__def) ).
thf(1580,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_FunDef_Oin__rel @ E @ D @ C ) @ B ) @ A ) )
=> ( c_member @ ( tc_prod @ E @ D ) @ ( c_Product__Type_OPair @ E @ D @ B @ A ) @ C ) )
& ( ( c_member @ ( tc_prod @ E @ D ) @ ( c_Product__Type_OPair @ E @ D @ B @ A ) @ C )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_FunDef_Oin__rel @ E @ D @ C ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(479,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( c_Wellfounded_Oacc @ C @ A ) @ ( c_Wellfounded_Oacc @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acc__subset) ).
thf(2277,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( c_Wellfounded_Oacc @ C @ A ) @ ( c_Wellfounded_Oacc @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).
thf(224,axiom,
! [A: $i,B: $i,C: $i] : ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__upper1) ).
thf(1174,plain,
! [A: $i,B: $i,C: $i] : ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(342,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Equiv__Relations_Ocongruent @ F @ E @ D @ C )
=> ( ( c_member @ ( tc_prod @ F @ F ) @ ( c_Product__Type_OPair @ F @ F @ B @ A ) @ D )
=> ( ( hAPP @ C @ B )
= ( hAPP @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_congruentD) ).
thf(1676,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Equiv__Relations_Ocongruent @ F @ E @ D @ C )
=> ( ( c_member @ ( tc_prod @ F @ F ) @ ( c_Product__Type_OPair @ F @ F @ B @ A ) @ D )
=> ( ( hAPP @ C @ B )
= ( hAPP @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(297,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Wellfounded_Owf @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ A @ B )
=> ( c_Wellfounded_Owf @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__subset) ).
thf(1502,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Wellfounded_Owf @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ A @ B )
=> ( c_Wellfounded_Owf @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(359,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ D @ C ) @ ( c_Arrow__Order__Mirabelle_Omktop @ B @ A ) )
<=> ( ( D != A )
& ( ( C = A )
=> ( D != C ) )
& ( ( C != A )
=> ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ D @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__mktop) ).
thf(1751,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ D @ C ) @ ( c_Arrow__Order__Mirabelle_Omktop @ B @ A ) )
=> ( ( D != A )
& ( ( C = A )
=> ( D != C ) )
& ( ( C != A )
=> ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ D @ C ) @ B ) ) ) )
& ( ( ( D != A )
& ( ( C = A )
=> ( D != C ) )
& ( ( C != A )
=> ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ D @ C ) @ B ) ) )
=> ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ D @ C ) @ ( c_Arrow__Order__Mirabelle_Omktop @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(99,axiom,
! [A: $i,B: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
<=> ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__empty) ).
thf(788,plain,
! [A: $i,B: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
& ( ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(443,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ C ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) )
=> ( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ C @ A ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) )
=> ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ A ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__trans) ).
thf(2150,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ C ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) )
=> ( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ C @ A ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) )
=> ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ A ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(273,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ C ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) )
=> ( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ C @ A ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) )
=> ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ A ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__rtrancl__trancl) ).
thf(1370,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ C ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) )
=> ( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ C @ A ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) )
=> ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ A ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(283,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Equiv__Relations_Oequiv @ E @ D @ C )
=> ( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ B @ A ) @ C )
=> ( ( c_Relation_OImage @ E @ E @ C @ ( c_Set_Oinsert @ E @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) )
= ( c_Relation_OImage @ E @ E @ C @ ( c_Set_Oinsert @ E @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equiv__class__eq) ).
thf(1423,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Equiv__Relations_Oequiv @ E @ D @ C )
=> ( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ B @ A ) @ C )
=> ( ( c_Relation_OImage @ E @ E @ C @ ( c_Set_Oinsert @ E @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) )
= ( c_Relation_OImage @ E @ E @ C @ ( c_Set_Oinsert @ E @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(115,axiom,
! [A: $i,B: $i] : ( c_Wellfounded_Owf @ B @ ( c_Wellfounded_Omeasure @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__measure) ).
thf(847,plain,
! [A: $i,B: $i] : ( c_Wellfounded_Owf @ B @ ( c_Wellfounded_Omeasure @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(271,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ B ) @ ( c_Transitive__Closure_Otrancl @ D @ ( c_Relation_Oconverse @ D @ D @ A ) ) )
=> ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ B ) @ ( c_Relation_Oconverse @ D @ D @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__converseD) ).
thf(1365,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ B ) @ ( c_Transitive__Closure_Otrancl @ D @ ( c_Relation_Oconverse @ D @ D @ A ) ) )
=> ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ B ) @ ( c_Relation_Oconverse @ D @ D @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(489,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Wellfounded_Oacyclic @ D @ ( c_Set_Oinsert @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ B ) @ A ) )
<=> ( ( c_Wellfounded_Oacyclic @ D @ A )
& ~ ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ B @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acyclic__insert) ).
thf(2332,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_Wellfounded_Oacyclic @ D @ ( c_Set_Oinsert @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ B ) @ A ) )
=> ( ( c_Wellfounded_Oacyclic @ D @ A )
& ~ ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ B @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) ) )
& ( ( ( c_Wellfounded_Oacyclic @ D @ A )
& ~ ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ B @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) )
=> ( c_Wellfounded_Oacyclic @ D @ ( c_Set_Oinsert @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).
thf(59,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ~ ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__le__cases) ).
thf(665,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ~ ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(454,axiom,
! [A: $i,B: $i] :
( ( c_Wellfounded_Owf @ B @ A )
<=> ! [C: $i] :
( ? [D: $i] : ( c_member @ B @ D @ C )
=> ? [D: $i] :
( ( c_member @ B @ D @ C )
& ! [E: $i] :
( ( c_member @ ( tc_prod @ B @ B ) @ ( c_Product__Type_OPair @ B @ B @ E @ D ) @ A )
=> ~ ( c_member @ B @ E @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__eq__minimal) ).
thf(2179,plain,
! [A: $i,B: $i] :
( ( ( c_Wellfounded_Owf @ B @ A )
=> ! [C: $i] :
( ? [D: $i] : ( c_member @ B @ D @ C )
=> ? [D: $i] :
( ( c_member @ B @ D @ C )
& ! [E: $i] :
( ( c_member @ ( tc_prod @ B @ B ) @ ( c_Product__Type_OPair @ B @ B @ E @ D ) @ A )
=> ~ ( c_member @ B @ E @ C ) ) ) ) )
& ( ! [C: $i] :
( ? [D: $i] : ( c_member @ B @ D @ C )
=> ? [D: $i] :
( ( c_member @ B @ D @ C )
& ! [E: $i] :
( ( c_member @ ( tc_prod @ B @ B ) @ ( c_Product__Type_OPair @ B @ B @ E @ D ) @ A )
=> ~ ( c_member @ B @ E @ C ) ) ) )
=> ( c_Wellfounded_Owf @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).
thf(235,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( c_Set_Oinsert @ E @ D @ ( c_Set_Oinsert @ E @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) )
= ( c_Set_Oinsert @ E @ B @ ( c_Set_Oinsert @ E @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) ) )
<=> ( ( ( D = B )
& ( C = A ) )
| ( ( D = A )
& ( C = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_doubleton__eq__iff) ).
thf(1210,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( ( c_Set_Oinsert @ E @ D @ ( c_Set_Oinsert @ E @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) )
= ( c_Set_Oinsert @ E @ B @ ( c_Set_Oinsert @ E @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) ) )
=> ( ( ( D = B )
& ( C = A ) )
| ( ( D = A )
& ( C = B ) ) ) )
& ( ( ( ( D = B )
& ( C = A ) )
| ( ( D = A )
& ( C = B ) ) )
=> ( ( c_Set_Oinsert @ E @ D @ ( c_Set_Oinsert @ E @ C @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) )
= ( c_Set_Oinsert @ E @ B @ ( c_Set_Oinsert @ E @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(64,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_member @ C @ B @ ( c_Set_Oinsert @ C @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) )
=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_singletonE) ).
thf(682,plain,
! [A: $i,B: $i,C: $i] :
( ( c_member @ C @ B @ ( c_Set_Oinsert @ C @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(313,axiom,
! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ( c_member @ ( tc_prod @ B @ B ) @ ( c_Product__Type_OPair @ B @ B @ C @ D ) @ A )
=> ( ( c_member @ ( tc_prod @ B @ B ) @ ( c_Product__Type_OPair @ B @ B @ D @ C ) @ A )
=> ( C = D ) ) )
=> ( c_Relation_Oantisym @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_antisymI) ).
thf(1573,plain,
! [A: $i,B: $i] :
( ! [C: $i,D: $i] :
( ( c_member @ ( tc_prod @ B @ B ) @ ( c_Product__Type_OPair @ B @ B @ C @ D ) @ A )
=> ( ( c_member @ ( tc_prod @ B @ B ) @ ( c_Product__Type_OPair @ B @ B @ D @ C ) @ A )
=> ( C = D ) ) )
=> ( c_Relation_Oantisym @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(30,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__sup @ C )
=> ( ( c_Lattices_Osemilattice__sup__class_Osup @ C @ B @ ( c_Lattices_Osemilattice__sup__class_Osup @ C @ B @ A ) )
= ( c_Lattices_Osemilattice__sup__class_Osup @ C @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__left__idem) ).
thf(583,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__sup @ C )
=> ( ( c_Lattices_Osemilattice__sup__class_Osup @ C @ B @ ( c_Lattices_Osemilattice__sup__class_Osup @ C @ B @ A ) )
= ( c_Lattices_Osemilattice__sup__class_Osup @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(458,axiom,
! [A: $i] : ( c_Order__Relation_Opartial__order__on @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_partial__order__on__empty) ).
thf(2200,plain,
! [A: $i] : ( c_Order__Relation_Opartial__order__on @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( class_Lattices_Osemilattice__sup @ B )
=> ( ( c_Lattices_Osemilattice__sup__class_Osup @ B @ A @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__idem) ).
thf(522,plain,
! [A: $i,B: $i] :
( ( class_Lattices_Osemilattice__sup @ B )
=> ( ( c_Lattices_Osemilattice__sup__class_Osup @ B @ A @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(277,axiom,
! [A: $i] : ( c_Order__Relation_Olinear__order__on @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_lnear__order__on__empty) ).
thf(1392,plain,
! [A: $i] : ( c_Order__Relation_Olinear__order__on @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(466,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Wellfounded_Owf @ C @ B )
=> ( c_Wellfounded_Owf @ C @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__Int1) ).
thf(2228,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Wellfounded_Owf @ C @ B )
=> ( c_Wellfounded_Owf @ C @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).
thf(69,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A ) @ A )
= ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__Diff__cancel2) ).
thf(697,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A ) @ A )
= ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(403,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ D @ C ) )
=> ( ( hBOOL @ ( hAPP @ B @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ A @ tc_HOL_Obool ) @ D @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf1I) ).
thf(1983,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ D @ C ) )
=> ( ( hBOOL @ ( hAPP @ B @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ A @ tc_HOL_Obool ) @ D @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(446,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Order__Relation_Opreorder__on @ D @ ( c_Relation_OField @ D @ C ) @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ ( c_Relation_OField @ D @ C ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ A @ ( c_Relation_OField @ D @ C ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Relation_OImage @ D @ D @ C @ B ) @ ( c_Relation_OImage @ D @ D @ C @ A ) )
<=> ! [E: $i] :
( ( c_member @ D @ E @ B )
=> ? [F: $i] :
( ( c_member @ D @ F @ A )
& ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ F @ E ) @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__Image__Image__iff) ).
thf(2157,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Order__Relation_Opreorder__on @ D @ ( c_Relation_OField @ D @ C ) @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ ( c_Relation_OField @ D @ C ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ A @ ( c_Relation_OField @ D @ C ) )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Relation_OImage @ D @ D @ C @ B ) @ ( c_Relation_OImage @ D @ D @ C @ A ) )
=> ! [E: $i] :
( ( c_member @ D @ E @ B )
=> ? [F: $i] :
( ( c_member @ D @ F @ A )
& ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ F @ E ) @ C ) ) ) )
& ( ! [E: $i] :
( ( c_member @ D @ E @ B )
=> ? [F: $i] :
( ( c_member @ D @ F @ A )
& ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ F @ E ) @ C ) ) )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Relation_OImage @ D @ D @ C @ B ) @ ( c_Relation_OImage @ D @ D @ C @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(246,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Relation_OImage @ C @ B @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__empty) ).
thf(1270,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Relation_OImage @ C @ B @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(173,axiom,
class_Orderings_Obot @ tc_HOL_Obool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Orderings_Obot) ).
thf(1017,plain,
class_Orderings_Obot @ tc_HOL_Obool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(43,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Set_Oinsert @ D @ A @ C ) @ ( c_Set_Oinsert @ D @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__mono) ).
thf(615,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Set_Oinsert @ D @ A @ C ) @ ( c_Set_Oinsert @ D @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(209,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Wellfounded_Owf @ C @ B )
=> ( ( c_Wellfounded_Owf @ C @ A )
=> ( ( ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( c_Relation_ODomain @ C @ C @ B ) @ ( c_Relation_ORange @ C @ C @ A ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( c_Wellfounded_Owf @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__Un) ).
thf(1121,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Wellfounded_Owf @ C @ B )
=> ( ( c_Wellfounded_Owf @ C @ A )
=> ( ( ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( c_Relation_ODomain @ C @ C @ B ) @ ( c_Relation_ORange @ C @ C @ A ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( c_Wellfounded_Owf @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(317,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Order__Relation_Opartial__order__on @ D @ ( c_Relation_OField @ D @ C ) @ C )
=> ( ( c_member @ D @ B @ ( c_Relation_OField @ D @ C ) )
=> ( ( c_member @ D @ A @ ( c_Relation_OField @ D @ C ) )
=> ( ( ( c_Relation_OImage @ D @ D @ C @ ( c_Set_Oinsert @ D @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) )
= ( c_Relation_OImage @ D @ D @ C @ ( c_Set_Oinsert @ D @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) )
<=> ( B = A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Partial__order__eq__Image1__Image1__iff) ).
thf(1587,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Order__Relation_Opartial__order__on @ D @ ( c_Relation_OField @ D @ C ) @ C )
=> ( ( c_member @ D @ B @ ( c_Relation_OField @ D @ C ) )
=> ( ( c_member @ D @ A @ ( c_Relation_OField @ D @ C ) )
=> ( ( ( ( c_Relation_OImage @ D @ D @ C @ ( c_Set_Oinsert @ D @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) )
= ( c_Relation_OImage @ D @ D @ C @ ( c_Set_Oinsert @ D @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( c_Relation_OImage @ D @ D @ C @ ( c_Set_Oinsert @ D @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) )
= ( c_Relation_OImage @ D @ D @ C @ ( c_Set_Oinsert @ D @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(340,axiom,
! [A: $i] : ( c_Order__Relation_Opreorder__on @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_preorder__on__empty) ).
thf(1672,plain,
! [A: $i] : ( c_Order__Relation_Opreorder__on @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(169,axiom,
! [A: $i,B: $i] :
( ( class_Groups_Ominus @ B )
=> ( class_Groups_Ominus @ ( tc_fun @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Groups_Ominus) ).
thf(1006,plain,
! [A: $i,B: $i] :
( ( class_Groups_Ominus @ B )
=> ( class_Groups_Ominus @ ( tc_fun @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(383,axiom,
! [A: $i] : ( c_Relation_Orefl__on @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_refl__on__empty) ).
thf(1878,plain,
! [A: $i] : ( c_Relation_Orefl__on @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(353,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i] :
~ ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ E @ E ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) )
=> ( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ B @ A ) @ C )
=> ( B != A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_irrefl__trancl__rD) ).
thf(1719,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i] :
~ ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ E @ E ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) )
=> ( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ B @ A ) @ C )
=> ( B != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(41,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__inf @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ C @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__greatest) ).
thf(610,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__inf @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ C @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(208,axiom,
! [A: $i,B: $i] :
( ( class_Lattices_Obounded__lattice__bot @ B )
=> ( ( c_Lattices_Osemilattice__sup__class_Osup @ B @ ( c_Orderings_Obot__class_Obot @ B ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__bot__left) ).
thf(1118,plain,
! [A: $i,B: $i] :
( ( class_Lattices_Obounded__lattice__bot @ B )
=> ( ( c_Lattices_Osemilattice__sup__class_Osup @ B @ ( c_Orderings_Obot__class_Obot @ B ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(471,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Wellfounded_Owf @ D @ ( c_Set_Oinsert @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ B ) @ A ) )
<=> ( ( c_Wellfounded_Owf @ D @ A )
& ~ ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ B @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__insert) ).
thf(2245,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_Wellfounded_Owf @ D @ ( c_Set_Oinsert @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ B ) @ A ) )
=> ( ( c_Wellfounded_Owf @ D @ A )
& ~ ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ B @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) ) )
& ( ( ( c_Wellfounded_Owf @ D @ A )
& ~ ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ B @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) )
=> ( c_Wellfounded_Owf @ D @ ( c_Set_Oinsert @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
thf(266,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ B ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) )
=> ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ B @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ ( c_Relation_Oconverse @ D @ D @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__converseI) ).
thf(1350,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ B ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) )
=> ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ B @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ ( c_Relation_Oconverse @ D @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(3,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__sup @ C )
=> ( ( c_Lattices_Osemilattice__sup__class_Osup @ C @ B @ ( c_Lattices_Osemilattice__sup__class_Osup @ C @ B @ A ) )
= ( c_Lattices_Osemilattice__sup__class_Osup @ C @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup_Oleft__idem) ).
thf(517,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__sup @ C )
=> ( ( c_Lattices_Osemilattice__sup__class_Osup @ C @ B @ ( c_Lattices_Osemilattice__sup__class_Osup @ C @ B @ A ) )
= ( c_Lattices_Osemilattice__sup__class_Osup @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(518,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( class_Lattices_Osemilattice__sup @ C )
| ( ( c_Lattices_Osemilattice__sup__class_Osup @ C @ B @ ( c_Lattices_Osemilattice__sup__class_Osup @ C @ B @ A ) )
= ( c_Lattices_Osemilattice__sup__class_Osup @ C @ B @ A ) ) ),
inference(cnf,[status(esa)],[517]) ).
thf(519,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Osemilattice__sup__class_Osup @ C @ B @ ( c_Lattices_Osemilattice__sup__class_Osup @ C @ B @ A ) )
= ( c_Lattices_Osemilattice__sup__class_Osup @ C @ B @ A ) )
| ~ ( class_Lattices_Osemilattice__sup @ C ) ),
inference(lifteq,[status(thm)],[518]) ).
thf(85,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
| ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linorder__linear) ).
thf(742,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Olinorder @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
| ( c_Orderings_Oord__class_Oless__eq @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(127,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ ( c_Set_Oinsert @ D @ B @ A ) )
= ( c_Set_Oinsert @ D @ B @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__insert__right) ).
thf(884,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ ( c_Set_Oinsert @ D @ B @ A ) )
= ( c_Set_Oinsert @ D @ B @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(178,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__sup @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ A @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Lattices_Osemilattice__sup__class_Osup @ D @ C @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__least) ).
thf(1028,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__sup @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ A @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Lattices_Osemilattice__sup__class_Osup @ D @ C @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(269,axiom,
! [A: $i,B: $i,C: $i] : ( c_member @ C @ B @ ( c_Set_Oinsert @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insertI1) ).
thf(1361,plain,
! [A: $i,B: $i,C: $i] : ( c_member @ C @ B @ ( c_Set_Oinsert @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(399,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ F @ E ) @ D ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ F @ A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ E ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__predicate2D) ).
thf(1964,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ F @ E ) @ D ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ F @ A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ E ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(487,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_member @ ( tc_prod @ C @ C ) @ ( c_Product__Type_OPair @ C @ C @ B @ A ) @ ( c_Relation_OId @ C ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pair__in__Id__conv) ).
thf(2323,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_member @ ( tc_prod @ C @ C ) @ ( c_Product__Type_OPair @ C @ C @ B @ A ) @ ( c_Relation_OId @ C ) )
=> ( B = A ) )
& ( ( B = A )
=> ( c_member @ ( tc_prod @ C @ C ) @ ( c_Product__Type_OPair @ C @ C @ B @ A ) @ ( c_Relation_OId @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).
thf(65,axiom,
! [A: $i,B: $i] :
( ( c_Relation_OField @ B @ ( c_Relation_Oconverse @ B @ B @ A ) )
= ( c_Relation_OField @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Field__converse) ).
thf(686,plain,
! [A: $i,B: $i] :
( ( c_Relation_OField @ B @ ( c_Relation_Oconverse @ B @ B @ A ) )
= ( c_Relation_OField @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(483,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Relation_Orefl__on @ E @ D @ C )
=> ( ( c_Relation_Orefl__on @ E @ B @ A )
=> ( c_Relation_Orefl__on @ E @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) @ D @ B ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ ( tc_prod @ E @ E ) @ tc_HOL_Obool ) @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_refl__on__Int) ).
thf(2312,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Relation_Orefl__on @ E @ D @ C )
=> ( ( c_Relation_Orefl__on @ E @ B @ A )
=> ( c_Relation_Orefl__on @ E @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) @ D @ B ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ ( tc_prod @ E @ E ) @ tc_HOL_Obool ) @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).
thf(234,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Olattice @ C )
=> ( ( c_Lattices_Osemilattice__inf__class_Oinf @ C @ B @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C @ B @ A ) )
= ( c_Lattices_Osemilattice__inf__class_Oinf @ C @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__aci_I4_J) ).
thf(1207,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Olattice @ C )
=> ( ( c_Lattices_Osemilattice__inf__class_Oinf @ C @ B @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C @ B @ A ) )
= ( c_Lattices_Osemilattice__inf__class_Oinf @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(485,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ ( c_Relation_Oconverse @ C @ C @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) )
=> ~ ( c_member @ ( tc_prod @ C @ C ) @ ( c_Product__Type_OPair @ C @ C @ A @ A ) @ ( c_Transitive__Closure_Otrancl @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_irrefl__tranclI) ).
thf(2317,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ ( c_Relation_Oconverse @ C @ C @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) ) )
=> ~ ( c_member @ ( tc_prod @ C @ C ) @ ( c_Product__Type_OPair @ C @ C @ A @ A ) @ ( c_Transitive__Closure_Otrancl @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).
thf(73,axiom,
! [A: $i,B: $i] :
( ( c_Relation_OImage @ B @ B @ ( c_Relation_OId @ B ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__Id) ).
thf(706,plain,
! [A: $i,B: $i] :
( ( c_Relation_OImage @ B @ B @ ( c_Relation_OId @ B ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(368,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( c_member @ ( tc_prod @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) @ ( c_Product__Type_OPair @ H @ G @ F @ E ) @ ( c_Product__Type_OPair @ H @ G @ D @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ H @ G ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ A @ F ) @ E ) )
=> ( ! [I: $i,J: $i] :
( ( c_member @ ( tc_prod @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) @ ( c_Product__Type_OPair @ H @ G @ F @ E ) @ ( c_Product__Type_OPair @ H @ G @ I @ J ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ H @ G ) @ B ) )
=> ! [K: $i,L: $i] :
( ( c_member @ ( tc_prod @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) @ ( c_Product__Type_OPair @ H @ G @ I @ J ) @ ( c_Product__Type_OPair @ H @ G @ K @ L ) ) @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ A @ I ) @ J ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ K ) @ L ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ D ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__induct2) ).
thf(1810,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( c_member @ ( tc_prod @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) @ ( c_Product__Type_OPair @ H @ G @ F @ E ) @ ( c_Product__Type_OPair @ H @ G @ D @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ H @ G ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ A @ F ) @ E ) )
=> ( ! [I: $i,J: $i] :
( ( c_member @ ( tc_prod @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) @ ( c_Product__Type_OPair @ H @ G @ F @ E ) @ ( c_Product__Type_OPair @ H @ G @ I @ J ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ H @ G ) @ B ) )
=> ! [K: $i,L: $i] :
( ( c_member @ ( tc_prod @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) @ ( c_Product__Type_OPair @ H @ G @ I @ J ) @ ( c_Product__Type_OPair @ H @ G @ K @ L ) ) @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ A @ I ) @ J ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ K ) @ L ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ D ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(451,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ C ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) )
=> ( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ C @ A ) @ B )
=> ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ A ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl_Ortrancl__into__rtrancl) ).
thf(2172,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ C ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) )
=> ( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ C @ A ) @ B )
=> ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ A ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).
thf(63,axiom,
! [A: $i,B: $i] :
( ( c_Set_Othe__elem @ B @ ( c_Set_Oinsert @ B @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_the__elem__eq) ).
thf(679,plain,
! [A: $i,B: $i] :
( ( c_Set_Othe__elem @ B @ ( c_Set_Oinsert @ B @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(158,axiom,
! [A: $i,B: $i] :
( ( c_Equiv__Relations_Oquotient @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_quotient__empty) ).
thf(970,plain,
! [A: $i,B: $i] :
( ( c_Equiv__Relations_Oquotient @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ B @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(481,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ D @ C ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ B @ A ) )
<=> ( ( C != A )
& ( ( D = A )
=> ( D != C ) )
& ( ( D != A )
=> ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ D @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__mkbot) ).
thf(2285,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ D @ C ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ B @ A ) )
=> ( ( C != A )
& ( ( D = A )
=> ( D != C ) )
& ( ( D != A )
=> ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ D @ C ) @ B ) ) ) )
& ( ( ( C != A )
& ( ( D = A )
=> ( D != C ) )
& ( ( D != A )
=> ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ D @ C ) @ B ) ) )
=> ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ D @ C ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).
thf(71,axiom,
! [A: $i,B: $i] :
( ( class_Orderings_Oord @ B )
=> ( class_Orderings_Oord @ ( tc_fun @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Oord) ).
thf(701,plain,
! [A: $i,B: $i] :
( ( class_Orderings_Oord @ B )
=> ( class_Orderings_Oord @ ( tc_fun @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(255,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ D @ C @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) )
=> ( c_member @ D @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_IntD2) ).
thf(1297,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ D @ C @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) )
=> ( c_member @ D @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(302,axiom,
c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ v_P_H____ @ c_Arrow__Order__Mirabelle_OProf,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_A_I4_J) ).
thf(1530,plain,
c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ v_P_H____ @ c_Arrow__Order__Mirabelle_OProf,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(54,axiom,
class_Lattices_Olattice @ tc_HOL_Obool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Olattice) ).
thf(654,plain,
class_Lattices_Olattice @ tc_HOL_Obool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(470,axiom,
? [A: $i] : ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ A @ c_Arrow__Order__Mirabelle_OLin ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linear__alt) ).
thf(2243,plain,
? [A: $i] : ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ A @ c_Arrow__Order__Mirabelle_OLin ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(78,axiom,
! [A: $i,B: $i] :
( ( class_Lattices_Olattice @ B )
=> ( class_Lattices_Olattice @ ( tc_fun @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Lattices_Olattice) ).
thf(721,plain,
! [A: $i,B: $i] :
( ( class_Lattices_Olattice @ B )
=> ( class_Lattices_Olattice @ ( tc_fun @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(24,axiom,
class_Lattices_Osemilattice__sup @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Lattices_Osemilattice__sup) ).
thf(569,plain,
class_Lattices_Osemilattice__sup @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(477,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ D @ C @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) )
=> ( c_member @ D @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_IntD1) ).
thf(2272,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ D @ C @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) )
=> ( c_member @ D @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).
thf(39,axiom,
! [A: $i,B: $i,C: $i,D: $i] : ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Relation_ORange @ C @ D @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_HOL_Obool ) @ B @ A ) ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Relation_ORange @ C @ D @ B ) @ ( c_Relation_ORange @ C @ D @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Range__Int__subset) ).
thf(605,plain,
! [A: $i,B: $i,C: $i,D: $i] : ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Relation_ORange @ C @ D @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_HOL_Obool ) @ B @ A ) ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Relation_ORange @ C @ D @ B ) @ ( c_Relation_ORange @ C @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(46,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Relation_Orefl__on @ D @ ( c_Relation_OField @ D @ C ) @ C )
=> ( ( c_Relation_Oantisym @ D @ C )
=> ( ( c_member @ D @ B @ ( c_Relation_OField @ D @ C ) )
=> ( ( c_member @ D @ A @ ( c_Relation_OField @ D @ C ) )
=> ( ( ( c_Relation_OImage @ D @ D @ C @ ( c_Set_Oinsert @ D @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) )
= ( c_Relation_OImage @ D @ D @ C @ ( c_Set_Oinsert @ D @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) )
<=> ( B = A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Refl__antisym__eq__Image1__Image1__iff) ).
thf(622,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Relation_Orefl__on @ D @ ( c_Relation_OField @ D @ C ) @ C )
=> ( ( c_Relation_Oantisym @ D @ C )
=> ( ( c_member @ D @ B @ ( c_Relation_OField @ D @ C ) )
=> ( ( c_member @ D @ A @ ( c_Relation_OField @ D @ C ) )
=> ( ( ( ( c_Relation_OImage @ D @ D @ C @ ( c_Set_Oinsert @ D @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) )
= ( c_Relation_OImage @ D @ D @ C @ ( c_Set_Oinsert @ D @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( c_Relation_OImage @ D @ D @ C @ ( c_Set_Oinsert @ D @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) )
= ( c_Relation_OImage @ D @ D @ C @ ( c_Set_Oinsert @ D @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(113,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) )
= ( c_Equiv__Relations_Oquotient @ C @ B @ A ) )
<=> ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_quotient__is__empty2) ).
thf(837,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) )
= ( c_Equiv__Relations_Oquotient @ C @ B @ A ) )
=> ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) )
& ( ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) )
= ( c_Equiv__Relations_Oquotient @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(216,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Order__Relation_Olinear__order__on @ C @ B @ A )
<=> ( ( c_Order__Relation_Opartial__order__on @ C @ B @ A )
& ( c_Relation_Ototal__on @ C @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linear__order__on__def) ).
thf(1150,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Order__Relation_Olinear__order__on @ C @ B @ A )
=> ( ( c_Order__Relation_Opartial__order__on @ C @ B @ A )
& ( c_Relation_Ototal__on @ C @ B @ A ) ) )
& ( ( ( c_Order__Relation_Opartial__order__on @ C @ B @ A )
& ( c_Relation_Ototal__on @ C @ B @ A ) )
=> ( c_Order__Relation_Olinear__order__on @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(242,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Olattice @ D )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Lattices_Osemilattice__sup__class_Osup @ D @ C @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D @ B @ A ) ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D @ ( c_Lattices_Osemilattice__sup__class_Osup @ D @ C @ B ) @ ( c_Lattices_Osemilattice__sup__class_Osup @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distrib__sup__le) ).
thf(1249,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Olattice @ D )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Lattices_Osemilattice__sup__class_Osup @ D @ C @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D @ B @ A ) ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D @ ( c_Lattices_Osemilattice__sup__class_Osup @ D @ C @ B ) @ ( c_Lattices_Osemilattice__sup__class_Osup @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(427,axiom,
! [A: $i,B: $i] :
( ( c_member @ ( tc_prod @ B @ B ) @ A @ ( c_Relation_OId @ B ) )
=> ~ ! [C: $i] :
( A
!= ( c_Product__Type_OPair @ B @ B @ C @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_IdE) ).
thf(2052,plain,
! [A: $i,B: $i] :
( ( c_member @ ( tc_prod @ B @ B ) @ A @ ( c_Relation_OId @ B ) )
=> ~ ! [C: $i] :
( A
!= ( c_Product__Type_OPair @ B @ B @ C @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(241,axiom,
! [A: $i,B: $i] :
( ( c_Transitive__Closure_Otrancl @ B @ ( c_Transitive__Closure_Ortrancl @ B @ A ) )
= ( c_Transitive__Closure_Ortrancl @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__trancl__absorb) ).
thf(1246,plain,
! [A: $i,B: $i] :
( ( c_Transitive__Closure_Otrancl @ B @ ( c_Transitive__Closure_Ortrancl @ B @ A ) )
= ( c_Transitive__Closure_Ortrancl @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(401,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ B @ A )
=> ( ( c_Relation_Osingle__valued @ D @ C @ A )
=> ( c_Relation_Osingle__valued @ D @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_single__valued__subset) ).
thf(1979,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ B @ A )
=> ( ( c_Relation_Osingle__valued @ D @ C @ A )
=> ( c_Relation_Osingle__valued @ D @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(97,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Olattice @ D )
=> ( ( c_Lattices_Osemilattice__inf__class_Oinf @ D @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D @ C @ B ) @ A )
= ( c_Lattices_Osemilattice__inf__class_Oinf @ D @ C @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__aci_I2_J) ).
thf(779,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Olattice @ D )
=> ( ( c_Lattices_Osemilattice__inf__class_Oinf @ D @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D @ C @ B ) @ A )
= ( c_Lattices_Osemilattice__inf__class_Oinf @ D @ C @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(232,axiom,
! [A: $i,B: $i] :
( ( c_Transitive__Closure_Ortrancl @ B @ ( c_Transitive__Closure_Ortrancl @ B @ A ) )
= ( c_Transitive__Closure_Ortrancl @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__idemp) ).
thf(1202,plain,
! [A: $i,B: $i] :
( ( c_Transitive__Closure_Ortrancl @ B @ ( c_Transitive__Closure_Ortrancl @ B @ A ) )
= ( c_Transitive__Closure_Ortrancl @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(198,axiom,
! [A: $i,B: $i,C: $i] : ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ ( c_Set_Oinsert @ C @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__insertI) ).
thf(1086,plain,
! [A: $i,B: $i,C: $i] : ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ ( c_Set_Oinsert @ C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(49,axiom,
! [A: $i,B: $i] : ( c_Relation_Oantisym @ B @ ( c_Relation_OId__on @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_antisym__Id__on) ).
thf(633,plain,
! [A: $i,B: $i] : ( c_Relation_Oantisym @ B @ ( c_Relation_OId__on @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(424,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ D @ C @ ( c_Relation_ORange @ B @ D @ A ) )
=> ~ ! [E: $i] :
~ ( c_member @ ( tc_prod @ B @ D ) @ ( c_Product__Type_OPair @ B @ D @ E @ C ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_RangeE) ).
thf(2043,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ D @ C @ ( c_Relation_ORange @ B @ D @ A ) )
=> ~ ! [E: $i] :
~ ( c_member @ ( tc_prod @ B @ D ) @ ( c_Product__Type_OPair @ B @ D @ E @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(188,axiom,
! [A: $i,B: $i] :
( ( c_Wellfounded_Oacyclic @ B @ ( c_Relation_Oconverse @ B @ B @ A ) )
<=> ( c_Wellfounded_Oacyclic @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acyclic__converse) ).
thf(1054,plain,
! [A: $i,B: $i] :
( ( ( c_Wellfounded_Oacyclic @ B @ ( c_Relation_Oconverse @ B @ B @ A ) )
=> ( c_Wellfounded_Oacyclic @ B @ A ) )
& ( ( c_Wellfounded_Oacyclic @ B @ A )
=> ( c_Wellfounded_Oacyclic @ B @ ( c_Relation_Oconverse @ B @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(222,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Lattices_Osemilattice__sup @ E )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Lattices_Osemilattice__sup__class_Osup @ E @ D @ B ) @ ( c_Lattices_Osemilattice__sup__class_Osup @ E @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__mono) ).
thf(1170,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Lattices_Osemilattice__sup @ E )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Lattices_Osemilattice__sup__class_Osup @ E @ D @ B ) @ ( c_Lattices_Osemilattice__sup__class_Osup @ E @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(193,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Equiv__Relations_Oequiv @ E @ D @ C )
=> ( ( c_member @ ( tc_fun @ E @ tc_HOL_Obool ) @ B @ ( c_Equiv__Relations_Oquotient @ E @ D @ C ) )
=> ( ( c_member @ ( tc_fun @ E @ tc_HOL_Obool ) @ A @ ( c_Equiv__Relations_Oquotient @ E @ D @ C ) )
=> ( ( B = A )
| ( ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) @ B @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_quotient__disj) ).
thf(1071,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Equiv__Relations_Oequiv @ E @ D @ C )
=> ( ( c_member @ ( tc_fun @ E @ tc_HOL_Obool ) @ B @ ( c_Equiv__Relations_Oquotient @ E @ D @ C ) )
=> ( ( c_member @ ( tc_fun @ E @ tc_HOL_Obool ) @ A @ ( c_Equiv__Relations_Oquotient @ E @ D @ C ) )
=> ( ( B = A )
| ( ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) @ B @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(337,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Relation_Osingle__valued @ F @ E @ D )
=> ( ( c_member @ ( tc_prod @ F @ E ) @ ( c_Product__Type_OPair @ F @ E @ C @ B ) @ D )
=> ( ( c_member @ ( tc_prod @ F @ E ) @ ( c_Product__Type_OPair @ F @ E @ C @ A ) @ D )
=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_single__valuedD) ).
thf(1663,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Relation_Osingle__valued @ F @ E @ D )
=> ( ( c_member @ ( tc_prod @ F @ E ) @ ( c_Product__Type_OPair @ F @ E @ C @ B ) @ D )
=> ( ( c_member @ ( tc_prod @ F @ E ) @ ( c_Product__Type_OPair @ F @ E @ C @ A ) @ D )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(299,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Equiv__Relations_Oequiv @ E @ D @ C )
=> ( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ B @ A ) @ C )
<=> ( ( ( c_Relation_OImage @ E @ E @ C @ ( c_Set_Oinsert @ E @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) )
= ( c_Relation_OImage @ E @ E @ C @ ( c_Set_Oinsert @ E @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) ) )
& ( c_member @ E @ B @ D )
& ( c_member @ E @ A @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equiv__class__eq__iff) ).
thf(1515,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Equiv__Relations_Oequiv @ E @ D @ C )
=> ( ( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ B @ A ) @ C )
=> ( ( ( c_Relation_OImage @ E @ E @ C @ ( c_Set_Oinsert @ E @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) )
= ( c_Relation_OImage @ E @ E @ C @ ( c_Set_Oinsert @ E @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) ) )
& ( c_member @ E @ B @ D )
& ( c_member @ E @ A @ D ) ) )
& ( ( ( ( c_Relation_OImage @ E @ E @ C @ ( c_Set_Oinsert @ E @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) )
= ( c_Relation_OImage @ E @ E @ C @ ( c_Set_Oinsert @ E @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) ) )
& ( c_member @ E @ B @ D )
& ( c_member @ E @ A @ D ) )
=> ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ B @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(221,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Relation_OImage @ E @ D @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) @ B @ A ) )
= ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Relation_OImage @ E @ D @ C @ B ) @ ( c_Relation_OImage @ E @ D @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__Un) ).
thf(1167,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Relation_OImage @ E @ D @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) @ B @ A ) )
= ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Relation_OImage @ E @ D @ C @ B ) @ ( c_Relation_OImage @ E @ D @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( class_Lattices_Osemilattice__inf @ B )
=> ( ( c_Lattices_Osemilattice__inf__class_Oinf @ B @ A @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf_Oidem) ).
thf(530,plain,
! [A: $i,B: $i] :
( ( class_Lattices_Osemilattice__inf @ B )
=> ( ( c_Lattices_Osemilattice__inf__class_Oinf @ B @ A @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(226,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__sup @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( ( c_Lattices_Osemilattice__sup__class_Osup @ C @ A @ B )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__absorb1) ).
thf(1185,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__sup @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( ( c_Lattices_Osemilattice__sup__class_Osup @ C @ A @ B )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(357,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_member @ ( tc_prod @ F @ F ) @ ( c_Product__Type_OPair @ F @ F @ E @ D ) @ ( c_Relation_Oinv__image @ C @ F @ B @ A ) )
<=> ( c_member @ ( tc_prod @ C @ C ) @ ( c_Product__Type_OPair @ C @ C @ ( hAPP @ A @ E ) @ ( hAPP @ A @ D ) ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__inv__image) ).
thf(1732,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( c_member @ ( tc_prod @ F @ F ) @ ( c_Product__Type_OPair @ F @ F @ E @ D ) @ ( c_Relation_Oinv__image @ C @ F @ B @ A ) )
=> ( c_member @ ( tc_prod @ C @ C ) @ ( c_Product__Type_OPair @ C @ C @ ( hAPP @ A @ E ) @ ( hAPP @ A @ D ) ) @ B ) )
& ( ( c_member @ ( tc_prod @ C @ C ) @ ( c_Product__Type_OPair @ C @ C @ ( hAPP @ A @ E ) @ ( hAPP @ A @ D ) ) @ B )
=> ( c_member @ ( tc_prod @ F @ F ) @ ( c_Product__Type_OPair @ F @ F @ E @ D ) @ ( c_Relation_Oinv__image @ C @ F @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(287,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E != D )
=> ( ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ C @ c_Arrow__Order__Mirabelle_OLin )
=> ( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ B @ A ) @ ( c_Arrow__Order__Mirabelle_Obelow @ C @ E @ D ) )
<=> ( ( B != A )
& ( ( A = E )
=> ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ B @ D ) @ C ) )
& ( ( A != E )
=> ( ( ( B = E )
=> ( ( A = D )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ D @ A ) @ C ) ) )
& ( ( B != E )
=> ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ B @ A ) @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__below) ).
thf(1434,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E != D )
=> ( ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ C @ c_Arrow__Order__Mirabelle_OLin )
=> ( ( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ B @ A ) @ ( c_Arrow__Order__Mirabelle_Obelow @ C @ E @ D ) )
=> ( ( B != A )
& ( ( A = E )
=> ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ B @ D ) @ C ) )
& ( ( A != E )
=> ( ( ( B = E )
=> ( ( A = D )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ D @ A ) @ C ) ) )
& ( ( B != E )
=> ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ B @ A ) @ C ) ) ) ) ) )
& ( ( ( B != A )
& ( ( A = E )
=> ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ B @ D ) @ C ) )
& ( ( A != E )
=> ( ( ( B = E )
=> ( ( A = D )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ D @ A ) @ C ) ) )
& ( ( B != E )
=> ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ B @ A ) @ C ) ) ) ) )
=> ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ B @ A ) @ ( c_Arrow__Order__Mirabelle_Obelow @ C @ E @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(377,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Lattices_Olattice @ E )
=> ( ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ E ) @ C @ B ) @ A )
= ( c_Lattices_Osemilattice__sup__class_Osup @ E @ ( hAPP @ C @ A ) @ ( hAPP @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__apply) ).
thf(1857,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Lattices_Olattice @ E )
=> ( ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ E ) @ C @ B ) @ A )
= ( c_Lattices_Osemilattice__sup__class_Osup @ E @ ( hAPP @ C @ A ) @ ( hAPP @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(252,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Transitive__Closure_Ortrancl @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ A ) ) )
= ( c_Transitive__Closure_Ortrancl @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__Un__rtrancl) ).
thf(1286,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Transitive__Closure_Ortrancl @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ A ) ) )
= ( c_Transitive__Closure_Ortrancl @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(181,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ D @ C @ B )
=> ( ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ ( c_Set_Oinsert @ D @ C @ A ) )
= ( c_Set_Oinsert @ D @ C @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__insert__right__if1) ).
thf(1035,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ D @ C @ B )
=> ( ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ ( c_Set_Oinsert @ D @ C @ A ) )
= ( c_Set_Oinsert @ D @ C @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(455,axiom,
! [A: $i,B: $i,C: $i] :
( ! [D: $i,E: $i] :
( ( c_member @ ( tc_prod @ C @ B ) @ ( c_Product__Type_OPair @ C @ B @ D @ E ) @ A )
=> ! [F: $i] :
( ( c_member @ ( tc_prod @ C @ B ) @ ( c_Product__Type_OPair @ C @ B @ D @ F ) @ A )
=> ( E = F ) ) )
=> ( c_Relation_Osingle__valued @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_single__valuedI) ).
thf(2189,plain,
! [A: $i,B: $i,C: $i] :
( ! [D: $i,E: $i] :
( ( c_member @ ( tc_prod @ C @ B ) @ ( c_Product__Type_OPair @ C @ B @ D @ E ) @ A )
=> ! [F: $i] :
( ( c_member @ ( tc_prod @ C @ B ) @ ( c_Product__Type_OPair @ C @ B @ D @ F ) @ A )
=> ( E = F ) ) )
=> ( c_Relation_Osingle__valued @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(324,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Relation_Orefl__on @ E @ D @ C )
=> ( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ B @ A ) @ C )
=> ( c_member @ E @ B @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_refl__onD1) ).
thf(1616,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Relation_Orefl__on @ E @ D @ C )
=> ( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ B @ A ) @ C )
=> ( c_member @ E @ B @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(95,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Olattice @ D )
=> ( ( c_Lattices_Osemilattice__inf__class_Oinf @ D @ C @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D @ B @ A ) )
= ( c_Lattices_Osemilattice__inf__class_Oinf @ D @ B @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__aci_I3_J) ).
thf(773,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Olattice @ D )
=> ( ( c_Lattices_Osemilattice__inf__class_Oinf @ D @ C @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D @ B @ A ) )
= ( c_Lattices_Osemilattice__inf__class_Oinf @ D @ B @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(31,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Odistrib__lattice @ D )
=> ( ( c_Lattices_Osemilattice__inf__class_Oinf @ D @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ D @ B @ A ) )
= ( c_Lattices_Osemilattice__sup__class_Osup @ D @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D @ C @ B ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__distrib1) ).
thf(586,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Odistrib__lattice @ D )
=> ( ( c_Lattices_Osemilattice__inf__class_Oinf @ D @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ D @ B @ A ) )
= ( c_Lattices_Osemilattice__sup__class_Osup @ D @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D @ C @ B ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(490,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_member @ ( tc_prod @ F @ F ) @ ( c_Product__Type_OPair @ F @ F @ E @ D ) @ C )
=> ( ( hAPP @ ( c_Recdef_Ocut @ F @ B @ A @ C @ D ) @ E )
= ( hAPP @ A @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_cut__apply) ).
thf(2338,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_member @ ( tc_prod @ F @ F ) @ ( c_Product__Type_OPair @ F @ F @ E @ D ) @ C )
=> ( ( hAPP @ ( c_Recdef_Ocut @ F @ B @ A @ C @ D ) @ E )
= ( hAPP @ A @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).
thf(409,axiom,
! [A: $i] : ( c_Wellfounded_Owf @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__empty) ).
thf(1996,plain,
! [A: $i] : ( c_Wellfounded_Owf @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(510,axiom,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] :
( ( c_member @ ( tc_prod @ C @ C ) @ ( c_Product__Type_OPair @ C @ C @ D @ B ) @ A )
=> ( c_member @ C @ D @ ( c_Wellfounded_Oacc @ C @ A ) ) )
=> ( c_member @ C @ B @ ( c_Wellfounded_Oacc @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acc_OaccI) ).
thf(2423,plain,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] :
( ( c_member @ ( tc_prod @ C @ C ) @ ( c_Product__Type_OPair @ C @ C @ D @ B ) @ A )
=> ( c_member @ C @ D @ ( c_Wellfounded_Oacc @ C @ A ) ) )
=> ( c_member @ C @ B @ ( c_Wellfounded_Oacc @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).
thf(58,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Olattice @ D )
=> ( ( c_Lattices_Osemilattice__sup__class_Osup @ D @ ( c_Lattices_Osemilattice__sup__class_Osup @ D @ C @ B ) @ A )
= ( c_Lattices_Osemilattice__sup__class_Osup @ D @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ D @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__aci_I6_J) ).
thf(662,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Olattice @ D )
=> ( ( c_Lattices_Osemilattice__sup__class_Osup @ D @ ( c_Lattices_Osemilattice__sup__class_Osup @ D @ C @ B ) @ A )
= ( c_Lattices_Osemilattice__sup__class_Osup @ D @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ D @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(77,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A )
= ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__commute) ).
thf(718,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A )
= ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(453,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ D @ C @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) )
=> ~ ( ( c_member @ D @ C @ B )
=> ~ ( c_member @ D @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_IntE) ).
thf(2176,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ D @ C @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) )
=> ~ ( ( c_member @ D @ C @ B )
=> ~ ( c_member @ D @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(350,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ C ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) )
=> ( ( hBOOL @ ( hAPP @ A @ C ) )
=> ( ! [F: $i,G: $i] :
( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ F @ G ) @ B )
=> ( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ G @ C ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) )
=> ( ( hBOOL @ ( hAPP @ A @ G ) )
=> ( hBOOL @ ( hAPP @ A @ F ) ) ) ) )
=> ( hBOOL @ ( hAPP @ A @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converse__rtrancl__induct) ).
thf(1698,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ C ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) )
=> ( ( hBOOL @ ( hAPP @ A @ C ) )
=> ( ! [F: $i,G: $i] :
( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ F @ G ) @ B )
=> ( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ G @ C ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) )
=> ( ( hBOOL @ ( hAPP @ A @ G ) )
=> ( hBOOL @ ( hAPP @ A @ F ) ) ) ) )
=> ( hBOOL @ ( hAPP @ A @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(420,axiom,
v_a_H____ != v_b_H____,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_A_I2_J) ).
thf(2033,plain,
v_a_H____ != v_b_H____,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(108,axiom,
! [A: $i,B: $i,C: $i] : ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__lower2) ).
thf(824,plain,
! [A: $i,B: $i,C: $i] : ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(247,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Equiv__Relations_Oequiv @ D @ C @ B )
=> ( ( c_member @ D @ A @ C )
=> ( c_member @ D @ A @ ( c_Relation_OImage @ D @ D @ B @ ( c_Set_Oinsert @ D @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equiv__class__self) ).
thf(1273,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Equiv__Relations_Oequiv @ D @ C @ B )
=> ( ( c_member @ D @ A @ C )
=> ( c_member @ D @ A @ ( c_Relation_OImage @ D @ D @ B @ ( c_Set_Oinsert @ D @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(305,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ C ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) )
=> ( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ C @ A ) @ B )
=> ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ A ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Transitive__Closure_Otrancl__into__trancl) ).
thf(1548,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ C ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) )
=> ( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ C @ A ) @ B )
=> ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ A ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(118,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Wellfounded_Owf @ D @ C )
=> ( c_Wellfounded_Owf @ B @ ( c_Relation_Oinv__image @ D @ B @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__inv__image) ).
thf(856,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Wellfounded_Owf @ D @ C )
=> ( c_Wellfounded_Owf @ B @ ( c_Relation_Oinv__image @ D @ B @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(26,axiom,
class_Lattices_Obounded__lattice__bot @ tc_HOL_Obool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Obounded__lattice__bot) ).
thf(573,plain,
class_Lattices_Obounded__lattice__bot @ tc_HOL_Obool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(66,axiom,
! [A: $i,B: $i] :
( ( class_Lattices_Obounded__lattice__bot @ B )
=> ( ( c_Lattices_Osemilattice__inf__class_Oinf @ B @ ( c_Orderings_Obot__class_Obot @ B ) @ A )
= ( c_Orderings_Obot__class_Obot @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__bot__left) ).
thf(689,plain,
! [A: $i,B: $i] :
( ( class_Lattices_Obounded__lattice__bot @ B )
=> ( ( c_Lattices_Osemilattice__inf__class_Oinf @ B @ ( c_Orderings_Obot__class_Obot @ B ) @ A )
= ( c_Orderings_Obot__class_Obot @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(498,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B )
=> ( ( hBOOL @ ( hAPP @ C @ A ) )
=> ( hBOOL @ ( hAPP @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_predicate1D) ).
thf(2376,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B )
=> ( ( hBOOL @ ( hAPP @ C @ A ) )
=> ( hBOOL @ ( hAPP @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).
thf(328,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ D @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ B @ tc_HOL_Obool ) @ A @ D ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup1I2) ).
thf(1631,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ D @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ B @ tc_HOL_Obool ) @ A @ D ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(156,axiom,
! [A: $i,B: $i] :
( ( class_Orderings_Obot @ B )
=> ( class_Orderings_Obot @ ( tc_fun @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Orderings_Obot) ).
thf(965,plain,
! [A: $i,B: $i] :
( ( class_Orderings_Obot @ B )
=> ( class_Orderings_Obot @ ( tc_fun @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(88,axiom,
! [A: $i,B: $i] :
( ( c_Wellfounded_Owf @ B @ A )
=> ( c_Wellfounded_Oacyclic @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__acyclic) ).
thf(750,plain,
! [A: $i,B: $i] :
( ( c_Wellfounded_Owf @ B @ A )
=> ( c_Wellfounded_Oacyclic @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(355,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Wellfounded_Owf @ D @ C )
=> ( ( c_Wellfounded_Owf @ B @ A )
=> ( c_Wellfounded_Owf @ ( tc_prod @ D @ B ) @ ( c_Wellfounded_Olex__prod @ D @ B @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__lex__prod) ).
thf(1727,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Wellfounded_Owf @ D @ C )
=> ( ( c_Wellfounded_Owf @ B @ A )
=> ( c_Wellfounded_Owf @ ( tc_prod @ D @ B ) @ ( c_Wellfounded_Olex__prod @ D @ B @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(243,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
<=> ! [D: $i] :
( ( c_member @ C @ D @ B )
=> ! [E: $i] :
( ( c_member @ C @ E @ A )
=> ( D != E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_disjoint__iff__not__equal) ).
thf(1251,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ! [D: $i] :
( ( c_member @ C @ D @ B )
=> ! [E: $i] :
( ( c_member @ C @ E @ A )
=> ( D != E ) ) ) )
& ( ! [D: $i] :
( ( c_member @ C @ D @ B )
=> ! [E: $i] :
( ( c_member @ C @ E @ A )
=> ( D != E ) ) )
=> ( ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(45,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__sup @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Lattices_Osemilattice__sup__class_Osup @ D @ C @ B ) @ A )
<=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ A )
& ( c_Orderings_Oord__class_Oless__eq @ D @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__sup__iff) ).
thf(618,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__sup @ D )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Lattices_Osemilattice__sup__class_Osup @ D @ C @ B ) @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ A )
& ( c_Orderings_Oord__class_Oless__eq @ D @ B @ A ) ) )
& ( ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ A )
& ( c_Orderings_Oord__class_Oless__eq @ D @ B @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Lattices_Osemilattice__sup__class_Osup @ D @ C @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(418,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ D @ C @ ( c_Wellfounded_Oacc @ D @ B ) )
=> ( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ A @ C ) @ B )
=> ( c_member @ D @ A @ ( c_Wellfounded_Oacc @ D @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acc__downward) ).
thf(2028,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ D @ C @ ( c_Wellfounded_Oacc @ D @ B ) )
=> ( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ A @ C ) @ B )
=> ( c_member @ D @ A @ ( c_Wellfounded_Oacc @ D @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(257,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf1D1) ).
thf(1301,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(21,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__sup @ D )
=> ( ( c_Lattices_Osemilattice__sup__class_Osup @ D @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ D @ B @ A ) )
= ( c_Lattices_Osemilattice__sup__class_Osup @ D @ B @ ( c_Lattices_Osemilattice__sup__class_Osup @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__left__commute) ).
thf(562,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__sup @ D )
=> ( ( c_Lattices_Osemilattice__sup__class_Osup @ D @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ D @ B @ A ) )
= ( c_Lattices_Osemilattice__sup__class_Osup @ D @ B @ ( c_Lattices_Osemilattice__sup__class_Osup @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(426,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F
= ( c_Recdef_Owfrec @ E @ D @ C @ B ) )
=> ( ( c_Wellfounded_Owf @ E @ C )
=> ( ( hAPP @ F @ A )
= ( hAPP @ ( hAPP @ B @ ( c_Recdef_Ocut @ E @ D @ F @ C @ A ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_def__wfrec) ).
thf(2048,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F
= ( c_Recdef_Owfrec @ E @ D @ C @ B ) )
=> ( ( c_Wellfounded_Owf @ E @ C )
=> ( ( hAPP @ F @ A )
= ( hAPP @ ( hAPP @ B @ ( c_Recdef_Ocut @ E @ D @ F @ C @ A ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(414,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_member @ F @ E @ D )
=> ( ( c_member @ ( tc_prod @ F @ C ) @ ( c_Product__Type_OPair @ F @ C @ E @ B ) @ A )
=> ( c_member @ C @ B @ ( c_Relation_OImage @ F @ C @ A @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rev__ImageI) ).
thf(2016,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_member @ F @ E @ D )
=> ( ( c_member @ ( tc_prod @ F @ C ) @ ( c_Product__Type_OPair @ F @ C @ E @ B ) @ A )
=> ( c_member @ C @ B @ ( c_Relation_OImage @ F @ C @ A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(275,axiom,
! [A: $i] : ( c_Relation_Oantisym @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_antisym__empty) ).
thf(1388,plain,
! [A: $i] : ( c_Relation_Oantisym @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(153,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Relation_ORange @ C @ B @ ( c_Relation_Oconverse @ B @ C @ A ) )
= ( c_Relation_ODomain @ B @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Range__converse) ).
thf(958,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Relation_ORange @ C @ B @ ( c_Relation_Oconverse @ B @ C @ A ) )
= ( c_Relation_ODomain @ B @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(210,axiom,
! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__refl) ).
thf(1124,plain,
! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(465,axiom,
! [A: $i] :
( ( c_Relation_OId__on @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Id__on__empty) ).
thf(2225,plain,
! [A: $i] :
( ( c_Relation_OId__on @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(82,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Relation_Orefl__on @ C @ B @ ( c_Relation_Oconverse @ C @ C @ A ) )
<=> ( c_Relation_Orefl__on @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_refl__on__converse) ).
thf(732,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Relation_Orefl__on @ C @ B @ ( c_Relation_Oconverse @ C @ C @ A ) )
=> ( c_Relation_Orefl__on @ C @ B @ A ) )
& ( ( c_Relation_Orefl__on @ C @ B @ A )
=> ( c_Relation_Orefl__on @ C @ B @ ( c_Relation_Oconverse @ C @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(124,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Set_Oinsert @ C @ B @ A )
= ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( c_Set_Oinsert @ C @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__is__Un) ).
thf(875,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Set_Oinsert @ C @ B @ A )
= ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( c_Set_Oinsert @ C @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(109,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( c_member @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ ( c_Set_Oinsert @ D @ C @ A ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__insert) ).
thf(826,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( c_member @ D @ C @ B )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ ( c_Set_Oinsert @ D @ C @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ ( c_Set_Oinsert @ D @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(28,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__inf @ C )
=> ( ( c_Lattices_Osemilattice__inf__class_Oinf @ C @ B @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C @ B @ A ) )
= ( c_Lattices_Osemilattice__inf__class_Oinf @ C @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf_Oleft__idem) ).
thf(577,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__inf @ C )
=> ( ( c_Lattices_Osemilattice__inf__class_Oinf @ C @ B @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C @ B @ A ) )
= ( c_Lattices_Osemilattice__inf__class_Oinf @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(75,axiom,
! [A: $i] : ( c_Relation_Osingle__valued @ A @ A @ ( c_Relation_OId @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_single__valued__Id) ).
thf(711,plain,
! [A: $i] : ( c_Relation_Osingle__valued @ A @ A @ ( c_Relation_OId @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(236,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B ) @ A )
= ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__assoc) ).
thf(1226,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B ) @ A )
= ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(14,axiom,
class_Lattices_Odistrib__lattice @ tc_HOL_Obool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Odistrib__lattice) ).
thf(545,plain,
class_Lattices_Odistrib__lattice @ tc_HOL_Obool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(285,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ B ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) )
=> ? [E: $i] :
( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ E ) @ A )
& ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ E @ B ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_tranclD) ).
thf(1428,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ B ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) )
=> ? [E: $i] :
( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ E ) @ A )
& ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ E @ B ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(339,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ B ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) )
=> ( ~ ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ B ) @ A )
=> ~ ! [E: $i] :
( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ E ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) )
=> ~ ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ E @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_tranclE) ).
thf(1669,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ B ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) )
=> ( ~ ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ B ) @ A )
=> ~ ! [E: $i] :
( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ E ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) )
=> ~ ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ E @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(76,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Relation_Ototal__on @ C @ B @ ( c_Relation_Oconverse @ C @ C @ A ) )
<=> ( c_Relation_Ototal__on @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_total__on__converse) ).
thf(713,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Relation_Ototal__on @ C @ B @ ( c_Relation_Oconverse @ C @ C @ A ) )
=> ( c_Relation_Ototal__on @ C @ B @ A ) )
& ( ( c_Relation_Ototal__on @ C @ B @ A )
=> ( c_Relation_Ototal__on @ C @ B @ ( c_Relation_Oconverse @ C @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(240,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_member @ C @ B @ ( c_Set_Oinsert @ C @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_singleton__iff) ).
thf(1239,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_member @ C @ B @ ( c_Set_Oinsert @ C @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) )
=> ( B = A ) )
& ( ( B = A )
=> ( c_member @ C @ B @ ( c_Set_Oinsert @ C @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(200,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A ) @ A )
= ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__idemp) ).
thf(1090,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A ) @ A )
= ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(103,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oord @ D )
=> ( ( C = B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ord__eq__le__trans) ).
thf(804,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Orderings_Oord @ D )
=> ( ( C = B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(493,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ C ) @ B )
=> ( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ C @ A ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) )
=> ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ A ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converse__rtrancl__into__rtrancl) ).
thf(2346,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ C ) @ B )
=> ( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ C @ A ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) )
=> ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ A ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).
thf(437,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ B ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) )
=> ( ~ ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ B ) @ A )
=> ~ ! [E: $i] :
( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ E ) @ A )
=> ~ ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ E @ B ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converse__tranclE) ).
thf(2119,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ B ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) )
=> ( ~ ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ B ) @ A )
=> ~ ! [E: $i] :
( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ E ) @ A )
=> ~ ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ E @ B ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(134,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B ) @ A )
= ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ A ) @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__Int__distrib2) ).
thf(900,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B ) @ A )
= ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ A ) @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(111,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Relation_Oconverse @ D @ D @ ( c_Relation_Oinv__image @ C @ D @ B @ A ) )
= ( c_Relation_Oinv__image @ C @ D @ ( c_Relation_Oconverse @ C @ C @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converse__inv__image) ).
thf(831,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Relation_Oconverse @ D @ D @ ( c_Relation_Oinv__image @ C @ D @ B @ A ) )
= ( c_Relation_Oinv__image @ C @ D @ ( c_Relation_Oconverse @ C @ C @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(500,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Wellfounded_Owf @ C @ B )
=> ( c_member @ C @ A @ ( c_Wellfounded_Oacc @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acc__wfD) ).
thf(2383,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Wellfounded_Owf @ C @ B )
=> ( c_member @ C @ A @ ( c_Wellfounded_Oacc @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).
thf(387,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Wellfounded_Owf @ D @ C )
=> ( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ B @ A ) @ C )
=> ~ ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ A @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__asym) ).
thf(1894,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Wellfounded_Owf @ D @ C )
=> ( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ B @ A ) @ C )
=> ~ ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ A @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(301,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( c_member @ D @ C @ ( c_Relation_ODomain @ D @ D @ B ) )
=> ( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ A ) @ ( c_Transitive__Closure_Ortrancl @ D @ B ) )
<=> ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Not__Domain__rtrancl) ).
thf(1524,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( c_member @ D @ C @ ( c_Relation_ODomain @ D @ D @ B ) )
=> ( ( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ A ) @ ( c_Transitive__Closure_Ortrancl @ D @ B ) )
=> ( C = A ) )
& ( ( C = A )
=> ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ A ) @ ( c_Transitive__Closure_Ortrancl @ D @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(83,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Odistrib__lattice @ D )
=> ( ( c_Lattices_Osemilattice__inf__class_Oinf @ D @ ( c_Lattices_Osemilattice__sup__class_Osup @ D @ C @ B ) @ A )
= ( c_Lattices_Osemilattice__sup__class_Osup @ D @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D @ C @ A ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__distrib2) ).
thf(737,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Odistrib__lattice @ D )
=> ( ( c_Lattices_Osemilattice__inf__class_Oinf @ D @ ( c_Lattices_Osemilattice__sup__class_Osup @ D @ C @ B ) @ A )
= ( c_Lattices_Osemilattice__sup__class_Osup @ D @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D @ C @ A ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(457,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Relation_ODomain @ D @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ B @ A ) )
= ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Relation_ODomain @ D @ C @ B ) @ ( c_Relation_ODomain @ D @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Domain__Un__eq) ).
thf(2197,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Relation_ODomain @ D @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ B @ A ) )
= ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Relation_ODomain @ D @ C @ B ) @ ( c_Relation_ODomain @ D @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(516,plain,
( ~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a_H____ @ v_b_H____ ) @ ( hAPP @ v_F @ v_P_H____ ) )
| ~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a____ @ v_b____ ) @ ( hAPP @ v_F @ v_P____ ) ) ),
inference(cnf,[status(esa)],[512]) ).
thf(2461,plain,
( ( ( hAPP @ v_F @ v_P_H____ )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) )
| ~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a_H____ @ v_b_H____ ) @ ( hAPP @ v_F @ v_P_H____ ) )
| ( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a____ @ v_b____ ) @ ( hAPP @ v_F @ v_P____ ) )
!= ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a____ @ v_b____ ) @ ( hAPP @ v_F @ v_P____ ) ) ) ),
inference(paramod_ordered,[status(thm)],[2457,516]) ).
thf(2462,plain,
( ( ( hAPP @ v_F @ v_P_H____ )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) )
| ~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a_H____ @ v_b_H____ ) @ ( hAPP @ v_F @ v_P_H____ ) ) ),
inference(pattern_uni,[status(thm)],[2461:[]]) ).
thf(2485,plain,
( ( ( hAPP @ v_F @ v_P_H____ )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) )
| ( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a_H____ @ v_b_H____ ) @ ( hAPP @ v_F @ v_P_H____ ) )
!= ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a____ @ v_b____ ) @ ( hAPP @ v_F @ v_P____ ) ) ) ),
inference(paramod_ordered,[status(thm)],[2457,2462]) ).
thf(2488,plain,
( ( ( hAPP @ v_F @ v_P_H____ )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) )
| ( ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt )
!= ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a_H____ @ v_b_H____ )
!= ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a____ @ v_b____ ) )
| ( ( hAPP @ v_F @ v_P_H____ )
!= ( hAPP @ v_F @ v_P____ ) ) ),
inference(simp,[status(thm)],[2485]) ).
thf(2489,plain,
( ( ( hAPP @ v_F @ v_P_H____ )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) )
| ( ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a_H____ @ v_b_H____ )
!= ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a____ @ v_b____ ) )
| ( ( hAPP @ v_F @ v_P_H____ )
!= ( hAPP @ v_F @ v_P____ ) ) ),
inference(simp,[status(thm)],[2488]) ).
thf(2491,plain,
( ( ( hAPP @ v_F @ v_P_H____ )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) )
| ( ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a_H____ @ v_b_H____ )
!= ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a____ @ v_b____ ) )
| ( v_F != v_F )
| ( v_P_H____ != v_P____ ) ),
inference(simp,[status(thm)],[2489]) ).
thf(2494,plain,
( ( ( hAPP @ v_F @ v_P_H____ )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) )
| ( ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a_H____ @ v_b_H____ )
!= ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a____ @ v_b____ ) )
| ( v_P_H____ != v_P____ ) ),
inference(simp,[status(thm)],[2491]) ).
thf(2510,plain,
( ( ( hAPP @ v_F @ v_P_H____ )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) )
| ( ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_b____ @ v_a____ )
!= ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a____ @ v_b____ ) )
| ( v_P_H____ != v_P____ ) ),
inference(rewrite,[status(thm)],[2494,2117,2118]) ).
thf(161,axiom,
! [A: $i,B: $i,C: $i] :
( ( C = B )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ A @ tc_HOL_Obool ) @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equalityD1) ).
thf(979,plain,
! [A: $i,B: $i,C: $i] :
( ( C = B )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ A @ tc_HOL_Obool ) @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(294,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i] :
( ( hBOOL @ ( hAPP @ D @ E ) )
=> ( c_Wellfounded_Owf @ C @ ( hAPP @ B @ E ) ) )
=> ( c_Wellfounded_Owf @ ( tc_prod @ A @ C ) @ ( c_Recdef_Osame__fst @ A @ C @ D @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__same__fst) ).
thf(1492,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i] :
( ( hBOOL @ ( hAPP @ D @ E ) )
=> ( c_Wellfounded_Owf @ C @ ( hAPP @ B @ E ) ) )
=> ( c_Wellfounded_Owf @ ( tc_prod @ A @ C ) @ ( c_Recdef_Osame__fst @ A @ C @ D @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(320,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( c_Equiv__Relations_Oequiv @ G @ F @ E )
=> ( ( c_member @ ( tc_fun @ G @ tc_HOL_Obool ) @ D @ ( c_Equiv__Relations_Oquotient @ G @ F @ E ) )
=> ( ( c_member @ ( tc_fun @ G @ tc_HOL_Obool ) @ C @ ( c_Equiv__Relations_Oquotient @ G @ F @ E ) )
=> ( ( c_member @ G @ B @ D )
=> ( ( c_member @ G @ A @ C )
=> ( ( D = C )
<=> ( c_member @ ( tc_prod @ G @ G ) @ ( c_Product__Type_OPair @ G @ G @ B @ A ) @ E ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_quotient__eq__iff) ).
thf(1603,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( c_Equiv__Relations_Oequiv @ G @ F @ E )
=> ( ( c_member @ ( tc_fun @ G @ tc_HOL_Obool ) @ D @ ( c_Equiv__Relations_Oquotient @ G @ F @ E ) )
=> ( ( c_member @ ( tc_fun @ G @ tc_HOL_Obool ) @ C @ ( c_Equiv__Relations_Oquotient @ G @ F @ E ) )
=> ( ( c_member @ G @ B @ D )
=> ( ( c_member @ G @ A @ C )
=> ( ( ( D = C )
=> ( c_member @ ( tc_prod @ G @ G ) @ ( c_Product__Type_OPair @ G @ G @ B @ A ) @ E ) )
& ( ( c_member @ ( tc_prod @ G @ G ) @ ( c_Product__Type_OPair @ G @ G @ B @ A ) @ E )
=> ( D = C ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(52,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Relation_OImage @ C @ C @ ( c_Relation_OId__on @ C @ B ) @ A )
= ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__Id__on) ).
thf(649,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Relation_OImage @ C @ C @ ( c_Relation_OId__on @ C @ B ) @ A )
= ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(184,axiom,
! [A: $i,B: $i] :
( ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ ( c_Transitive__Closure_Otrancl @ B @ A ) @ ( c_Relation_OId @ B ) )
= ( c_Transitive__Closure_Ortrancl @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_reflcl__trancl) ).
thf(1043,plain,
! [A: $i,B: $i] :
( ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ ( c_Transitive__Closure_Otrancl @ B @ A ) @ ( c_Relation_OId @ B ) )
= ( c_Transitive__Closure_Ortrancl @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(312,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Orderings_Oord @ E )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ E ) @ C @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ E @ ( hAPP @ C @ A ) @ ( hAPP @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__funD) ).
thf(1571,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Orderings_Oord @ E )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ E ) @ C @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ E @ ( hAPP @ C @ A ) @ ( hAPP @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(37,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__inf @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D @ B @ A ) )
<=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
& ( c_Orderings_Oord__class_Oless__eq @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__inf__iff) ).
thf(599,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__inf @ D )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D @ B @ A ) )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
& ( c_Orderings_Oord__class_Oless__eq @ D @ C @ A ) ) )
& ( ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
& ( c_Orderings_Oord__class_Oless__eq @ D @ C @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ C @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(129,axiom,
class_Orderings_Obot @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Obot) ).
thf(890,plain,
class_Orderings_Obot @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(105,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Olattice @ C )
=> ( ( c_Lattices_Osemilattice__inf__class_Oinf @ C @ B @ ( c_Lattices_Osemilattice__sup__class_Osup @ C @ B @ A ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__absorb) ).
thf(811,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Olattice @ C )
=> ( ( c_Lattices_Osemilattice__inf__class_Oinf @ C @ B @ ( c_Lattices_Osemilattice__sup__class_Osup @ C @ B @ A ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(289,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ B ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) )
=> ( ( C = B )
| ( ( C != B )
& ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ B ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtranclD) ).
thf(1471,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ B ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) )
=> ( ( C = B )
| ( ( C != B )
& ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ B ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(417,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Relation_ODomain @ E @ D @ ( c_Set_Oinsert @ ( tc_prod @ E @ D ) @ ( c_Product__Type_OPair @ E @ D @ C @ B ) @ A ) )
= ( c_Set_Oinsert @ E @ C @ ( c_Relation_ODomain @ E @ D @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Domain__insert) ).
thf(2025,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Relation_ODomain @ E @ D @ ( c_Set_Oinsert @ ( tc_prod @ E @ D ) @ ( c_Product__Type_OPair @ E @ D @ C @ B ) @ A ) )
= ( c_Set_Oinsert @ E @ C @ ( c_Relation_ODomain @ E @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(48,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Wellfounded_Owf @ C @ B )
=> ( c_Wellfounded_Owf @ C @ ( c_Wellfounded_Omlex__prod @ C @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__mlex) ).
thf(631,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Wellfounded_Owf @ C @ B )
=> ( c_Wellfounded_Owf @ C @ ( c_Wellfounded_Omlex__prod @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(119,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( c_Equiv__Relations_Oquotient @ C @ B @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) )
<=> ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_quotient__is__empty) ).
thf(858,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( c_Equiv__Relations_Oquotient @ C @ B @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) )
=> ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) )
& ( ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( c_Equiv__Relations_Oquotient @ C @ B @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(408,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_member @ ( tc_prod @ D @ D ) @ C @ ( c_Transitive__Closure_Ortrancl @ D @ B ) )
| ( c_member @ ( tc_prod @ D @ D ) @ C @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) )
=> ( c_member @ ( tc_prod @ D @ D ) @ C @ ( c_Transitive__Closure_Ortrancl @ D @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__rtrancl__UnI) ).
thf(1993,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_member @ ( tc_prod @ D @ D ) @ C @ ( c_Transitive__Closure_Ortrancl @ D @ B ) )
| ( c_member @ ( tc_prod @ D @ D ) @ C @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) )
=> ( c_member @ ( tc_prod @ D @ D ) @ C @ ( c_Transitive__Closure_Ortrancl @ D @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_HOL_Obool ) @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(34,axiom,
! [A: $i,B: $i,C: $i] : ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A ) @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__subset) ).
thf(594,plain,
! [A: $i,B: $i,C: $i] : ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(392,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( c_member @ ( tc_prod @ ( tc_prod @ G @ F ) @ ( tc_prod @ G @ F ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ G @ F ) @ ( tc_prod @ G @ F ) @ ( c_Product__Type_OPair @ G @ F @ E @ D ) @ ( c_Product__Type_OPair @ G @ F @ C @ B ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ G @ F ) @ A ) )
=> ( ( ( c_Product__Type_OPair @ G @ F @ E @ D )
!= ( c_Product__Type_OPair @ G @ F @ C @ B ) )
=> ~ ! [H: $i,I: $i] :
( ( c_member @ ( tc_prod @ ( tc_prod @ G @ F ) @ ( tc_prod @ G @ F ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ G @ F ) @ ( tc_prod @ G @ F ) @ ( c_Product__Type_OPair @ G @ F @ E @ D ) @ ( c_Product__Type_OPair @ G @ F @ H @ I ) ) @ A )
=> ~ ( c_member @ ( tc_prod @ ( tc_prod @ G @ F ) @ ( tc_prod @ G @ F ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ G @ F ) @ ( tc_prod @ G @ F ) @ ( c_Product__Type_OPair @ G @ F @ H @ I ) @ ( c_Product__Type_OPair @ G @ F @ C @ B ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ G @ F ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converse__rtranclE2) ).
thf(1909,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( c_member @ ( tc_prod @ ( tc_prod @ G @ F ) @ ( tc_prod @ G @ F ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ G @ F ) @ ( tc_prod @ G @ F ) @ ( c_Product__Type_OPair @ G @ F @ E @ D ) @ ( c_Product__Type_OPair @ G @ F @ C @ B ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ G @ F ) @ A ) )
=> ( ( ( c_Product__Type_OPair @ G @ F @ E @ D )
!= ( c_Product__Type_OPair @ G @ F @ C @ B ) )
=> ~ ! [H: $i,I: $i] :
( ( c_member @ ( tc_prod @ ( tc_prod @ G @ F ) @ ( tc_prod @ G @ F ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ G @ F ) @ ( tc_prod @ G @ F ) @ ( c_Product__Type_OPair @ G @ F @ E @ D ) @ ( c_Product__Type_OPair @ G @ F @ H @ I ) ) @ A )
=> ~ ( c_member @ ( tc_prod @ ( tc_prod @ G @ F ) @ ( tc_prod @ G @ F ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ G @ F ) @ ( tc_prod @ G @ F ) @ ( c_Product__Type_OPair @ G @ F @ H @ I ) @ ( c_Product__Type_OPair @ G @ F @ C @ B ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ G @ F ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(379,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ D @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ B @ tc_HOL_Obool ) @ D @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup1I1) ).
thf(1862,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ D @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ B @ tc_HOL_Obool ) @ D @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(262,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( c_member @ ( tc_prod @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) @ ( c_Product__Type_OPair @ H @ G @ F @ E ) @ ( c_Product__Type_OPair @ H @ G @ D @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ H @ G ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ A @ D ) @ C ) )
=> ( ! [I: $i,J: $i,K: $i,L: $i] :
( ( c_member @ ( tc_prod @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) @ ( c_Product__Type_OPair @ H @ G @ I @ J ) @ ( c_Product__Type_OPair @ H @ G @ K @ L ) ) @ B )
=> ( ( c_member @ ( tc_prod @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) @ ( c_Product__Type_OPair @ H @ G @ K @ L ) @ ( c_Product__Type_OPair @ H @ G @ D @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ H @ G ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ A @ K ) @ L ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ I ) @ J ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ F ) @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converse__rtrancl__induct2) ).
thf(1325,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( c_member @ ( tc_prod @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) @ ( c_Product__Type_OPair @ H @ G @ F @ E ) @ ( c_Product__Type_OPair @ H @ G @ D @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ H @ G ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ A @ D ) @ C ) )
=> ( ! [I: $i,J: $i,K: $i,L: $i] :
( ( c_member @ ( tc_prod @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) @ ( c_Product__Type_OPair @ H @ G @ I @ J ) @ ( c_Product__Type_OPair @ H @ G @ K @ L ) ) @ B )
=> ( ( c_member @ ( tc_prod @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ H @ G ) @ ( tc_prod @ H @ G ) @ ( c_Product__Type_OPair @ H @ G @ K @ L ) @ ( c_Product__Type_OPair @ H @ G @ D @ C ) ) @ ( c_Transitive__Closure_Ortrancl @ ( tc_prod @ H @ G ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ A @ K ) @ L ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ I ) @ J ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ F ) @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(140,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Olattice @ D )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Lattices_Osemilattice__sup__class_Osup @ D @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D @ C @ B ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D @ C @ A ) ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ D @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_distrib__inf__le) ).
thf(915,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Olattice @ D )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ ( c_Lattices_Osemilattice__sup__class_Osup @ D @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D @ C @ B ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D @ C @ A ) ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ D @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(308,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf1D2) ).
thf(1556,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(190,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__sup @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
<=> ( ( c_Lattices_Osemilattice__sup__class_Osup @ C @ B @ A )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__iff__sup) ).
thf(1061,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__sup @ C )
=> ( ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( ( c_Lattices_Osemilattice__sup__class_Osup @ C @ B @ A )
= A ) )
& ( ( ( c_Lattices_Osemilattice__sup__class_Osup @ C @ B @ A )
= A )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(484,axiom,
! [A: $i,B: $i] :
~ ( c_member @ B @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_emptyE) ).
thf(2314,plain,
! [A: $i,B: $i] :
~ ( c_member @ B @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).
thf(440,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ B ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) )
<=> ( ( C = B )
| ( ( C != B )
& ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ B ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__eq__or__trancl) ).
thf(2129,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ B ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) )
=> ( ( C = B )
| ( ( C != B )
& ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ B ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) ) ) )
& ( ( ( C = B )
| ( ( C != B )
& ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ B ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) ) )
=> ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ B ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).
thf(492,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
~ ( c_member @ ( tc_prod @ B @ B ) @ ( c_Product__Type_OPair @ B @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ B @ A ) )
=> ( c_Wellfounded_Oacyclic @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acyclicI) ).
thf(2343,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
~ ( c_member @ ( tc_prod @ B @ B ) @ ( c_Product__Type_OPair @ B @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ B @ A ) )
=> ( c_Wellfounded_Oacyclic @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).
thf(70,axiom,
class_Groups_Ominus @ tc_HOL_Obool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Groups_Ominus) ).
thf(700,plain,
class_Groups_Ominus @ tc_HOL_Obool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(4,axiom,
class_Lattices_Osemilattice__sup @ tc_HOL_Obool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Osemilattice__sup) ).
thf(520,plain,
class_Lattices_Osemilattice__sup @ tc_HOL_Obool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(206,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Equiv__Relations_Oquotient @ C @ ( c_Set_Oinsert @ C @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ A )
= ( c_Set_Oinsert @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( c_Relation_OImage @ C @ C @ A @ ( c_Set_Oinsert @ C @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_singleton__quotient) ).
thf(1112,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Equiv__Relations_Oquotient @ C @ ( c_Set_Oinsert @ C @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) @ A )
= ( c_Set_Oinsert @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( c_Relation_OImage @ C @ C @ A @ ( c_Set_Oinsert @ C @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_fun @ C @ tc_HOL_Obool ) @ tc_HOL_Obool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(345,axiom,
c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ v_P____ @ c_Arrow__Order__Mirabelle_OProf,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_A_I3_J) ).
thf(1688,plain,
c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ v_P____ @ c_Arrow__Order__Mirabelle_OProf,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(162,axiom,
! [A: $i] :
( ( c_Transitive__Closure_Ortrancl @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) ) )
= ( c_Relation_OId @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__empty) ).
thf(983,plain,
! [A: $i] :
( ( c_Transitive__Closure_Ortrancl @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) ) )
= ( c_Relation_OId @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(395,axiom,
! [A: $i] :
( ( c_Arrow__Order__Mirabelle_OIIA @ A )
<=> ! [B: $i] :
( ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ B @ c_Arrow__Order__Mirabelle_OProf )
=> ! [C: $i] :
( ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ C @ c_Arrow__Order__Mirabelle_OProf )
=> ! [D: $i,E: $i] :
( ! [F: $i] :
( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ D @ E ) @ ( hAPP @ B @ F ) )
<=> ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ D @ E ) @ ( hAPP @ C @ F ) ) )
=> ( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ D @ E ) @ ( hAPP @ A @ B ) )
<=> ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ D @ E ) @ ( hAPP @ A @ C ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_IIA__def) ).
thf(1926,plain,
! [A: $i] :
( ( ( c_Arrow__Order__Mirabelle_OIIA @ A )
=> ! [B: $i] :
( ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ B @ c_Arrow__Order__Mirabelle_OProf )
=> ! [C: $i] :
( ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ C @ c_Arrow__Order__Mirabelle_OProf )
=> ! [D: $i,E: $i] :
( ! [F: $i] :
( ( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ D @ E ) @ ( hAPP @ B @ F ) )
=> ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ D @ E ) @ ( hAPP @ C @ F ) ) )
& ( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ D @ E ) @ ( hAPP @ C @ F ) )
=> ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ D @ E ) @ ( hAPP @ B @ F ) ) ) )
=> ( ( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ D @ E ) @ ( hAPP @ A @ B ) )
=> ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ D @ E ) @ ( hAPP @ A @ C ) ) )
& ( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ D @ E ) @ ( hAPP @ A @ C ) )
=> ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ D @ E ) @ ( hAPP @ A @ B ) ) ) ) ) ) ) )
& ( ! [B: $i] :
( ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ B @ c_Arrow__Order__Mirabelle_OProf )
=> ! [C: $i] :
( ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ C @ c_Arrow__Order__Mirabelle_OProf )
=> ! [D: $i,E: $i] :
( ! [F: $i] :
( ( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ D @ E ) @ ( hAPP @ B @ F ) )
=> ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ D @ E ) @ ( hAPP @ C @ F ) ) )
& ( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ D @ E ) @ ( hAPP @ C @ F ) )
=> ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ D @ E ) @ ( hAPP @ B @ F ) ) ) )
=> ( ( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ D @ E ) @ ( hAPP @ A @ B ) )
=> ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ D @ E ) @ ( hAPP @ A @ C ) ) )
& ( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ D @ E ) @ ( hAPP @ A @ C ) )
=> ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ D @ E ) @ ( hAPP @ A @ B ) ) ) ) ) ) )
=> ( c_Arrow__Order__Mirabelle_OIIA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(94,axiom,
! [A: $i,B: $i] :
( ( c_Relation_Oantisym @ B @ ( c_Relation_Oconverse @ B @ B @ A ) )
<=> ( c_Relation_Oantisym @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_antisym__converse) ).
thf(768,plain,
! [A: $i,B: $i] :
( ( ( c_Relation_Oantisym @ B @ ( c_Relation_Oconverse @ B @ B @ A ) )
=> ( c_Relation_Oantisym @ B @ A ) )
& ( ( c_Relation_Oantisym @ B @ A )
=> ( c_Relation_Oantisym @ B @ ( c_Relation_Oconverse @ B @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(68,axiom,
! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_empty__subsetI) ).
thf(695,plain,
! [A: $i,B: $i] : ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(431,axiom,
! [A: $i,B: $i] :
( ( c_Relation_ODomain @ B @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ B @ A ) @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Domain__empty) ).
thf(2064,plain,
! [A: $i,B: $i] :
( ( c_Relation_ODomain @ B @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ B @ A ) @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(225,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
<=> ( ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
& ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__empty) ).
thf(1176,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
& ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) )
& ( ( ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
& ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) )
=> ( ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(163,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Set_Oinsert @ D @ C @ B ) @ A )
<=> ( ( c_member @ D @ C @ A )
& ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__subset) ).
thf(986,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Set_Oinsert @ D @ C @ B ) @ A )
=> ( ( c_member @ D @ C @ A )
& ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) ) )
& ( ( ( c_member @ D @ C @ A )
& ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Set_Oinsert @ D @ C @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(167,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ D @ C @ B )
=> ( ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Set_Oinsert @ D @ C @ A ) @ B )
= ( c_Set_Oinsert @ D @ C @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__insert__left__if1) ).
thf(1000,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ D @ C @ B )
=> ( ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Set_Oinsert @ D @ C @ A ) @ B )
= ( c_Set_Oinsert @ D @ C @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(290,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Orderings_Oord @ E )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ E ) @ C @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ E @ ( hAPP @ C @ A ) @ ( hAPP @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__funE) ).
thf(1477,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Orderings_Oord @ E )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ E ) @ C @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ E @ ( hAPP @ C @ A ) @ ( hAPP @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(502,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Wellfounded_Oacyclic @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ A @ B )
=> ( c_Wellfounded_Oacyclic @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acyclic__subset) ).
thf(2390,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Wellfounded_Oacyclic @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ A @ B )
=> ( c_Wellfounded_Oacyclic @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).
thf(460,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ C @ c_Arrow__Order__Mirabelle_OLin )
=> ( ( B != A )
=> ( ~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ B @ A ) @ C )
<=> ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ A @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_notin__Lin__iff) ).
thf(2207,plain,
! [A: $i,B: $i,C: $i] :
( ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ C @ c_Arrow__Order__Mirabelle_OLin )
=> ( ( B != A )
=> ( ( ~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ B @ A ) @ C )
=> ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ A @ B ) @ C ) )
& ( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ A @ B ) @ C )
=> ~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ B @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).
thf(367,axiom,
! [A: $i] :
( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a____ @ v_b____ ) @ ( hAPP @ v_P____ @ A ) )
<=> ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a_H____ @ v_b_H____ ) @ ( hAPP @ v_P_H____ @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_A_I5_J) ).
thf(1805,plain,
! [A: $i] :
( ( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a____ @ v_b____ ) @ ( hAPP @ v_P____ @ A ) )
=> ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a_H____ @ v_b_H____ ) @ ( hAPP @ v_P_H____ @ A ) ) )
& ( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a_H____ @ v_b_H____ ) @ ( hAPP @ v_P_H____ @ A ) )
=> ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a____ @ v_b____ ) @ ( hAPP @ v_P____ @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(433,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E != D )
=> ( ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ C @ c_Arrow__Order__Mirabelle_OLin )
=> ( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ B @ A ) @ ( c_Arrow__Order__Mirabelle_Oabove @ C @ E @ D ) )
<=> ( ( B != A )
& ( ( B = D )
=> ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ E @ A ) @ C ) )
& ( ( B != D )
=> ( ( ( A = D )
=> ( ( B = E )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ B @ E ) @ C ) ) )
& ( ( A != D )
=> ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ B @ A ) @ C ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__above) ).
thf(2069,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E != D )
=> ( ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ C @ c_Arrow__Order__Mirabelle_OLin )
=> ( ( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ B @ A ) @ ( c_Arrow__Order__Mirabelle_Oabove @ C @ E @ D ) )
=> ( ( B != A )
& ( ( B = D )
=> ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ E @ A ) @ C ) )
& ( ( B != D )
=> ( ( ( A = D )
=> ( ( B = E )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ B @ E ) @ C ) ) )
& ( ( A != D )
=> ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ B @ A ) @ C ) ) ) ) ) )
& ( ( ( B != A )
& ( ( B = D )
=> ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ E @ A ) @ C ) )
& ( ( B != D )
=> ( ( ( A = D )
=> ( ( B = E )
| ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ B @ E ) @ C ) ) )
& ( ( A != D )
=> ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ B @ A ) @ C ) ) ) ) )
=> ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ B @ A ) @ ( c_Arrow__Order__Mirabelle_Oabove @ C @ E @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(139,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) )
= ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__left__commute) ).
thf(912,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) )
= ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(5,axiom,
class_Lattices_Osemilattice__inf @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Lattices_Osemilattice__inf) ).
thf(521,plain,
class_Lattices_Osemilattice__inf @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(461,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Relation_Oantisym @ D @ C )
=> ( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ B @ A ) @ C )
=> ( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ A @ B ) @ C )
=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_antisymD) ).
thf(2212,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Relation_Oantisym @ D @ C )
=> ( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ B @ A ) @ C )
=> ( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ A @ B ) @ C )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(2170,plain,
v_a____ != v_b____,
inference(polarity_switch,[status(thm)],[2169]) ).
thf(2171,plain,
v_b____ != v_a____,
inference(lifteq,[status(thm)],[2170]) ).
thf(191,axiom,
! [A: $i,B: $i] :
( ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__empty__left) ).
thf(1066,plain,
! [A: $i,B: $i] :
( ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(122,axiom,
! [A: $i] : ( c_Relation_Oantisym @ A @ ( c_Relation_OId @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_antisym__Id) ).
thf(868,plain,
! [A: $i] : ( c_Relation_Oantisym @ A @ ( c_Relation_OId @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(117,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Order__Relation_Olinear__order__on @ C @ B @ ( c_Relation_Oconverse @ C @ C @ A ) )
<=> ( c_Order__Relation_Olinear__order__on @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_linear__order__on__converse) ).
thf(851,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Order__Relation_Olinear__order__on @ C @ B @ ( c_Relation_Oconverse @ C @ C @ A ) )
=> ( c_Order__Relation_Olinear__order__on @ C @ B @ A ) )
& ( ( c_Order__Relation_Olinear__order__on @ C @ B @ A )
=> ( c_Order__Relation_Olinear__order__on @ C @ B @ ( c_Relation_Oconverse @ C @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(203,axiom,
! [A: $i,B: $i] :
( ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__empty__left) ).
thf(1102,plain,
! [A: $i,B: $i] :
( ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ B @ tc_HOL_Obool ) @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(348,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ C ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) )
=> ( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ C @ A ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) )
=> ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ A ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__trancl__trancl) ).
thf(1694,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ C ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) )
=> ( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ C @ A ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) )
=> ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ A ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(143,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__greatest) ).
thf(922,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(327,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Equiv__Relations_Oequiv @ E @ D @ C )
=> ( ( c_member @ E @ B @ D )
=> ( ( c_member @ E @ A @ D )
=> ( ( ( c_Equiv__Relations_Oquotient @ E @ ( c_Set_Oinsert @ E @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ C )
= ( c_Equiv__Relations_Oquotient @ E @ ( c_Set_Oinsert @ E @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ C ) )
<=> ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ B @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__equiv__class__iff2) ).
thf(1626,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Equiv__Relations_Oequiv @ E @ D @ C )
=> ( ( c_member @ E @ B @ D )
=> ( ( c_member @ E @ A @ D )
=> ( ( ( ( c_Equiv__Relations_Oquotient @ E @ ( c_Set_Oinsert @ E @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ C )
= ( c_Equiv__Relations_Oquotient @ E @ ( c_Set_Oinsert @ E @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ C ) )
=> ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ B @ A ) @ C ) )
& ( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ B @ A ) @ C )
=> ( ( c_Equiv__Relations_Oquotient @ E @ ( c_Set_Oinsert @ E @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ C )
= ( c_Equiv__Relations_Oquotient @ E @ ( c_Set_Oinsert @ E @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(469,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_member @ ( tc_prod @ C @ C ) @ B @ ( c_Relation_OId__on @ C @ A ) )
=> ~ ! [D: $i] :
( ( c_member @ C @ D @ A )
=> ( B
!= ( c_Product__Type_OPair @ C @ C @ D @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Id__onE) ).
thf(2239,plain,
! [A: $i,B: $i,C: $i] :
( ( c_member @ ( tc_prod @ C @ C ) @ B @ ( c_Relation_OId__on @ C @ A ) )
=> ~ ! [D: $i] :
( ( c_member @ C @ D @ A )
=> ( B
!= ( c_Product__Type_OPair @ C @ C @ D @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).
thf(258,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Relation_Orefl__on @ E @ D @ C )
=> ( ( c_Relation_Orefl__on @ E @ B @ A )
=> ( c_Relation_Orefl__on @ E @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) @ D @ B ) @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ E @ E ) @ tc_HOL_Obool ) @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_refl__on__Un) ).
thf(1304,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Relation_Orefl__on @ E @ D @ C )
=> ( ( c_Relation_Orefl__on @ E @ B @ A )
=> ( c_Relation_Orefl__on @ E @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) @ D @ B ) @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ E @ E ) @ tc_HOL_Obool ) @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(32,axiom,
! [A: $i,B: $i] :
( ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ ( c_Transitive__Closure_Ortrancl @ B @ A ) @ ( c_Relation_OId @ B ) )
= ( c_Transitive__Closure_Ortrancl @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__reflcl__absorb) ).
thf(589,plain,
! [A: $i,B: $i] :
( ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ ( c_Transitive__Closure_Ortrancl @ B @ A ) @ ( c_Relation_OId @ B ) )
= ( c_Transitive__Closure_Ortrancl @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(150,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Order__Relation_Opreorder__on @ C @ B @ ( c_Relation_Oconverse @ C @ C @ A ) )
<=> ( c_Order__Relation_Opreorder__on @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_preorder__on__converse) ).
thf(944,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Order__Relation_Opreorder__on @ C @ B @ ( c_Relation_Oconverse @ C @ C @ A ) )
=> ( c_Order__Relation_Opreorder__on @ C @ B @ A ) )
& ( ( c_Order__Relation_Opreorder__on @ C @ B @ A )
=> ( c_Order__Relation_Opreorder__on @ C @ B @ ( c_Relation_Oconverse @ C @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(100,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Olattice @ D )
=> ( ( c_Lattices_Osemilattice__sup__class_Osup @ D @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ D @ B @ A ) )
= ( c_Lattices_Osemilattice__sup__class_Osup @ D @ B @ ( c_Lattices_Osemilattice__sup__class_Osup @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__aci_I7_J) ).
thf(795,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Olattice @ D )
=> ( ( c_Lattices_Osemilattice__sup__class_Osup @ D @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ D @ B @ A ) )
= ( c_Lattices_Osemilattice__sup__class_Osup @ D @ B @ ( c_Lattices_Osemilattice__sup__class_Osup @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(282,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ! [G: $i] :
( ( c_member @ ( tc_prod @ F @ F ) @ ( c_Product__Type_OPair @ F @ F @ G @ E ) @ D )
=> ( c_Recdef_Owfrec__rel @ F @ C @ D @ B @ G @ ( hAPP @ A @ G ) ) )
=> ( c_Recdef_Owfrec__rel @ F @ C @ D @ B @ E @ ( hAPP @ ( hAPP @ B @ A ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wfrec__rel_Ointros) ).
thf(1420,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ! [G: $i] :
( ( c_member @ ( tc_prod @ F @ F ) @ ( c_Product__Type_OPair @ F @ F @ G @ E ) @ D )
=> ( c_Recdef_Owfrec__rel @ F @ C @ D @ B @ G @ ( hAPP @ A @ G ) ) )
=> ( c_Recdef_Owfrec__rel @ F @ C @ D @ B @ E @ ( hAPP @ ( hAPP @ B @ A ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(145,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__inf @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( ( c_Lattices_Osemilattice__inf__class_Oinf @ C @ B @ A )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__absorb1) ).
thf(927,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__inf @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( ( c_Lattices_Osemilattice__inf__class_Oinf @ C @ B @ A )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(249,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__inf @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D @ B @ A ) )
=> ~ ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ~ ( c_Orderings_Oord__class_Oless__eq @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__infE) ).
thf(1277,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__inf @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D @ B @ A ) )
=> ~ ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ~ ( c_Orderings_Oord__class_Oless__eq @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( class_Lattices_Osemilattice__sup @ B )
=> ( ( c_Lattices_Osemilattice__sup__class_Osup @ B @ A @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup_Oidem) ).
thf(553,plain,
! [A: $i,B: $i] :
( ( class_Lattices_Osemilattice__sup @ B )
=> ( ( c_Lattices_Osemilattice__sup__class_Osup @ B @ A @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(186,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A )
=> ( ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__absorb1) ).
thf(1049,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A )
=> ( ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(406,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ B ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) )
=> ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ B ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__into__rtrancl) ).
thf(1990,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ B ) @ ( c_Transitive__Closure_Otrancl @ D @ A ) )
=> ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ B ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(44,axiom,
class_Groups_Ominus @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Groups_Ominus) ).
thf(617,plain,
class_Groups_Ominus @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(459,axiom,
( ( ( v_a____ != v_b_H____ )
& ( v_b____ != v_a_H____ ) )
=> ( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a____ @ v_b____ ) @ ( hAPP @ v_F @ v_P____ ) )
<=> ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a_H____ @ v_b_H____ ) @ ( hAPP @ v_F @ v_P_H____ ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_calculation_I1_J) ).
thf(2202,plain,
( ( ( v_a____ != v_b_H____ )
& ( v_b____ != v_a_H____ ) )
=> ( ( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a____ @ v_b____ ) @ ( hAPP @ v_F @ v_P____ ) )
=> ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a_H____ @ v_b_H____ ) @ ( hAPP @ v_F @ v_P_H____ ) ) )
& ( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a_H____ @ v_b_H____ ) @ ( hAPP @ v_F @ v_P_H____ ) )
=> ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a____ @ v_b____ ) @ ( hAPP @ v_F @ v_P____ ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(174,axiom,
! [A: $i,B: $i] :
( ( c_Wellfounded_Owf @ B @ ( c_Relation_Oconverse @ B @ B @ A ) )
=> ( c_Wellfounded_Owf @ B @ ( c_Relation_Oconverse @ B @ B @ ( c_Transitive__Closure_Otrancl @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__converse__trancl) ).
thf(1018,plain,
! [A: $i,B: $i] :
( ( c_Wellfounded_Owf @ B @ ( c_Relation_Oconverse @ B @ B @ A ) )
=> ( c_Wellfounded_Owf @ B @ ( c_Relation_Oconverse @ B @ B @ ( c_Transitive__Closure_Otrancl @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(473,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Relation_OField @ D @ ( c_Set_Oinsert @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ B ) @ A ) )
= ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Set_Oinsert @ D @ C @ ( c_Set_Oinsert @ D @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) @ ( c_Relation_OField @ D @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Field__insert) ).
thf(2256,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Relation_OField @ D @ ( c_Set_Oinsert @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ B ) @ A ) )
= ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Set_Oinsert @ D @ C @ ( c_Set_Oinsert @ D @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) @ ( c_Relation_OField @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).
thf(96,axiom,
! [A: $i,B: $i] :
( ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ B @ tc_HOL_Obool ) @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__empty__right) ).
thf(776,plain,
! [A: $i,B: $i] :
( ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ B @ tc_HOL_Obool ) @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(168,axiom,
! [A: $i,B: $i] :
( ( c_Transitive__Closure_Ortrancl @ B @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ A @ ( c_Relation_OId @ B ) ) )
= ( c_Transitive__Closure_Ortrancl @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__reflcl) ).
thf(1003,plain,
! [A: $i,B: $i] :
( ( c_Transitive__Closure_Ortrancl @ B @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ A @ ( c_Relation_OId @ B ) ) )
= ( c_Transitive__Closure_Ortrancl @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(29,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__inf @ D )
=> ( ( c_Lattices_Osemilattice__inf__class_Oinf @ D @ C @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D @ B @ A ) )
= ( c_Lattices_Osemilattice__inf__class_Oinf @ D @ B @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__left__commute) ).
thf(580,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__inf @ D )
=> ( ( c_Lattices_Osemilattice__inf__class_Oinf @ D @ C @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D @ B @ A ) )
= ( c_Lattices_Osemilattice__inf__class_Oinf @ D @ B @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(319,axiom,
! [A: $i] :
( ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( c_Relation_Oconverse @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ A ) @ c_Arrow__Order__Mirabelle_OLin )
<=> ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ A @ c_Arrow__Order__Mirabelle_OLin ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converse__in__Lin) ).
thf(1598,plain,
! [A: $i] :
( ( ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( c_Relation_Oconverse @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ A ) @ c_Arrow__Order__Mirabelle_OLin )
=> ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ A @ c_Arrow__Order__Mirabelle_OLin ) )
& ( ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ A @ c_Arrow__Order__Mirabelle_OLin )
=> ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( c_Relation_Oconverse @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ A ) @ c_Arrow__Order__Mirabelle_OLin ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(177,axiom,
! [A: $i,B: $i] :
( ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ B @ tc_HOL_Obool ) @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__empty__right) ).
thf(1025,plain,
! [A: $i,B: $i] :
( ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ B @ tc_HOL_Obool ) @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(128,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) )
= ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__Int) ).
thf(887,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) )
= ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(311,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ D @ C @ ( c_Relation_ODomain @ D @ B @ A ) )
<=> ? [E: $i] : ( c_member @ ( tc_prod @ D @ B ) @ ( c_Product__Type_OPair @ D @ B @ C @ E ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Domain__iff) ).
thf(1566,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_member @ D @ C @ ( c_Relation_ODomain @ D @ B @ A ) )
=> ? [E: $i] : ( c_member @ ( tc_prod @ D @ B ) @ ( c_Product__Type_OPair @ D @ B @ C @ E ) @ A ) )
& ( ? [E: $i] : ( c_member @ ( tc_prod @ D @ B ) @ ( c_Product__Type_OPair @ D @ B @ C @ E ) @ A )
=> ( c_member @ D @ C @ ( c_Relation_ODomain @ D @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(303,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Relation_Ototal__on @ C @ B @ A )
<=> ! [D: $i] :
( ( c_member @ C @ D @ B )
=> ! [E: $i] :
( ( c_member @ C @ E @ B )
=> ( ( D != E )
=> ( ( c_member @ ( tc_prod @ C @ C ) @ ( c_Product__Type_OPair @ C @ C @ D @ E ) @ A )
| ( c_member @ ( tc_prod @ C @ C ) @ ( c_Product__Type_OPair @ C @ C @ E @ D ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_total__on__def) ).
thf(1531,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Relation_Ototal__on @ C @ B @ A )
=> ! [D: $i] :
( ( c_member @ C @ D @ B )
=> ! [E: $i] :
( ( c_member @ C @ E @ B )
=> ( ( D != E )
=> ( ( c_member @ ( tc_prod @ C @ C ) @ ( c_Product__Type_OPair @ C @ C @ D @ E ) @ A )
| ( c_member @ ( tc_prod @ C @ C ) @ ( c_Product__Type_OPair @ C @ C @ E @ D ) @ A ) ) ) ) ) )
& ( ! [D: $i] :
( ( c_member @ C @ D @ B )
=> ! [E: $i] :
( ( c_member @ C @ E @ B )
=> ( ( D != E )
=> ( ( c_member @ ( tc_prod @ C @ C ) @ ( c_Product__Type_OPair @ C @ C @ D @ E ) @ A )
| ( c_member @ ( tc_prod @ C @ C ) @ ( c_Product__Type_OPair @ C @ C @ E @ D ) @ A ) ) ) ) )
=> ( c_Relation_Ototal__on @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(365,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B ) @ A ) )
=> ~ ( ( hBOOL @ ( hAPP @ C @ A ) )
=> ~ ( hBOOL @ ( hAPP @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf1E) ).
thf(1798,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B ) @ A ) )
=> ~ ( ( hBOOL @ ( hAPP @ C @ A ) )
=> ~ ( hBOOL @ ( hAPP @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(322,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( c_Relation_OField @ C @ B ) @ ( c_Relation_OField @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mono__Field) ).
thf(1611,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( c_Relation_OField @ C @ B ) @ ( c_Relation_OField @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(217,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ A @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__least) ).
thf(1156,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ A @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(363,axiom,
! [A: $i,B: $i] :
( ( c_Relation_ORange @ B @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ B @ A ) @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Range__empty) ).
thf(1790,plain,
! [A: $i,B: $i] :
( ( c_Relation_ORange @ B @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ B @ A ) @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ A @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(448,axiom,
! [A: $i,B: $i,C: $i] : ( c_member @ ( tc_prod @ C @ C ) @ ( c_Product__Type_OPair @ C @ C @ B @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl_Ortrancl__refl) ).
thf(2165,plain,
! [A: $i,B: $i,C: $i] : ( c_member @ ( tc_prod @ C @ C ) @ ( c_Product__Type_OPair @ C @ C @ B @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).
thf(330,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ E @ ( c_Product__Type_OPair @ D @ C @ B @ A ) ) )
=> ( hBOOL @ ( c_Product__Type_Ocurry @ D @ C @ tc_HOL_Obool @ E @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_curryI) ).
thf(1637,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ E @ ( c_Product__Type_OPair @ D @ C @ B @ A ) ) )
=> ( hBOOL @ ( c_Product__Type_Ocurry @ D @ C @ tc_HOL_Obool @ E @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(227,axiom,
! [A: $i,B: $i] :
( ( class_Orderings_Obot @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Orderings_Obot__class_Obot @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bot__least) ).
thf(1188,plain,
! [A: $i,B: $i] :
( ( class_Orderings_Obot @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ B @ ( c_Orderings_Obot__class_Obot @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(182,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A )
=> ( ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) @ A @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__absorb1) ).
thf(1038,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A )
=> ( ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) @ A @ B )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(381,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Product__Type_Oprod_Oprod__rec @ F @ E @ D @ C @ ( c_Product__Type_OPair @ F @ E @ B @ A ) )
= ( hAPP @ ( hAPP @ C @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_prod_Orecs) ).
thf(1869,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Product__Type_Oprod_Oprod__rec @ F @ E @ D @ C @ ( c_Product__Type_OPair @ F @ E @ B @ A ) )
= ( hAPP @ ( hAPP @ C @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(362,axiom,
! [A: $i,B: $i] :
( ( c_Relation_Oirrefl @ B @ A )
<=> ! [C: $i] :
~ ( c_member @ ( tc_prod @ B @ B ) @ ( c_Product__Type_OPair @ B @ B @ C @ C ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_irrefl__def) ).
thf(1785,plain,
! [A: $i,B: $i] :
( ( ( c_Relation_Oirrefl @ B @ A )
=> ! [C: $i] :
~ ( c_member @ ( tc_prod @ B @ B ) @ ( c_Product__Type_OPair @ B @ B @ C @ C ) @ A ) )
& ( ! [C: $i] :
~ ( c_member @ ( tc_prod @ B @ B ) @ ( c_Product__Type_OPair @ B @ B @ C @ C ) @ A )
=> ( c_Relation_Oirrefl @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(390,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A )
=> ( c_member @ D @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__rev__mp) ).
thf(1901,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A )
=> ( c_member @ D @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(343,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_member @ C @ B @ ( c_fequal @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__mem) ).
thf(1679,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_member @ C @ B @ ( c_fequal @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( c_member @ C @ B @ ( c_fequal @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(2467,plain,
( ( ( hAPP @ v_F @ v_P____ )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) )
| ( ( hAPP @ v_F @ v_P_H____ )
!= ( hAPP @ v_F @ v_P____ ) )
| ( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[2466]) ).
thf(2468,plain,
( ( ( hAPP @ v_F @ v_P____ )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) )
| ( ( hAPP @ v_F @ v_P_H____ )
!= ( hAPP @ v_F @ v_P____ ) ) ),
inference(simp,[status(thm)],[2467]) ).
thf(152,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_member @ D @ C @ B )
=> ( ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ ( c_Set_Oinsert @ D @ C @ A ) )
= ( c_Set_Oinsert @ D @ C @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) ) ) )
& ( ~ ( c_member @ D @ C @ B )
=> ( ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ ( c_Set_Oinsert @ D @ C @ A ) )
= ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__insert__right) ).
thf(951,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_member @ D @ C @ B )
=> ( ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ ( c_Set_Oinsert @ D @ C @ A ) )
= ( c_Set_Oinsert @ D @ C @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) ) ) )
& ( ~ ( c_member @ D @ C @ B )
=> ( ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ ( c_Set_Oinsert @ D @ C @ A ) )
= ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(104,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A )
=> ( ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__absorb2) ).
thf(808,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A )
=> ( ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(428,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ D @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_predicate2D) ).
thf(2056,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ F @ ( tc_fun @ E @ tc_HOL_Obool ) ) @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ D @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(375,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( c_member @ D @ C @ B )
=> ( C = A ) )
=> ( c_member @ D @ C @ ( c_Set_Oinsert @ D @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insertCI) ).
thf(1849,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( c_member @ D @ C @ B )
=> ( C = A ) )
=> ( c_member @ D @ C @ ( c_Set_Oinsert @ D @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(72,axiom,
! [A: $i] :
( ( c_Relation_Oconverse @ A @ A @ ( c_Relation_OId @ A ) )
= ( c_Relation_OId @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converse__Id) ).
thf(703,plain,
! [A: $i] :
( ( c_Relation_Oconverse @ A @ A @ ( c_Relation_OId @ A ) )
= ( c_Relation_OId @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(499,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ~ ( c_member @ B @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equals0D) ).
thf(2379,plain,
! [A: $i,B: $i,C: $i] :
( ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ~ ( c_member @ B @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).
thf(480,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ D @ C @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) )
<=> ( ( c_member @ D @ C @ B )
& ( c_member @ D @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__iff) ).
thf(2279,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_member @ D @ C @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) )
=> ( ( c_member @ D @ C @ B )
& ( c_member @ D @ C @ A ) ) )
& ( ( ( c_member @ D @ C @ B )
& ( c_member @ D @ C @ A ) )
=> ( c_member @ D @ C @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).
thf(170,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__sup @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Lattices_Osemilattice__sup__class_Osup @ C @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__ge1) ).
thf(1008,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__sup @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Lattices_Osemilattice__sup__class_Osup @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(419,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Product__Type_Ocurry @ F @ E @ D @ C @ B @ A )
= ( hAPP @ C @ ( c_Product__Type_OPair @ F @ E @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_curry__conv) ).
thf(2030,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Product__Type_Ocurry @ F @ E @ D @ C @ B @ A )
= ( hAPP @ C @ ( c_Product__Type_OPair @ F @ E @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(274,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i] :
( ( c_member @ D @ E @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B ) )
=> ( hBOOL @ ( hAPP @ A @ E ) ) )
<=> ( ! [E: $i] :
( ( c_member @ D @ E @ C )
=> ( hBOOL @ ( hAPP @ A @ E ) ) )
& ! [E: $i] :
( ( c_member @ D @ E @ B )
=> ( hBOOL @ ( hAPP @ A @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ball__Un) ).
thf(1372,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ! [E: $i] :
( ( c_member @ D @ E @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B ) )
=> ( hBOOL @ ( hAPP @ A @ E ) ) )
=> ( ! [E: $i] :
( ( c_member @ D @ E @ C )
=> ( hBOOL @ ( hAPP @ A @ E ) ) )
& ! [E: $i] :
( ( c_member @ D @ E @ B )
=> ( hBOOL @ ( hAPP @ A @ E ) ) ) ) )
& ( ( ! [E: $i] :
( ( c_member @ D @ E @ C )
=> ( hBOOL @ ( hAPP @ A @ E ) ) )
& ! [E: $i] :
( ( c_member @ D @ E @ B )
=> ( hBOOL @ ( hAPP @ A @ E ) ) ) )
=> ! [E: $i] :
( ( c_member @ D @ E @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B ) )
=> ( hBOOL @ ( hAPP @ A @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(42,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Relation_Osingle__valued @ E @ D @ ( c_Relation_Oconverse @ D @ E @ C ) )
=> ( ( c_Relation_OImage @ D @ E @ C @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) )
= ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( c_Relation_OImage @ D @ E @ C @ B ) @ ( c_Relation_OImage @ D @ E @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__Int__eq) ).
thf(612,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Relation_Osingle__valued @ E @ D @ ( c_Relation_Oconverse @ D @ E @ C ) )
=> ( ( c_Relation_OImage @ D @ E @ C @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) )
= ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( c_Relation_OImage @ D @ E @ C @ B ) @ ( c_Relation_OImage @ D @ E @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(507,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_member @ E @ D @ ( c_Relation_OImage @ C @ E @ B @ A ) )
<=> ? [F: $i] :
( ( c_member @ C @ F @ A )
& ( c_member @ ( tc_prod @ C @ E ) @ ( c_Product__Type_OPair @ C @ E @ F @ D ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__iff) ).
thf(2411,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( c_member @ E @ D @ ( c_Relation_OImage @ C @ E @ B @ A ) )
=> ? [F: $i] :
( ( c_member @ C @ F @ A )
& ( c_member @ ( tc_prod @ C @ E ) @ ( c_Product__Type_OPair @ C @ E @ F @ D ) @ B ) ) )
& ( ? [F: $i] :
( ( c_member @ C @ F @ A )
& ( c_member @ ( tc_prod @ C @ E ) @ ( c_Product__Type_OPair @ C @ E @ F @ D ) @ B ) )
=> ( c_member @ E @ D @ ( c_Relation_OImage @ C @ E @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).
thf(86,axiom,
! [A: $i,B: $i] :
( ( c_Transitive__Closure_Otrancl @ B @ ( c_Relation_Oconverse @ B @ B @ A ) )
= ( c_Relation_Oconverse @ B @ B @ ( c_Transitive__Closure_Otrancl @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__converse) ).
thf(744,plain,
! [A: $i,B: $i] :
( ( c_Transitive__Closure_Otrancl @ B @ ( c_Relation_Oconverse @ B @ B @ A ) )
= ( c_Relation_Oconverse @ B @ B @ ( c_Transitive__Closure_Otrancl @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(511,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F != E )
=> ( ( D != C )
=> ( ( F != C )
=> ( ( E != D )
=> ( ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ B @ c_Arrow__Order__Mirabelle_OProf )
=> ( ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ A @ c_Arrow__Order__Mirabelle_OProf )
=> ( ! [G: $i] :
( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ F @ E ) @ ( hAPP @ B @ G ) )
<=> ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ D @ C ) @ ( hAPP @ A @ G ) ) )
=> ( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ F @ E ) @ ( hAPP @ v_F @ B ) )
=> ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ D @ C ) @ ( hAPP @ v_F @ A ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact__C1_C) ).
thf(2426,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F != E )
=> ( ( D != C )
=> ( ( F != C )
=> ( ( E != D )
=> ( ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ B @ c_Arrow__Order__Mirabelle_OProf )
=> ( ( c_member @ ( tc_fun @ tc_Arrow__Order__Mirabelle_Oindi @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) @ A @ c_Arrow__Order__Mirabelle_OProf )
=> ( ! [G: $i] :
( ( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ F @ E ) @ ( hAPP @ B @ G ) )
=> ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ D @ C ) @ ( hAPP @ A @ G ) ) )
& ( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ D @ C ) @ ( hAPP @ A @ G ) )
=> ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ F @ E ) @ ( hAPP @ B @ G ) ) ) )
=> ( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ F @ E ) @ ( hAPP @ v_F @ B ) )
=> ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ D @ C ) @ ( hAPP @ v_F @ A ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).
thf(402,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B )
=> ( ( c_member @ D @ A @ C )
=> ( c_member @ D @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_in__mono) ).
thf(1981,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B )
=> ( ( c_member @ D @ A @ C )
=> ( c_member @ D @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(56,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__sup @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( ( c_Lattices_Osemilattice__sup__class_Osup @ C @ B @ A )
= A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__absorb2) ).
thf(656,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__sup @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ C @ B @ A )
=> ( ( c_Lattices_Osemilattice__sup__class_Osup @ C @ B @ A )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(366,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( c_member @ D @ C @ B )
=> ( c_member @ D @ C @ A ) )
=> ( c_member @ D @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UnCI) ).
thf(1802,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( c_member @ D @ C @ B )
=> ( c_member @ D @ C @ A ) )
=> ( c_member @ D @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(176,axiom,
! [A: $i,B: $i,C: $i] : ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A ) @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__lower1) ).
thf(1023,plain,
! [A: $i,B: $i,C: $i] : ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(486,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ D @ C @ ( c_Set_Oinsert @ D @ B @ A ) )
=> ( ( C != B )
=> ( c_member @ D @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insertE) ).
thf(2320,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ D @ C @ ( c_Set_Oinsert @ D @ B @ A ) )
=> ( ( C != B )
=> ( c_member @ D @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).
thf(187,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Wellfounded_OwfP @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A @ B )
=> ( c_Wellfounded_OwfP @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wfP__subset) ).
thf(1052,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Wellfounded_OwfP @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ ( tc_fun @ C @ tc_HOL_Obool ) ) @ A @ B )
=> ( c_Wellfounded_OwfP @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(298,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Recdef_Owfrec__rel @ F @ E @ D @ C @ B @ A )
<=> ? [G: $i] :
( ( A
= ( hAPP @ ( hAPP @ C @ G ) @ B ) )
& ! [H: $i] :
( ( c_member @ ( tc_prod @ F @ F ) @ ( c_Product__Type_OPair @ F @ F @ H @ B ) @ D )
=> ( c_Recdef_Owfrec__rel @ F @ E @ D @ C @ H @ ( hAPP @ G @ H ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wfrec__rel_Osimps) ).
thf(1504,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( c_Recdef_Owfrec__rel @ F @ E @ D @ C @ B @ A )
=> ? [G: $i] :
( ( A
= ( hAPP @ ( hAPP @ C @ G ) @ B ) )
& ! [H: $i] :
( ( c_member @ ( tc_prod @ F @ F ) @ ( c_Product__Type_OPair @ F @ F @ H @ B ) @ D )
=> ( c_Recdef_Owfrec__rel @ F @ E @ D @ C @ H @ ( hAPP @ G @ H ) ) ) ) )
& ( ? [G: $i] :
( ( A
= ( hAPP @ ( hAPP @ C @ G ) @ B ) )
& ! [H: $i] :
( ( c_member @ ( tc_prod @ F @ F ) @ ( c_Product__Type_OPair @ F @ F @ H @ B ) @ D )
=> ( c_Recdef_Owfrec__rel @ F @ E @ D @ C @ H @ ( hAPP @ G @ H ) ) ) )
=> ( c_Recdef_Owfrec__rel @ F @ E @ D @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(80,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) )
= ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__left__commute) ).
thf(727,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) )
= ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(316,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Relation_Orefl__on @ E @ D @ C )
=> ( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ B @ A ) @ C )
=> ( c_member @ E @ A @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_refl__onD2) ).
thf(1585,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Relation_Orefl__on @ E @ D @ C )
=> ( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ B @ A ) @ C )
=> ( c_member @ E @ A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(214,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B ) @ A )
= ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) ) )
<=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__Int__assoc__eq) ).
thf(1140,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B ) @ A )
= ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) ) )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ A @ C ) )
& ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ A @ C )
=> ( ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B ) @ A )
= ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(413,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Wellfounded_Owf @ E @ D )
=> ( ( hAPP @ ( c_Recdef_Owfrec @ E @ C @ D @ B ) @ A )
= ( hAPP @ ( hAPP @ B @ ( c_Recdef_Ocut @ E @ C @ ( c_Recdef_Owfrec @ E @ C @ D @ B ) @ D @ A ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wfrec) ).
thf(2013,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Wellfounded_Owf @ E @ D )
=> ( ( hAPP @ ( c_Recdef_Owfrec @ E @ C @ D @ B ) @ A )
= ( hAPP @ ( hAPP @ B @ ( c_Recdef_Ocut @ E @ C @ ( c_Recdef_Owfrec @ E @ C @ D @ B ) @ D @ A ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(12,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__inf @ D )
=> ( ( c_Lattices_Osemilattice__inf__class_Oinf @ D @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D @ C @ B ) @ A )
= ( c_Lattices_Osemilattice__inf__class_Oinf @ D @ C @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf_Oassoc) ).
thf(539,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__inf @ D )
=> ( ( c_Lattices_Osemilattice__inf__class_Oinf @ D @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D @ C @ B ) @ A )
= ( c_Lattices_Osemilattice__inf__class_Oinf @ D @ C @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(462,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ B ) @ F )
=> ( ( hAPP @ ( c_Recdef_Ocut @ D @ A @ E @ F @ B ) @ C )
= ( hAPP @ E @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_tfl__cut__apply) ).
thf(2215,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ B ) @ F )
=> ( ( hAPP @ ( c_Recdef_Ocut @ D @ A @ E @ F @ B ) @ C )
= ( hAPP @ E @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).
thf(130,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__mono) ).
thf(891,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(211,axiom,
! [A: $i,B: $i] :
( ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ B @ tc_HOL_Obool ) @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__absorb) ).
thf(1126,plain,
! [A: $i,B: $i] :
( ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ B @ tc_HOL_Obool ) @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(205,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ ( c_Equiv__Relations_Oquotient @ D @ B @ A ) )
=> ~ ! [E: $i] :
( ( C
= ( c_Relation_OImage @ D @ D @ A @ ( c_Set_Oinsert @ D @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) )
=> ~ ( c_member @ D @ E @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_quotientE) ).
thf(1108,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ ( c_Equiv__Relations_Oquotient @ D @ B @ A ) )
=> ~ ! [E: $i] :
( ( C
= ( c_Relation_OImage @ D @ D @ A @ ( c_Set_Oinsert @ D @ E @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ D @ tc_HOL_Obool ) ) ) ) )
=> ~ ( c_member @ D @ E @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(410,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Equiv__Relations_Oequiv @ F @ E @ D )
=> ( ( c_member @ F @ C @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ F @ tc_HOL_Obool ) @ ( c_Relation_OImage @ F @ F @ D @ ( c_Set_Oinsert @ F @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ F @ tc_HOL_Obool ) ) ) ) @ ( c_Relation_OImage @ F @ F @ D @ ( c_Set_Oinsert @ F @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ F @ tc_HOL_Obool ) ) ) ) ) )
=> ( c_member @ ( tc_prod @ F @ F ) @ ( c_Product__Type_OPair @ F @ F @ B @ A ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equiv__class__nondisjoint) ).
thf(1998,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Equiv__Relations_Oequiv @ F @ E @ D )
=> ( ( c_member @ F @ C @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ F @ tc_HOL_Obool ) @ ( c_Relation_OImage @ F @ F @ D @ ( c_Set_Oinsert @ F @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ F @ tc_HOL_Obool ) ) ) ) @ ( c_Relation_OImage @ F @ F @ D @ ( c_Set_Oinsert @ F @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ F @ tc_HOL_Obool ) ) ) ) ) )
=> ( c_member @ ( tc_prod @ F @ F ) @ ( c_Product__Type_OPair @ F @ F @ B @ A ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(400,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( ( c_member @ B @ A @ D )
=> ~ ( c_member @ B @ A @ C ) )
=> ~ ( ~ ( c_member @ B @ A @ D )
=> ( c_member @ B @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equalityCE) ).
thf(1966,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( ( c_member @ B @ A @ D )
=> ~ ( c_member @ B @ A @ C ) )
=> ~ ( ~ ( c_member @ B @ A @ D )
=> ( c_member @ B @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(19,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__sup @ D )
=> ( ( c_Lattices_Osemilattice__sup__class_Osup @ D @ ( c_Lattices_Osemilattice__sup__class_Osup @ D @ C @ B ) @ A )
= ( c_Lattices_Osemilattice__sup__class_Osup @ D @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ D @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup_Oassoc) ).
thf(556,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__sup @ D )
=> ( ( c_Lattices_Osemilattice__sup__class_Osup @ D @ ( c_Lattices_Osemilattice__sup__class_Osup @ D @ C @ B ) @ A )
= ( c_Lattices_Osemilattice__sup__class_Osup @ D @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ D @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(160,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) )
= ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B ) @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__Int__distrib) ).
thf(976,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) )
= ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B ) @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(135,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Olattice @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Lattices_Osemilattice__sup__class_Osup @ C @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__ord_I4_J) ).
thf(903,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Olattice @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Lattices_Osemilattice__sup__class_Osup @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(523,plain,
! [B: $i,A: $i] :
( ~ ( class_Lattices_Osemilattice__sup @ B )
| ( ( c_Lattices_Osemilattice__sup__class_Osup @ B @ A @ A )
= A ) ),
inference(cnf,[status(esa)],[522]) ).
thf(524,plain,
! [B: $i,A: $i] :
( ( ( c_Lattices_Osemilattice__sup__class_Osup @ B @ A @ A )
= A )
| ~ ( class_Lattices_Osemilattice__sup @ B ) ),
inference(lifteq,[status(thm)],[523]) ).
thf(456,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Relation_Oconverse @ D @ C @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ B @ A ) )
= ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_HOL_Obool ) @ ( c_Relation_Oconverse @ D @ C @ B ) @ ( c_Relation_Oconverse @ D @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converse__Int) ).
thf(2194,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Relation_Oconverse @ D @ C @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ B @ A ) )
= ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_HOL_Obool ) @ ( c_Relation_Oconverse @ D @ C @ B ) @ ( c_Relation_Oconverse @ D @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).
thf(334,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_member @ E @ D @ ( c_Relation_OImage @ C @ E @ B @ A ) )
=> ~ ! [F: $i] :
( ( c_member @ ( tc_prod @ C @ E ) @ ( c_Product__Type_OPair @ C @ E @ F @ D ) @ B )
=> ~ ( c_member @ C @ F @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ImageE) ).
thf(1654,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_member @ E @ D @ ( c_Relation_OImage @ C @ E @ B @ A ) )
=> ~ ! [F: $i] :
( ( c_member @ ( tc_prod @ C @ E ) @ ( c_Product__Type_OPair @ C @ E @ F @ D ) @ B )
=> ~ ( c_member @ C @ F @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(281,axiom,
! [A: $i,B: $i] :
( ? [C: $i] : ( c_member @ B @ C @ A )
<=> ( A
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ex__in__conv) ).
thf(1412,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] : ( c_member @ B @ C @ A )
=> ( A
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) ) )
& ( ( A
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ tc_HOL_Obool ) ) )
=> ? [C: $i] : ( c_member @ B @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(171,axiom,
! [A: $i,B: $i,C: $i] :
( ( C = B )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ A @ tc_HOL_Obool ) @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equalityD2) ).
thf(1010,plain,
! [A: $i,B: $i,C: $i] :
( ( C = B )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ A @ tc_HOL_Obool ) @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(276,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ D @ C @ B )
=> ( c_member @ D @ C @ ( c_Set_Oinsert @ D @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insertI2) ).
thf(1390,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ D @ C @ B )
=> ( c_member @ D @ C @ ( c_Set_Oinsert @ D @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(253,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ B ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) )
=> ( ( C != B )
=> ~ ! [E: $i] :
( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ E ) @ A )
=> ~ ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ E @ B ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converse__rtranclE) ).
thf(1289,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ B ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) )
=> ( ( C != B )
=> ~ ! [E: $i] :
( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ E ) @ A )
=> ~ ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ E @ B ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(114,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ A @ B )
=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equalityI) ).
thf(844,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ A @ B )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(332,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ C ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) )
=> ( ( hBOOL @ ( hAPP @ A @ D ) )
=> ( ! [F: $i] :
( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ F ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) )
=> ! [G: $i] :
( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ F @ G ) @ B )
=> ( ( hBOOL @ ( hAPP @ A @ F ) )
=> ( hBOOL @ ( hAPP @ A @ G ) ) ) ) )
=> ( hBOOL @ ( hAPP @ A @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__induct) ).
thf(1646,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ C ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) )
=> ( ( hBOOL @ ( hAPP @ A @ D ) )
=> ( ! [F: $i] :
( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ F ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) )
=> ! [G: $i] :
( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ F @ G ) @ B )
=> ( ( hBOOL @ ( hAPP @ A @ F ) )
=> ( hBOOL @ ( hAPP @ A @ G ) ) ) ) )
=> ( hBOOL @ ( hAPP @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(154,axiom,
! [A: $i,B: $i] : ( c_Relation_Osingle__valued @ B @ B @ ( c_Relation_OId__on @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_single__valued__Id__on) ).
thf(961,plain,
! [A: $i,B: $i] : ( c_Relation_Osingle__valued @ B @ B @ ( c_Relation_OId__on @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(452,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ B ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) )
=> ( ( c_member @ D @ B @ ( c_Wellfounded_Oacc @ D @ A ) )
=> ( c_member @ D @ C @ ( c_Wellfounded_Oacc @ D @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_acc__downwards__aux) ).
thf(2174,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ B ) @ ( c_Transitive__Closure_Ortrancl @ D @ A ) )
=> ( ( c_member @ D @ B @ ( c_Wellfounded_Oacc @ D @ A ) )
=> ( c_member @ D @ C @ ( c_Wellfounded_Oacc @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(472,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ C ) @ ( c_Transitive__Closure_Ortrancl @ E @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ E @ E ) @ tc_HOL_Obool ) @ B @ A ) ) )
=> ( ! [F: $i] :
( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ F ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) )
=> ! [G: $i] :
( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ F @ G ) @ A )
=> ( F = G ) ) )
=> ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ C ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__Un__separatorE) ).
thf(2251,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ C ) @ ( c_Transitive__Closure_Ortrancl @ E @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ E @ E ) @ tc_HOL_Obool ) @ B @ A ) ) )
=> ( ! [F: $i] :
( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ F ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) )
=> ! [G: $i] :
( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ F @ G ) @ A )
=> ( F = G ) ) )
=> ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ C ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).
thf(391,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( c_member @ D @ C @ B )
=> ( ~ ( c_member @ D @ C @ A )
=> ( ( ( c_Set_Oinsert @ D @ C @ B )
= ( c_Set_Oinsert @ D @ C @ A ) )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__ident) ).
thf(1903,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( c_member @ D @ C @ B )
=> ( ~ ( c_member @ D @ C @ A )
=> ( ( ( ( c_Set_Oinsert @ D @ C @ B )
= ( c_Set_Oinsert @ D @ C @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( c_Set_Oinsert @ D @ C @ B )
= ( c_Set_Oinsert @ D @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(292,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ D @ C @ B ) @ A ) )
<=> ( ( C = A )
| ( hBOOL @ ( hAPP @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__code) ).
thf(1481,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ D @ C @ B ) @ A ) )
=> ( ( C = A )
| ( hBOOL @ ( hAPP @ B @ A ) ) ) )
& ( ( ( C = A )
| ( hBOOL @ ( hAPP @ B @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Set_Oinsert @ D @ C @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(53,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) @ D @ B ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__mono) ).
thf(652,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) @ D @ B ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ E @ tc_HOL_Obool ) @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(376,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( c_member @ C @ B @ ( c_Wellfounded_Oacc @ C @ A ) )
=> ~ ! [D: $i] :
( ( c_member @ ( tc_prod @ C @ C ) @ ( c_Product__Type_OPair @ C @ C @ D @ B ) @ A )
=> ( c_member @ C @ D @ ( c_Wellfounded_Oacc @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__acc__down) ).
thf(1854,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( c_member @ C @ B @ ( c_Wellfounded_Oacc @ C @ A ) )
=> ~ ! [D: $i] :
( ( c_member @ ( tc_prod @ C @ C ) @ ( c_Product__Type_OPair @ C @ C @ D @ B ) @ A )
=> ( c_member @ C @ D @ ( c_Wellfounded_Oacc @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(370,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ D @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) )
<=> ( ( c_member @ D @ C @ B )
| ( c_member @ D @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__iff) ).
thf(1822,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_member @ D @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) )
=> ( ( c_member @ D @ C @ B )
| ( c_member @ D @ C @ A ) ) )
& ( ( ( c_member @ D @ C @ B )
| ( c_member @ D @ C @ A ) )
=> ( c_member @ D @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(155,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) @ D @ B ) @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__mono) ).
thf(963,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) @ D @ B ) @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ E @ tc_HOL_Obool ) @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(449,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ C ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) )
=> ( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ C @ A ) @ B )
=> ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ A ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__into__trancl1) ).
thf(2167,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ C ) @ ( c_Transitive__Closure_Ortrancl @ E @ B ) )
=> ( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ C @ A ) @ B )
=> ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ A ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).
thf(264,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ C ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) )
=> ( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ C @ A ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) )
=> ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ A ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__trans) ).
thf(1341,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ C ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) )
=> ( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ C @ A ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) )
=> ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ A ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(132,axiom,
! [A: $i,B: $i,C: $i] : ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__upper2) ).
thf(896,plain,
! [A: $i,B: $i,C: $i] : ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(341,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Wellfounded_Owf @ C @ B )
=> ~ ( c_member @ ( tc_prod @ C @ C ) @ ( c_Product__Type_OPair @ C @ C @ A @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__irrefl) ).
thf(1674,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Wellfounded_Owf @ C @ B )
=> ~ ( c_member @ ( tc_prod @ C @ C ) @ ( c_Product__Type_OPair @ C @ C @ A @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(331,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( c_Relation_ODomain @ C @ B @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
<=> ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ C @ B ) @ tc_HOL_Obool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Domain__empty__iff) ).
thf(1639,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( c_Relation_ODomain @ C @ B @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
=> ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ C @ B ) @ tc_HOL_Obool ) ) ) )
& ( ( A
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ C @ B ) @ tc_HOL_Obool ) ) )
=> ( ( c_Relation_ODomain @ C @ B @ A )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(165,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A ) )
= ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__left__absorb) ).
thf(995,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A ) )
= ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(444,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ G @ F ) )
=> ( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ C ) @ ( hAPP @ B @ F ) )
=> ( c_member @ ( tc_prod @ ( tc_prod @ A @ E ) @ ( tc_prod @ A @ E ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ A @ E ) @ ( tc_prod @ A @ E ) @ ( c_Product__Type_OPair @ A @ E @ F @ D ) @ ( c_Product__Type_OPair @ A @ E @ F @ C ) ) @ ( c_Recdef_Osame__fst @ A @ E @ G @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_same__fstI) ).
thf(2152,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ G @ F ) )
=> ( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ C ) @ ( hAPP @ B @ F ) )
=> ( c_member @ ( tc_prod @ ( tc_prod @ A @ E ) @ ( tc_prod @ A @ E ) ) @ ( c_Product__Type_OPair @ ( tc_prod @ A @ E ) @ ( tc_prod @ A @ E ) @ ( c_Product__Type_OPair @ A @ E @ F @ D ) @ ( c_Product__Type_OPair @ A @ E @ F @ C ) ) @ ( c_Recdef_Osame__fst @ A @ E @ G @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(475,axiom,
c_Arrow__Order__Mirabelle_Ounanimity @ v_F,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_u) ).
thf(2262,plain,
c_Arrow__Order__Mirabelle_Ounanimity @ v_F,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).
thf(179,axiom,
! [A: $i,B: $i] :
( ( c_Relation_ODomain @ B @ B @ ( c_Transitive__Closure_Otrancl @ B @ A ) )
= ( c_Relation_ODomain @ B @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__domain) ).
thf(1030,plain,
! [A: $i,B: $i] :
( ( c_Relation_ODomain @ B @ B @ ( c_Transitive__Closure_Otrancl @ B @ A ) )
= ( c_Relation_ODomain @ B @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(346,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ B ) @ ( c_Relation_Oconverse @ D @ D @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) )
=> ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ B ) @ ( c_Transitive__Closure_Otrancl @ D @ ( c_Relation_Oconverse @ D @ D @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__converseI) ).
thf(1689,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ B ) @ ( c_Relation_Oconverse @ D @ D @ ( c_Transitive__Closure_Otrancl @ D @ A ) ) )
=> ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ B ) @ ( c_Transitive__Closure_Otrancl @ D @ ( c_Relation_Oconverse @ D @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(23,axiom,
class_Lattices_Osemilattice__inf @ tc_HOL_Obool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL__Obool__Lattices_Osemilattice__inf) ).
thf(568,plain,
class_Lattices_Osemilattice__inf @ tc_HOL_Obool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(423,axiom,
! [A: $i,B: $i] :
( ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ B @ c_Arrow__Order__Mirabelle_OLin )
=> ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ B @ A ) @ c_Arrow__Order__Mirabelle_OLin ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mkbot__Lin) ).
thf(2041,plain,
! [A: $i,B: $i] :
( ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ B @ c_Arrow__Order__Mirabelle_OLin )
=> ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ B @ A ) @ c_Arrow__Order__Mirabelle_OLin ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(488,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ D @ C @ B )
=> ( c_member @ D @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UnI1) ).
thf(2330,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ D @ C @ B )
=> ( c_member @ D @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).
thf(229,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Set_Oinsert @ D @ C @ ( c_Set_Oinsert @ D @ B @ A ) )
= ( c_Set_Oinsert @ D @ B @ ( c_Set_Oinsert @ D @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__commute) ).
thf(1193,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Set_Oinsert @ D @ C @ ( c_Set_Oinsert @ D @ B @ A ) )
= ( c_Set_Oinsert @ D @ B @ ( c_Set_Oinsert @ D @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(92,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Olattice @ C )
=> ( ( c_Lattices_Osemilattice__sup__class_Osup @ C @ B @ A )
= ( c_Lattices_Osemilattice__sup__class_Osup @ C @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__aci_I5_J) ).
thf(763,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Olattice @ C )
=> ( ( c_Lattices_Osemilattice__sup__class_Osup @ C @ B @ A )
= ( c_Lattices_Osemilattice__sup__class_Osup @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(16,axiom,
class_Lattices_Odistrib__lattice @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Lattices_Odistrib__lattice) ).
thf(549,plain,
class_Lattices_Odistrib__lattice @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(11,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__inf @ C )
=> ( ( c_Lattices_Osemilattice__inf__class_Oinf @ C @ B @ A )
= ( c_Lattices_Osemilattice__inf__class_Oinf @ C @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__commute) ).
thf(536,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Osemilattice__inf @ C )
=> ( ( c_Lattices_Osemilattice__inf__class_Oinf @ C @ B @ A )
= ( c_Lattices_Osemilattice__inf__class_Oinf @ C @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(219,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Relation_ORange @ C @ B @ A )
= ( c_Relation_ODomain @ B @ C @ ( c_Relation_Oconverse @ C @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Range__def) ).
thf(1161,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Relation_ORange @ C @ B @ A )
= ( c_Relation_ODomain @ B @ C @ ( c_Relation_Oconverse @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(60,axiom,
! [A: $i,B: $i] :
( ( c_Relation_Oconverse @ B @ B @ ( c_Relation_OId__on @ B @ A ) )
= ( c_Relation_OId__on @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converse__Id__on) ).
thf(667,plain,
! [A: $i,B: $i] :
( ( c_Relation_Oconverse @ B @ B @ ( c_Relation_OId__on @ B @ A ) )
= ( c_Relation_OId__on @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(254,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ ( c_fequal @ B ) @ A ) )
| ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_c__fequal__1) ).
thf(1294,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ ( c_fequal @ B ) @ A ) )
| ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(195,axiom,
class_Orderings_Olinorder @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Olinorder) ).
thf(1077,plain,
class_Orderings_Olinorder @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(495,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ C ) @ B )
=> ( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ C @ A ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) )
=> ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ A ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__into__trancl2) ).
thf(2362,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ C ) @ B )
=> ( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ C @ A ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) )
=> ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ D @ A ) @ ( c_Transitive__Closure_Otrancl @ E @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).
thf(467,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B )
=> ( ( c_member @ D @ A @ C )
=> ( c_member @ D @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_set__mp) ).
thf(2230,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B )
=> ( ( c_member @ D @ A @ C )
=> ( c_member @ D @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).
thf(421,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Product__Type_Ointernal__split @ F @ E @ D @ C @ ( c_Product__Type_OPair @ F @ E @ B @ A ) )
= ( hAPP @ ( hAPP @ C @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_internal__split__conv) ).
thf(2036,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Product__Type_Ointernal__split @ F @ E @ D @ C @ ( c_Product__Type_OPair @ F @ E @ B @ A ) )
= ( hAPP @ ( hAPP @ C @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(260,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ F @ tc_HOL_Obool ) @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( c_Relation_OImage @ F @ E @ D @ B ) @ ( c_Relation_OImage @ F @ E @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__mono) ).
thf(1309,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_HOL_Obool ) @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ F @ tc_HOL_Obool ) @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( c_Relation_OImage @ F @ E @ D @ B ) @ ( c_Relation_OImage @ F @ E @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(441,axiom,
( ( ( v_a____ != v_b_H____ )
& ( v_b____ = v_a_H____ ) )
=> ( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a____ @ v_b____ ) @ ( hAPP @ v_F @ v_P____ ) )
<=> ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a_H____ @ v_b_H____ ) @ ( hAPP @ v_F @ v_P_H____ ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_calculation_I3_J) ).
thf(2142,plain,
( ( ( v_a____ != v_b_H____ )
& ( v_b____ = v_a_H____ ) )
=> ( ( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a____ @ v_b____ ) @ ( hAPP @ v_F @ v_P____ ) )
=> ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a_H____ @ v_b_H____ ) @ ( hAPP @ v_F @ v_P_H____ ) ) )
& ( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a_H____ @ v_b_H____ ) @ ( hAPP @ v_F @ v_P_H____ ) )
=> ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ v_a____ @ v_b____ ) @ ( hAPP @ v_F @ v_P____ ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).
thf(463,axiom,
! [A: $i,B: $i] :
( ( c_Nitpick_Orefl_H @ B @ A )
<=> ! [C: $i] : ( c_member @ ( tc_prod @ B @ B ) @ ( c_Product__Type_OPair @ B @ B @ C @ C ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nitpick_Orefl_H__def) ).
thf(2218,plain,
! [A: $i,B: $i] :
( ( ( c_Nitpick_Orefl_H @ B @ A )
=> ! [C: $i] : ( c_member @ ( tc_prod @ B @ B ) @ ( c_Product__Type_OPair @ B @ B @ C @ C ) @ A ) )
& ( ! [C: $i] : ( c_member @ ( tc_prod @ B @ B ) @ ( c_Product__Type_OPair @ B @ B @ C @ C ) @ A )
=> ( c_Nitpick_Orefl_H @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(89,axiom,
! [A: $i,B: $i,C: $i] :
( ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) ) )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_less__by__empty) ).
thf(752,plain,
! [A: $i,B: $i,C: $i] :
( ( C
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) ) )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_HOL_Obool ) @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(250,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B ) @ A )
= ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ A ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__Diff) ).
thf(1280,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B ) @ A )
= ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ A ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(314,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ D @ C @ B )
=> ( ( c_member @ D @ C @ A )
=> ( c_member @ D @ C @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_IntI) ).
thf(1578,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ D @ C @ B )
=> ( ( c_member @ D @ C @ A )
=> ( c_member @ D @ C @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(501,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Equiv__Relations_Oequiv @ E @ D @ C )
=> ( ( c_member @ E @ B @ D )
=> ( ( c_member @ E @ A @ D )
=> ( ( ( c_Relation_OImage @ E @ E @ C @ ( c_Set_Oinsert @ E @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) )
= ( c_Relation_OImage @ E @ E @ C @ ( c_Set_Oinsert @ E @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) ) )
<=> ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ B @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eq__equiv__class__iff) ).
thf(2385,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Equiv__Relations_Oequiv @ E @ D @ C )
=> ( ( c_member @ E @ B @ D )
=> ( ( c_member @ E @ A @ D )
=> ( ( ( ( c_Relation_OImage @ E @ E @ C @ ( c_Set_Oinsert @ E @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) )
= ( c_Relation_OImage @ E @ E @ C @ ( c_Set_Oinsert @ E @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) ) )
=> ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ B @ A ) @ C ) )
& ( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ B @ A ) @ C )
=> ( ( c_Relation_OImage @ E @ E @ C @ ( c_Set_Oinsert @ E @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) )
= ( c_Relation_OImage @ E @ E @ C @ ( c_Set_Oinsert @ E @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).
thf(157,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( c_member @ D @ C @ B )
=> ( ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Set_Oinsert @ D @ C @ A ) @ B )
= ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__insert__left__if0) ).
thf(967,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( c_member @ D @ C @ B )
=> ( ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Set_Oinsert @ D @ C @ A ) @ B )
= ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(237,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Olattice @ C )
=> ( ( c_Lattices_Osemilattice__sup__class_Osup @ C @ B @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C @ B @ A ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sup__inf__absorb) ).
thf(1229,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Olattice @ C )
=> ( ( c_Lattices_Osemilattice__sup__class_Osup @ C @ B @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C @ B @ A ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(304,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Equiv__Relations_Oequiv @ E @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( c_Relation_OImage @ E @ E @ C @ ( c_Set_Oinsert @ E @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) ) @ ( c_Relation_OImage @ E @ E @ C @ ( c_Set_Oinsert @ E @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) ) )
=> ( ( c_member @ E @ B @ D )
=> ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ A @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__equiv__class) ).
thf(1546,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Equiv__Relations_Oequiv @ E @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( c_Relation_OImage @ E @ E @ C @ ( c_Set_Oinsert @ E @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) ) @ ( c_Relation_OImage @ E @ E @ C @ ( c_Set_Oinsert @ E @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) ) )
=> ( ( c_member @ E @ B @ D )
=> ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ A @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(318,axiom,
! [A: $i,B: $i] :
( ( B != A )
=> ? [C: $i] :
( ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ C @ c_Arrow__Order__Mirabelle_OLin )
& ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ B @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_complete__Lin) ).
thf(1593,plain,
! [A: $i,B: $i] :
( ( B != A )
=> ? [C: $i] :
( ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ C @ c_Arrow__Order__Mirabelle_OLin )
& ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ B @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(121,axiom,
class_Lattices_Olattice @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Lattices_Olattice) ).
thf(867,plain,
class_Lattices_Olattice @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(120,axiom,
! [A: $i,B: $i,C: $i,D: $i] : ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Relation_ODomain @ D @ C @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ B @ A ) ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Relation_ODomain @ D @ C @ B ) @ ( c_Relation_ODomain @ D @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Domain__Int__subset) ).
thf(865,plain,
! [A: $i,B: $i,C: $i,D: $i] : ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Relation_ODomain @ D @ C @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_HOL_Obool ) @ B @ A ) ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Relation_ODomain @ D @ C @ B ) @ ( c_Relation_ODomain @ D @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(38,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Lattices_Osemilattice__inf @ E )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Lattices_Osemilattice__inf__class_Oinf @ E @ D @ B ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ E @ C @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__mono) ).
thf(603,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( class_Lattices_Osemilattice__inf @ E )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ E @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ E @ ( c_Lattices_Osemilattice__inf__class_Oinf @ E @ D @ B ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ E @ C @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(102,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__Diff__Int) ).
thf(801,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(270,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ E @ D ) @ ( hAPP @ E @ C ) )
=> ( ( c_member @ ( tc_prod @ B @ B ) @ ( c_Product__Type_OPair @ B @ B @ D @ C ) @ A )
=> ( c_member @ ( tc_prod @ B @ B ) @ ( c_Product__Type_OPair @ B @ B @ D @ C ) @ ( c_Wellfounded_Omlex__prod @ B @ E @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mlex__leq) ).
thf(1363,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat @ ( hAPP @ E @ D ) @ ( hAPP @ E @ C ) )
=> ( ( c_member @ ( tc_prod @ B @ B ) @ ( c_Product__Type_OPair @ B @ B @ D @ C ) @ A )
=> ( c_member @ ( tc_prod @ B @ B ) @ ( c_Product__Type_OPair @ B @ B @ D @ C ) @ ( c_Wellfounded_Omlex__prod @ B @ E @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(295,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Equiv__Relations_Oequiv @ E @ D @ C )
=> ( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ B @ A ) @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( c_Relation_OImage @ E @ E @ C @ ( c_Set_Oinsert @ E @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) ) @ ( c_Relation_OImage @ E @ E @ C @ ( c_Set_Oinsert @ E @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_equiv__class__subset) ).
thf(1495,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Equiv__Relations_Oequiv @ E @ D @ C )
=> ( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ B @ A ) @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( c_Relation_OImage @ E @ E @ C @ ( c_Set_Oinsert @ E @ B @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) ) @ ( c_Relation_OImage @ E @ E @ C @ ( c_Set_Oinsert @ E @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ E @ tc_HOL_Obool ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(335,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Obot @ C )
=> ( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ C ) ) @ A )
= ( c_Orderings_Obot__class_Obot @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bot__apply) ).
thf(1657,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Obot @ C )
=> ( ( hAPP @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ B @ C ) ) @ A )
= ( c_Orderings_Obot__class_Obot @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(180,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Olattice @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Lattices_Osemilattice__sup__class_Osup @ C @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__ord_I3_J) ).
thf(1033,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Olattice @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ B @ ( c_Lattices_Osemilattice__sup__class_Osup @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(223,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ E @ tc_HOL_Obool ) @ D @ A ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ E @ tc_HOL_Obool ) @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Diff__mono) ).
thf(1172,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) @ D @ C )
=> ( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) @ B @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ E @ tc_HOL_Obool ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ E @ tc_HOL_Obool ) @ D @ A ) @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ E @ tc_HOL_Obool ) @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(280,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ D @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) )
=> ( ~ ( c_member @ D @ C @ B )
=> ( c_member @ D @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_UnE) ).
thf(1410,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ D @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) )
=> ( ~ ( c_member @ D @ C @ B )
=> ( c_member @ D @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(508,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( hAPP @ B @ C )
= ( hAPP @ A @ C ) )
=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ext) ).
thf(2417,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( hAPP @ B @ C )
= ( hAPP @ A @ C ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).
thf(464,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Wellfounded_Owf @ D @ C )
=> ( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ B @ A ) @ C )
=> ~ ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ A @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__not__sym) ).
thf(2223,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Wellfounded_Owf @ D @ C )
=> ( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ B @ A ) @ C )
=> ~ ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ A @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(50,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A ) )
= ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Un__left__absorb) ).
thf(635,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A ) )
= ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(201,axiom,
! [A: $i,B: $i] :
( ( c_Wellfounded_Owf @ B @ A )
=> ( c_Wellfounded_OwfP @ B @ ( c_FunDef_Oin__rel @ B @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_wf__in__rel) ).
thf(1093,plain,
! [A: $i,B: $i] :
( ( c_Wellfounded_Owf @ B @ A )
=> ( c_Wellfounded_OwfP @ B @ ( c_FunDef_Oin__rel @ B @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(84,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ ( c_Set_Oinsert @ D @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__insertI2) ).
thf(740,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ ( c_Set_Oinsert @ D @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(267,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Relation_Osingle__valued @ E @ E @ D )
=> ( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ C @ B ) @ ( c_Transitive__Closure_Ortrancl @ E @ D ) )
=> ( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ C @ A ) @ ( c_Transitive__Closure_Ortrancl @ E @ D ) )
=> ( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ B @ A ) @ ( c_Transitive__Closure_Ortrancl @ E @ D ) )
| ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ A @ B ) @ ( c_Transitive__Closure_Ortrancl @ E @ D ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_single__valued__confluent) ).
thf(1352,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Relation_Osingle__valued @ E @ E @ D )
=> ( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ C @ B ) @ ( c_Transitive__Closure_Ortrancl @ E @ D ) )
=> ( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ C @ A ) @ ( c_Transitive__Closure_Ortrancl @ E @ D ) )
=> ( ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ B @ A ) @ ( c_Transitive__Closure_Ortrancl @ E @ D ) )
| ( c_member @ ( tc_prod @ E @ E ) @ ( c_Product__Type_OPair @ E @ E @ A @ B ) @ ( c_Transitive__Closure_Ortrancl @ E @ D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(245,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Olattice @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C @ B @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_inf__sup__ord_I2_J) ).
thf(1268,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Lattices_Olattice @ C )
=> ( c_Orderings_Oord__class_Oless__eq @ C @ ( c_Lattices_Osemilattice__inf__class_Oinf @ C @ B @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(35,axiom,
class_Orderings_Oord @ tc_Nat_Onat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Oord) ).
thf(596,plain,
class_Orderings_Oord @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( class_Lattices_Odistrib__lattice @ B )
=> ( class_Lattices_Odistrib__lattice @ ( tc_fun @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun__Lattices_Odistrib__lattice) ).
thf(528,plain,
! [A: $i,B: $i] :
( ( class_Lattices_Odistrib__lattice @ B )
=> ( class_Lattices_Odistrib__lattice @ ( tc_fun @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(306,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( c_member @ B @ D @ A )
=> ( c_member @ ( tc_prod @ B @ B ) @ ( c_Product__Type_OPair @ B @ B @ D @ C ) @ ( c_Relation_OId__on @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Id__on__eqI) ).
thf(1550,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( c_member @ B @ D @ A )
=> ( c_member @ ( tc_prod @ B @ B ) @ ( c_Product__Type_OPair @ B @ B @ D @ C ) @ ( c_Relation_OId__on @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(79,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) )
!= ( c_Set_Oinsert @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_empty__not__insert) ).
thf(723,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) )
!= ( c_Set_Oinsert @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(256,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B )
=> ( ( c_member @ D @ A @ C )
=> ( c_member @ D @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subsetD) ).
thf(1299,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B )
=> ( ( c_member @ D @ A @ C )
=> ( c_member @ D @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(385,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( c_member @ B @ A @ D )
<=> ( c_member @ B @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eqset__imp__iff) ).
thf(1885,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( ( c_member @ B @ A @ D )
=> ( c_member @ B @ A @ C ) )
& ( ( c_member @ B @ A @ C )
=> ( c_member @ B @ A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(279,axiom,
! [A: $i,B: $i] :
( ( c_Relation_Oantisym @ B @ A )
<=> ! [C: $i,D: $i] :
( ( c_member @ ( tc_prod @ B @ B ) @ ( c_Product__Type_OPair @ B @ B @ C @ D ) @ A )
=> ( ( c_member @ ( tc_prod @ B @ B ) @ ( c_Product__Type_OPair @ B @ B @ D @ C ) @ A )
=> ( C = D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_antisym__def) ).
thf(1399,plain,
! [A: $i,B: $i] :
( ( ( c_Relation_Oantisym @ B @ A )
=> ! [C: $i,D: $i] :
( ( c_member @ ( tc_prod @ B @ B ) @ ( c_Product__Type_OPair @ B @ B @ C @ D ) @ A )
=> ( ( c_member @ ( tc_prod @ B @ B ) @ ( c_Product__Type_OPair @ B @ B @ D @ C ) @ A )
=> ( C = D ) ) ) )
& ( ! [C: $i,D: $i] :
( ( c_member @ ( tc_prod @ B @ B ) @ ( c_Product__Type_OPair @ B @ B @ C @ D ) @ A )
=> ( ( c_member @ ( tc_prod @ B @ B ) @ ( c_Product__Type_OPair @ B @ B @ D @ C ) @ A )
=> ( C = D ) ) )
=> ( c_Relation_Oantisym @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(40,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B ) @ A )
= ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__assoc) ).
thf(607,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B ) @ A )
= ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(239,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) )
= ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Int__Un__distrib) ).
thf(1236,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) )
= ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B ) @ ( c_Lattices_Osemilattice__inf__class_Oinf @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(439,axiom,
! [A: $i,B: $i] :
( ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ B @ c_Arrow__Order__Mirabelle_OLin )
=> ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( c_Arrow__Order__Mirabelle_Omktop @ B @ A ) @ c_Arrow__Order__Mirabelle_OLin ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_mktop__Lin) ).
thf(2127,plain,
! [A: $i,B: $i] :
( ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ B @ c_Arrow__Order__Mirabelle_OLin )
=> ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( c_Arrow__Order__Mirabelle_Omktop @ B @ A ) @ c_Arrow__Order__Mirabelle_OLin ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(371,axiom,
! [A: $i,B: $i,C: $i] :
( ( C != B )
=> ( ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ A @ c_Arrow__Order__Mirabelle_OLin )
=> ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( c_Arrow__Order__Mirabelle_Oabove @ A @ C @ B ) @ c_Arrow__Order__Mirabelle_OLin ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_above__Lin) ).
thf(1829,plain,
! [A: $i,B: $i,C: $i] :
( ( C != B )
=> ( ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ A @ c_Arrow__Order__Mirabelle_OLin )
=> ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ ( c_Arrow__Order__Mirabelle_Oabove @ A @ C @ B ) @ c_Arrow__Order__Mirabelle_OLin ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(212,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( c_Relation_OImage @ C @ C @ B @ A ) @ A )
=> ( ( c_Relation_OImage @ C @ C @ ( c_Transitive__Closure_Ortrancl @ C @ B ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Image__closed__trancl) ).
thf(1129,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ ( c_Relation_OImage @ C @ C @ B @ A ) @ A )
=> ( ( c_Relation_OImage @ C @ C @ ( c_Transitive__Closure_Ortrancl @ C @ B ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(137,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__sup @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ D @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__supI2) ).
thf(908,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__sup @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ D @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(164,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Set_Oinsert @ C @ B @ ( c_Set_Oinsert @ C @ B @ A ) )
= ( c_Set_Oinsert @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_insert__absorb2) ).
thf(992,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Set_Oinsert @ C @ B @ ( c_Set_Oinsert @ C @ B @ A ) )
= ( c_Set_Oinsert @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(384,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ D @ C @ ( c_Relation_ORange @ B @ D @ A ) )
<=> ? [E: $i] : ( c_member @ ( tc_prod @ B @ D ) @ ( c_Product__Type_OPair @ B @ D @ E @ C ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Range__iff) ).
thf(1880,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_member @ D @ C @ ( c_Relation_ORange @ B @ D @ A ) )
=> ? [E: $i] : ( c_member @ ( tc_prod @ B @ D ) @ ( c_Product__Type_OPair @ B @ D @ E @ C ) @ A ) )
& ( ? [E: $i] : ( c_member @ ( tc_prod @ B @ D ) @ ( c_Product__Type_OPair @ B @ D @ E @ C ) @ A )
=> ( c_member @ D @ C @ ( c_Relation_ORange @ B @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(286,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Nitpick_Owf__wfrec_H @ E @ D @ C @ B @ A )
= ( hAPP @ ( hAPP @ B @ ( c_Recdef_Ocut @ E @ D @ ( c_Nitpick_Owf__wfrec @ E @ D @ C @ B ) @ C @ A ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Nitpick_Owf__wfrec_H__def) ).
thf(1431,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Nitpick_Owf__wfrec_H @ E @ D @ C @ B @ A )
= ( hAPP @ ( hAPP @ B @ ( c_Recdef_Ocut @ E @ D @ ( c_Nitpick_Owf__wfrec @ E @ D @ C @ B ) @ C @ A ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(272,axiom,
! [A: $i] :
( ( c_Transitive__Closure_Otrancl @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_trancl__empty) ).
thf(1367,plain,
! [A: $i] :
( ( c_Transitive__Closure_Otrancl @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) ) )
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ A @ A ) @ tc_HOL_Obool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(398,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_member @ ( tc_prod @ E @ D ) @ ( c_Product__Type_OPair @ E @ D @ C @ B ) @ ( c_Relation_Oconverse @ D @ E @ A ) )
=> ( c_member @ ( tc_prod @ D @ E ) @ ( c_Product__Type_OPair @ D @ E @ B @ C ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_converseD) ).
thf(1962,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_member @ ( tc_prod @ E @ D ) @ ( c_Product__Type_OPair @ E @ D @ C @ B ) @ ( c_Relation_Oconverse @ D @ E @ A ) )
=> ( c_member @ ( tc_prod @ D @ E ) @ ( c_Product__Type_OPair @ D @ E @ B @ C ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(358,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ? [E: $i] :
( ( c_member @ D @ E @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B ) )
& ( hBOOL @ ( hAPP @ A @ E ) ) )
<=> ( ? [E: $i] :
( ( c_member @ D @ E @ C )
& ( hBOOL @ ( hAPP @ A @ E ) ) )
| ? [E: $i] :
( ( c_member @ D @ E @ B )
& ( hBOOL @ ( hAPP @ A @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_bex__Un) ).
thf(1737,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ? [E: $i] :
( ( c_member @ D @ E @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B ) )
& ( hBOOL @ ( hAPP @ A @ E ) ) )
=> ( ? [E: $i] :
( ( c_member @ D @ E @ C )
& ( hBOOL @ ( hAPP @ A @ E ) ) )
| ? [E: $i] :
( ( c_member @ D @ E @ B )
& ( hBOOL @ ( hAPP @ A @ E ) ) ) ) )
& ( ( ? [E: $i] :
( ( c_member @ D @ E @ C )
& ( hBOOL @ ( hAPP @ A @ E ) ) )
| ? [E: $i] :
( ( c_member @ D @ E @ B )
& ( hBOOL @ ( hAPP @ A @ E ) ) ) )
=> ? [E: $i] :
( ( c_member @ D @ E @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ D @ tc_HOL_Obool ) @ C @ B ) )
& ( hBOOL @ ( hAPP @ A @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(57,axiom,
! [A: $i,B: $i] :
( ( c_Relation_ODomain @ B @ B @ ( c_Relation_OId__on @ B @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Domain__Id__on) ).
thf(659,plain,
! [A: $i,B: $i] :
( ( c_Relation_ODomain @ B @ B @ ( c_Relation_OId__on @ B @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(415,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ C @ c_Arrow__Order__Mirabelle_OLin )
=> ( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ B @ A ) @ C )
=> ~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ A @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Lin__irrefl) ).
thf(2018,plain,
! [A: $i,B: $i,C: $i] :
( ( c_member @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) @ C @ c_Arrow__Order__Mirabelle_OLin )
=> ( ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ B @ A ) @ C )
=> ~ ( c_member @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Product__Type_OPair @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt @ A @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(429,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( c_Product__Type_Ocurry @ E @ D @ tc_HOL_Obool @ C @ B @ A ) )
=> ( hBOOL @ ( hAPP @ C @ ( c_Product__Type_OPair @ E @ D @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_curryE) ).
thf(2059,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( c_Product__Type_Ocurry @ E @ D @ tc_HOL_Obool @ C @ B @ A ) )
=> ( hBOOL @ ( hAPP @ C @ ( c_Product__Type_OPair @ E @ D @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(293,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ D @ C @ B )
=> ( ~ ( c_member @ D @ C @ A )
=> ( c_member @ D @ C @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_DiffI) ).
thf(1490,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ D @ C @ B )
=> ( ~ ( c_member @ D @ C @ A )
=> ( c_member @ D @ C @ ( c_Groups_Ominus__class_Ominus @ ( tc_fun @ D @ tc_HOL_Obool ) @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(199,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__inf @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ C @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__infI) ).
thf(1088,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__inf @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ A )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ C @ ( c_Lattices_Osemilattice__inf__class_Oinf @ D @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(435,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ B ) @ ( c_Relation_OId__on @ D @ A ) )
<=> ( ( C = B )
& ( c_member @ D @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Id__on__iff) ).
thf(2106,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ B ) @ ( c_Relation_OId__on @ D @ A ) )
=> ( ( C = B )
& ( c_member @ D @ C @ A ) ) )
& ( ( ( C = B )
& ( c_member @ D @ C @ A ) )
=> ( c_member @ ( tc_prod @ D @ D ) @ ( c_Product__Type_OPair @ D @ D @ C @ B ) @ ( c_Relation_OId__on @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(192,axiom,
! [A: $i,B: $i,C: $i] : ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rtrancl__Un__subset) ).
thf(1069,plain,
! [A: $i,B: $i,C: $i] : ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ A ) ) @ ( c_Transitive__Closure_Ortrancl @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_HOL_Obool ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(172,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ ( c_Set_Oinsert @ C @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) )
=> ( ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
| ( B
= ( c_Set_Oinsert @ C @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_subset__singletonD) ).
thf(1014,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Orderings_Oord__class_Oless__eq @ ( tc_fun @ C @ tc_HOL_Obool ) @ B @ ( c_Set_Oinsert @ C @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) )
=> ( ( B
= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) )
| ( B
= ( c_Set_Oinsert @ C @ A @ ( c_Orderings_Obot__class_Obot @ ( tc_fun @ C @ tc_HOL_Obool ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(33,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__sup @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ D @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_le__supI1) ).
thf(592,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Lattices_Osemilattice__sup @ D )
=> ( ( c_Orderings_Oord__class_Oless__eq @ D @ C @ B )
=> ( c_Orderings_Oord__class_Oless__eq @ D @ C @ ( c_Lattices_Osemilattice__sup__class_Osup @ D @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(2469,plain,
( ( ( hAPP @ v_F @ v_P____ )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) )
| ( v_F != v_F )
| ( v_P_H____ != v_P____ ) ),
inference(simp,[status(thm)],[2467]) ).
thf(2470,plain,
( ( ( hAPP @ v_F @ v_P____ )
!= ( c_Orderings_Obot__class_Obot @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_HOL_Obool ) ) )
| ( v_P_H____ != v_P____ ) ),
inference(simp,[status(thm)],[2469]) ).
thf(47759,plain,
$false,
inference(cvc4,[status(thm)],[2163,1469,1190,2341,1633,2263,1729,628,1899,893,1083,941,1950,1554,1686,1559,1105,1158,1924,730,1522,2395,1618,1205,2114,1793,677,597,1041,2117,2104,878,655,533,550,1164,1275,1872,814,1988,747,1354,930,670,1497,1705,1078,1426,1196,898,2348,2046,1914,1782,782,709,2020,1613,1724,565,1623,829,1095,973,1046,2400,2067,1265,1703,570,1985,2039,1660,1992,2466,949,542,1330,1860,2274,917,1832,934,1059,1132,2420,817,559,638,1892,1147,870,881,1115,1773,1815,1232,1847,2169,2403,1479,1609,924,756,2259,834,937,1960,1283,905,1864,2122,1020,574,766,1843,2367,1394,998,849,527,1696,1564,1896,692,2392,2154,1651,1074,2011,920,512,1691,546,1306,761,2118,798,1199,2364,1311,2232,2307,2061,2000,910,1343,2147,1666,1580,2277,1174,1676,1502,1751,788,2150,1370,1423,847,1365,2332,665,2179,1210,682,1573,583,2200,522,1392,2228,697,1983,2157,1270,1017,615,1121,1587,1672,1006,1878,1719,610,1118,2245,1350,519,742,884,1028,1361,1964,2323,686,2312,1207,2317,706,1810,2172,679,970,2285,701,1297,1530,654,2243,721,569,2272,605,622,837,1150,1249,2052,1246,1979,779,1202,1086,633,2043,1054,1170,1071,1663,1515,1167,530,1185,1732,1434,1857,1286,1035,2189,1616,773,586,2338,1996,2423,662,718,2176,1698,2033,824,1273,1548,856,573,689,2376,1631,965,750,1727,1251,618,2028,1301,562,2048,2016,1388,958,1124,2225,732,875,826,577,711,1226,545,1428,1669,713,1239,1090,2457,804,2346,2119,900,831,2383,1894,1524,737,2197,2510,979,1492,1603,649,1043,1571,599,890,811,1471,2025,631,858,1993,594,1909,1862,1325,915,1556,1061,2314,2129,2343,700,520,1112,1688,983,1926,768,695,2064,1176,986,1000,1477,2390,2207,1805,2069,912,521,2212,2171,1066,868,851,1102,1694,922,1626,2239,1304,589,944,795,1420,927,1277,553,1049,1990,617,2202,1018,2256,776,1003,580,1598,1025,887,1566,1531,1798,525,1611,1156,1790,2165,1637,1188,1038,1869,1785,1901,1679,2468,951,808,2056,1849,703,2379,2279,1008,2030,1372,612,2411,744,2426,1981,656,1802,1023,2320,1052,1504,727,1585,1140,2013,539,2215,891,1126,1108,1998,1966,556,976,903,524,2194,1654,1412,1010,1390,1289,844,1646,961,2174,2251,1903,1481,652,1854,1822,963,517,2167,1341,896,1674,1639,995,2152,2262,1030,1689,568,2041,2330,1193,763,549,536,1161,667,1294,1077,2362,2230,2036,1309,2142,2218,1348,752,1280,1578,2385,967,1229,1546,1593,867,865,603,801,1363,1495,1657,1033,1172,1410,2417,2223,635,1093,740,1352,1268,596,528,1550,723,1299,1885,1399,607,1236,2127,1829,1129,908,992,1880,1431,1367,1962,1737,659,2018,2059,1490,1088,2106,1069,1014,592,2470]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : SCT158+1 : TPTP v8.1.2. Released v5.2.0.
% 0.10/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n003.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Thu May 18 15:33:46 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.88/0.77 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.40/1.00 % [INFO] Parsing done (219ms).
% 1.40/1.00 % [INFO] Running in sequential loop mode.
% 2.22/1.19 % [INFO] eprover registered as external prover.
% 2.22/1.20 % [INFO] cvc4 registered as external prover.
% 2.22/1.20 % [INFO] Scanning for conjecture ...
% 2.40/1.31 % [INFO] Found a conjecture and 528 axioms. Running axiom selection ...
% 3.08/1.44 % [INFO] Axiom selection finished. Selected 509 axioms (removed 19 axioms).
% 4.09/1.70 % [INFO] Problem is first-order (TPTP FOF).
% 4.09/1.73 % [INFO] Type checking passed.
% 4.09/1.73 % [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 ...
% 95.72/22.38 % External prover 'cvc4' found a proof!
% 95.72/22.38 % [INFO] Killing All external provers ...
% 95.72/22.38 % Time passed: 21869ms (effective reasoning time: 21374ms)
% 95.72/22.38 % 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)>
% 95.72/22.38 % Axioms used in derivation (509): fact_wf__not__refl, fact_Int__insert__left__if1, fact_converseI, fact_Un__absorb1, fact_wfrec__rel_Ointros, fact_single__valued__Id__on, fact_insertCI, fact_ImageE, fact_wf__not__sym, fact_wf__inv__image, fact_converse__converse, fact_Field__empty, fact_converse__rtrancl__induct2, fact_singleton__iff, fact_refl__onD2, fact_Int__lower1, fact_cut__apply, fact_le__inf__iff, fact_sup1I1, fact_Range__Int__subset, fact_insert__iff, fact__C1_C, arity_Nat__Onat__Lattices_Olattice, fact_IIA__def, fact_UnI1, fact_insert__subset, fact_unanimity__def, fact_inf__sup__aci_I4_J, fact_Image__Int__eq, fact_inf_Oassoc, fact_rtranclD, fact_bot__apply, fact_sup__apply, fact_Un__mono, fact_Transitive__Closure_Otrancl__into__trancl, fact_prod_Orecs, fact_mono__Field, fact_curry__conv, fact_IdI, fact_insertI1, fact_Un__empty__left, fact_Un__insert__left, fact_in__mktop, fact_inf__absorb1, fact_equiv__class__eq, fact_in__mkbot, fact_sup__assoc, fact_curryE, fact_empty__not__insert, fact_rtrancl__empty, arity_fun__Lattices_Olattice, fact_rtrancl_Ortrancl__refl, fact_acc_Osimps, arity_Nat__Onat__Lattices_Osemilattice__inf, fact_sup__inf__absorb, fact_Int__left__commute, fact_r__into__trancl_H, fact_inf__sup__distrib2, fact_inf__sup__ord_I2_J, help_c__fequal__2, fact_wf__Int1, fact_acyclic__impl__antisym__rtrancl, fact_tranclD2, fact_below__Lin, fact_converse__rtrancl__induct, fact_rtrancl__mono, fact_rtrancl__subset__rtrancl, fact_insert__not__empty, fact_converse__rtranclE2, fact__C4_C, fact_split__paired__All, fact_Un__Diff__Int, fact_complete__Lin, fact_Diff__subset, fact_Field__Un, fact_acyclic__converse, fact_sup__absorb1, fact_equalityD2, fact_rtrancl__converse, fact_Int__insert__right, fact_Range__empty, fact_rev__ImageI, fact_tranclE, fact_linear__alt, fact_inf1D2, fact_acc_OaccI, fact_le__supI, fact_antisymI, fact_inf_Oleft__commute, fact_le__supI2, fact_converse__Int, fact_single__valued__Id, fact_predicate2D, fact_Int__empty__left, fact_sup__ge2, fact_Diff__idemp, fact_singleton__inject, fact_le__funD, fact_emptyE, fact_le__fun__def, fact_acc__subset, fact_wf__measure, fact_wf__irrefl, fact_Image__Un, fact_lnear__order__on__empty, fact_Domain__empty__iff, fact_in__mono, fact_Domain__Un__eq, fact_wf__lex__prod, fact_Int__absorb2, fact_Diff__subset__conv, fact_DiffE, fact_quotient__is__empty, arity_fun__Lattices_Osemilattice__inf, fact_sup__least, fact_Int__assoc, arity_HOL__Obool__Lattices_Olattice, fact_Int__Un__distrib, fact_equiv__class__subset, fact_rtrancl__subset, fact_quotient__eq__iff, fact_subset__singletonD, fact_Field__converse, fact_sup__eq__bot__iff, fact_wfE__pf, fact_single__valued__subset, fact_Id__on__iff, fact_insert__is__Un, fact_A_I4_J, fact_mkbot__Lin, fact_congruent2__implies__congruent, fact_minus__apply, fact_tfl__cut__apply, fact_wf__subset, fact_rtrancl__Un__separator__converseE, fact_inf__commute, fact_rtrancl__reflcl, fact_antisym__empty, fact_trancl__converse, fact_converse__inv__image, fact_Int__insert__left, fact_Domain__insert, fact_refl__onD, fact_sup__bot__left, fact__096a_A_061_Ab_H_A_G_Ab_A_061_Aa_H_096, fact_acc__downwards, arity_Nat__Onat__Lattices_Odistrib__lattice, fact_distrib__inf__le, fact_dictator__def, fact_sup1I2, fact_inf1I, fact_Domain__mono, fact_wf__Int2, fact_insert__code, arity_HOL__Obool__Lattices_Osemilattice__sup, arity_fun__Lattices_Osemilattice__sup, fact_calculation_I2_J, fact_Int__insert__right__if0, fact_Un__left__commute, fact_Un__empty, fact_inf_Oidem, fact_Domain__empty, fact_wf__empty, fact_Image__Id__on, fact_bot__least, fact_subset__Image1__Image1__iff, fact_le__infI2, fact_rtrancl__reflcl__absorb, fact_Domain__Diff__subset, fact_refl__on__empty, arity_Nat__Onat__Groups_Ominus, fact_rtrancl__Un__separatorE, fact_rtrancl__Un__rtrancl, fact_RangeI, arity_HOL__Obool__Groups_Ominus, fact_predicate1D, fact_DomainI, fact__C2_C, fact_inf__sup__ord_I1_J, fact_inf1E, fact_ex__in__conv, fact_eq__mem, fact_sup__left__commute, fact_subset__insertI, fact_notin__Lin__iff, fact_inf__left__commute, fact_Un__Int__crazy, arity_Nat__Onat__Lattices_Osemilattice__sup, fact_inf__left__idem, arity_HOL__Obool__Orderings_Oord, fact_Diff__partition, fact_Id__onE, fact_RangeE, fact_sup__left__idem, fact_insert__absorb2, fact_le__supI1, fact_converse__rtranclE, fact_partial__order__on__converse, fact_insertI2, fact_equals0D, fact_insert__absorb, fact_rtrancl__converseI, fact_Un__Image, fact_pair__in__Id__conv, fact_inf__bot__right, fact_subset__insert, fact_same__fstI, fact_in__rtrancl__UnI, fact_Un__Int__distrib2, fact_equalityD1, fact_Refl__antisym__eq__Image1__Image1__iff, fact_wf__Un, fact_le__funE, fact_wfrec, fact_eqset__imp__iff, fact_trancl__empty, fact_trancl__trans, fact_Int__Un__distrib2, fact_converse__rtrancl__into__rtrancl, fact_Un__insert__right, arity_Nat__Onat__Orderings_Oord, fact_rtrancl__trans, fact_less__by__empty, fact_trancl__converseD, fact_wf__converse__trancl, help_c__fequal__1, fact_in__above, fact_refl__on__Un, fact_insert__inter__insert, fact_A_I5_J, fact_singleton__quotient, fact_irrefl__def, fact_UnI2, fact_insert__commute, fact_distrib__sup__le, fact_Int__lower2, fact_subset__Un__eq, fact_le__iff__sup, fact_sup_Oassoc, fact_in__below, fact_Int__absorb, fact_ord__le__eq__trans, fact_antisym__subset, fact_le__infE, fact_all__not__in__conv, fact_mlex__leq, fact_set__mp, fact_inf__sup__absorb, fact_Image__singleton__iff, fact_wfrec__rel_Oequations, fact_r__r__into__trancl, fact_def__wfrec, fact_eq__equiv__class__iff2, fact_Image__Int__subset, fact_eq__equiv__class__iff, fact_subset__equiv__class, fact_total__on__def, fact_mktop__Lin, fact_A_I3_J, fact_irrefl__trancl__rD, fact_Diff__mono, fact_le__iff__inf, fact_bex__Un, fact_partial__order__on__def, fact_Range__Id__on, fact_inf__sup__aci_I8_J, fact_antisym__def, fact_sup__inf__distrib2, fact_sup1CI, fact_Image__empty, fact_rtrancl__into__trancl2, fact_Nitpick_Orefl_H__def, fact_Pair__inject, fact_equiv__class__nondisjoint, fact_reflcl__trancl, fact_inf_Ocommute, fact_double__diff, fact_inf__greatest, fact_sup__ge1, fact_wf__acc__iff, fact_Range__iff, arity_HOL__Obool__Lattices_Odistrib__lattice, arity_Nat__Onat__Orderings_Obot, fact_set__eq__subset, fact_acyclic__insert, fact_Un__Int__assoc__eq, fact_partial__order__on__empty, fact_linear__order__on__def, fact_subset__refl, fact_ext, fact_inf__le1, fact_acc__wfD, fact_equiv__class__eq__iff, fact_internal__split__conv, arity_fun__Orderings_Oord, fact_equalityI, fact_le__supE, fact_inf1D1, arity_fun__Orderings_Obot, fact_empty__iff, fact_single__valued__confluent, fact_le__infI, fact_wf__in__rel, fact_Image__closed__trancl, fact_Int__commute, arity_Nat__Onat__Orderings_Olinorder, fact_rtrancl__induct2, fact_rtrancl__trancl__absorb, fact_linorder__le__cases, fact_inf__apply, fact_Id__on__eqI, fact_acyclic__def, fact_Diff__Int, fact_sup__idem, fact_assms_I3_J, fact_converse__iff, fact_inf__mono, fact_trancl__range, fact_sup__mono, fact_rtrancl__eq__or__trancl, fact_refl__onD1, fact_total__on__empty, fact_insert__ident, fact_subset__Image__Image__iff, arity_HOL__Obool__Lattices_Obounded__lattice__bot, fact_curryD, fact_Un__absorb, fact_subset__empty, fact_singletonE, fact_trancl_Or__into__trancl, fact_trancl__into__rtrancl, fact_rtrancl__Un__subset, fact_Range__Diff__subset, fact_converse__tranclE, fact_A_I1_J, fact_sup_Oidem, fact_preorder__on__empty, fact_wf__eq__minimal, fact_acyclic__subset, fact_linear__order__on__converse, fact_IntD2, fact_quotientI, fact_tranclD, fact_Domain__iff, fact_eq__mem__trans, fact_Int__mono, fact_antisymD, fact_acc__downwards__aux, fact_Un__empty__right, fact_trancl__converseI, fact_converse__Id__on, fact_set__rev__mp, fact_converse__in__Lin, fact_DiffI, fact_inf__absorb2, fact_wf__insert, fact_converseD, fact_Range__def, fact_rtrancl__induct, fact_sup__commute, fact_antisym__converse, fact_rev__predicate2D, fact_linorder__linear, fact_trancl__into__trancl2, fact_single__valuedI, fact_subset__insertI2, fact_Un__absorb2, fact_Int__insert__right__if1, fact_single__valued__def, fact_trancl__rtrancl__absorb, arity_HOL__Obool__Lattices_Osemilattice__inf, fact_DomainE, fact_Domain__Int__subset, fact_antisym__reflcl, fact_UnCI, fact_rev__predicate1D, fact_quotient__disj, fact_in__lex__prod, fact_inf__sup__aci_I5_J, fact_inf__sup__aci_I3_J, fact_inf_Oleft__idem, fact_wf__trancl, fact_ball__Un, fact_Un__upper1, fact_refl__on__Int, fact_Int__absorb1, fact_calculation_I1_J, fact_Domain__Id__on, fact_cuts__eq, fact_congruentD, fact_equalityE, fact_Pair__eq, fact_tfl__wfrec, fact_in__rel__def, fact_inf__sup__ord_I4_J, fact_le__sup__iff, fact_inf__sup__distrib1, fact_empty__subsetI, fact_IdE, fact_inf__assoc, fact_rtrancl_Ortrancl__into__rtrancl, fact_rtranclE, fact_Lin__irrefl, fact_refl__on__converse, fact_Int__insert__left__if0, fact_insert__mono, fact_sup_Ocommute, fact_Un__Diff__cancel2, fact_Domain__converse, fact_Range__Un__eq, fact_wf__mlex, arity_fun__Groups_Ominus, fact_Nitpick_Owf__wfrec_H__def, fact_calculation_I3_J, fact_inf__le2, fact_equalityCE, fact_r__into__rtrancl, fact_A_I2_J, fact_rtrancl__into__trancl1, fact_Un__iff, fact_Not__Domain__rtrancl, fact_rtrancl__idemp, fact_subsetD, fact_Diff__Un, fact_eq__equiv__class, fact_Un__Diff, fact_quotientE, fact_total__on__converse, fact_trancl__rtrancl__trancl, fact_u, fact_sup1E, fact_inf__sup__aci_I7_J, fact_inf__sup__ord_I3_J, fact_IntI, fact_irrefl__tranclI, fact_wf__same__fst, fact_above__Lin, fact_Id__on__empty, fact_Int__empty__right, fact_inf__sup__aci_I6_J, fact_Range__insert, fact_in__inv__image, fact_the__elem__eq, fact_insertE, fact_sup__inf__distrib1, fact_acyclicI, fact_acc__downward, fact_Range__empty__iff, fact_antisym__Id__on, fact_quotient__is__empty2, fact_Un__commute, fact_eqelem__imp__iff, arity_HOL__Obool__Orderings_Obot, fact_Image__iff, fact_preorder__on__converse, fact_inf__sup__aci_I2_J, arity_fun__Lattices_Odistrib__lattice, fact_sup__bot__right, fact_converse__Un, fact_Int__greatest, fact_Un__least, fact_curryI, fact_well__order__on__def, fact_wf__acyclic, fact_subset__trans, fact_IntE, fact_sup__absorb2, fact_Int__left__absorb, fact_Range__converse, fact_wf__asym, fact_le__infI1, fact__C3_C, fact_Un__upper2, fact_IntD1, fact_antisym__Id, fact_Partial__order__eq__Image1__Image1__iff, fact_Int__iff, fact_Un__left__absorb, fact_sup_Oleft__idem, fact_mem__def, fact_refl__on__Id__on, fact_Un__Int__distrib, fact_inf__idem, fact_sup_Oleft__commute, fact_trancl__mono, fact_Field__insert, fact_Image__mono, fact_inf__sup__aci_I1_J, fact_rtrancl__converseD, fact_wfrec__rel_Osimps, fact_inf__bot__left, fact_ord__eq__le__trans, fact_UnE, fact_equiv__class__self, fact_rtrancl__trancl__trancl, fact_wfP__subset, fact_quotient__eqI, fact_not__acc__down, fact_doubleton__eq__iff, fact_Field__def, fact_Image__Id, fact_trancl__domain, fact_Un__assoc, fact_single__valuedD, fact_well__order__on__empty, fact_trancl__reflcl, fact_converse__Id, fact_quotient__empty, fact_disjoint__iff__not__equal
% 95.72/22.38 % No. of inferences in proof: 1058
% 95.72/22.38 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 21869 ms resp. 21374 ms w/o parsing
% 96.44/22.60 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 96.44/22.61 % [INFO] Killing All external provers ...
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