TSTP Solution File: SCT073-1 by Leo-III---1.7.7
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SCT073-1 : TPTP v8.1.2. Released v4.1.0.
% 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 11:50:23 EDT 2023
% Result : Unsatisfiable 10.06s 3.21s
% Output : Refutation 11.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 495
% Syntax : Number of formulae : 915 ( 225 unt; 76 typ; 0 def)
% Number of atoms : 1963 ( 436 equ; 0 cnn)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 16872 ( 906 ~;1124 |; 0 &;14842 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 12 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 213 ( 213 >; 0 *; 0 +; 0 <<)
% Number of symbols : 78 ( 76 usr; 8 con; 0-7 aty)
% Number of variables : 3096 ( 0 ^;3096 !; 0 ?;3096 :)
% Comments :
%------------------------------------------------------------------------------
thf(v_thesis_____type,type,
v_thesis____: $o ).
thf(c_Set_Oinsert_type,type,
c_Set_Oinsert: $i > $i > $i > $i ).
thf(hAPP_type,type,
hAPP: $i > $i > $i ).
thf(c_Set_Oimage_type,type,
c_Set_Oimage: $i > $i > $i > $i > $i ).
thf(c_in_type,type,
c_in: $i > $i > $i > $o ).
thf(c_Lattices_Olower__semilattice__class_Oinf_type,type,
c_Lattices_Olower__semilattice__class_Oinf: $i > $i > $i > $i ).
thf(tc_fun_type,type,
tc_fun: $i > $i > $i ).
thf(tc_bool_type,type,
tc_bool: $i ).
thf(c_Relation_Orefl__on_type,type,
c_Relation_Orefl__on: $i > $i > $i > $o ).
thf(c_ATP__Linkup_Osko__Relation__Xrefl__onI__1__1_type,type,
c_ATP__Linkup_Osko__Relation__Xrefl__onI__1__1: $i > $i > $i > $i ).
thf(c_lessequals_type,type,
c_lessequals: $i > $i > $i > $o ).
thf(c_Product__Type_OSigma_type,type,
c_Product__Type_OSigma: $i > $i > $i > $i > $i ).
thf(c_COMBK_type,type,
c_COMBK: $i > $i > $i > $i ).
thf(tc_prod_type,type,
tc_prod: $i > $i > $i ).
thf(c_Relation_OField_type,type,
c_Relation_OField: $i > $i > $i ).
thf(c_Relation_Oconverse_type,type,
c_Relation_Oconverse: $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Relation__Xrefl__on__def__1__1_type,type,
c_ATP__Linkup_Osko__Relation__Xrefl__on__def__1__1: $i > $i > $i > $i ).
thf(c_Relation_ORange_type,type,
c_Relation_ORange: $i > $i > $i > $i ).
thf(c_Pair_type,type,
c_Pair: $i > $i > $i > $i > $i ).
thf(c_Wellfounded_Owf_type,type,
c_Wellfounded_Owf: $i > $i > $o ).
thf(c_Lattices_Oupper__semilattice__class_Osup_type,type,
c_Lattices_Oupper__semilattice__class_Osup: $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Wellfounded__XwfI__1__1_type,type,
c_ATP__Linkup_Osko__Wellfounded__XwfI__1__1: $i > $i > $i > $i > $i ).
thf(c_Transitive__Closure_Otrancl_type,type,
c_Transitive__Closure_Otrancl: $i > $i > $i ).
thf(c_Relation_Osym_type,type,
c_Relation_Osym: $i > $i > $o ).
thf(c_Relation_Oinv__image_type,type,
c_Relation_Oinv__image: $i > $i > $i > $i > $i ).
thf(c_Finite__Set_Ofinite_type,type,
c_Finite__Set_Ofinite: $i > $i > $o ).
thf(c_Relation_ODomain_type,type,
c_Relation_ODomain: $i > $i > $i > $i ).
thf(c_Relation_Otrans_type,type,
c_Relation_Otrans: $i > $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_Equiv__Relations_Oquotient_type,type,
c_Equiv__Relations_Oquotient: $i > $i > $i > $i ).
thf(c_Relation_Orel__comp_type,type,
c_Relation_Orel__comp: $i > $i > $i > $i > $i > $i ).
thf(c_Equiv__Relations_Oequiv_type,type,
c_Equiv__Relations_Oequiv: $i > $i > $i > $o ).
thf(c_Wellfounded_Oacc_type,type,
c_Wellfounded_Oacc: $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Wellfounded__Xwf__acc__iff__1__1_type,type,
c_ATP__Linkup_Osko__Wellfounded__Xwf__acc__iff__1__1: $i > $i > $i ).
thf(c_Relation_Ototal__on_type,type,
c_Relation_Ototal__on: $i > $i > $i > $o ).
thf(c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1_type,type,
c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1: $i > $i > $i > $i ).
thf(c_Relation_OImage_type,type,
c_Relation_OImage: $i > $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1_type,type,
c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1: $i > $i > $i > $i ).
thf(c_Complete__Lattice_OSup__class_OSup_type,type,
c_Complete__Lattice_OSup__class_OSup: $i > $i > $i ).
thf(c_Relation_OId__on_type,type,
c_Relation_OId__on: $i > $i > $i ).
thf(c_Complete__Lattice_OInf__class_OInf_type,type,
c_Complete__Lattice_OInf__class_OInf: $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1_type,type,
c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1: $i > $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Product__Type__XSigma__mono__1__1_type,type,
c_ATP__Linkup_Osko__Product__Type__XSigma__mono__1__1: $i > $i > $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1_type,type,
c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1: $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1_type,type,
c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1: $i > $i > $i ).
thf(c_List_Osko__Recdef__Xcuts__eq__1__1_type,type,
c_List_Osko__Recdef__Xcuts__eq__1__1: $i > $i > $i > $i > $i > $i > $i ).
thf(c_Recdef_Ocut_type,type,
c_Recdef_Ocut: $i > $i > $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Relation__XImage__iff__1__1_type,type,
c_ATP__Linkup_Osko__Relation__XImage__iff__1__1: $i > $i > $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1_type,type,
c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1: $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1_type,type,
c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1: $i > $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Relation__XImageE__1__1_type,type,
c_ATP__Linkup_Osko__Relation__XImageE__1__1: $i > $i > $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Relation__XId__onE__1__1_type,type,
c_ATP__Linkup_Osko__Relation__XId__onE__1__1: $i > $i > $i > $i ).
thf(c_Arrow__Order__Mirabelle_OLin_type,type,
c_Arrow__Order__Mirabelle_OLin: $i ).
thf(tc_Arrow__Order__Mirabelle_Oalt_type,type,
tc_Arrow__Order__Mirabelle_Oalt: $i ).
thf(c_Arrow__Order__Mirabelle_Oabove_type,type,
c_Arrow__Order__Mirabelle_Oabove: $i > $i > $i > $i ).
thf(c_Arrow__Order__Mirabelle_Obelow_type,type,
c_Arrow__Order__Mirabelle_Obelow: $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Relation__XIdE__1__1_type,type,
c_ATP__Linkup_Osko__Relation__XIdE__1__1: $i > $i > $i ).
thf(c_Nitpick_Orefl_H_type,type,
c_Nitpick_Orefl_H: $i > $i > $o ).
thf(c_Arrow__Order__Mirabelle_Omkbot_type,type,
c_Arrow__Order__Mirabelle_Omkbot: $i > $i > $i ).
thf(c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1_type,type,
c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1: $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Relation__XDomainE__1__1_type,type,
c_ATP__Linkup_Osko__Relation__XDomainE__1__1: $i > $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Complete__Lattice__XInterI__1__1_type,type,
c_ATP__Linkup_Osko__Complete__Lattice__XInterI__1__1: $i > $i > $i > $i ).
thf(v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1_type,type,
v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1: $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1_type,type,
c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1: $i > $i > $i > $i > $i > $i > $i > $i ).
thf(c_Arrow__Order__Mirabelle_Omktop_type,type,
c_Arrow__Order__Mirabelle_Omktop: $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1_type,type,
c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1: $i > $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1_type,type,
c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1: $i > $i > $i > $i > $i ).
thf(c_List_Osko__Equiv__Relations__XquotientE__1__1_type,type,
c_List_Osko__Equiv__Relations__XquotientE__1__1: $i > $i > $i > $i > $i ).
thf(v_a_____type,type,
v_a____: $i ).
thf(v_b_____type,type,
v_b____: $i ).
thf(c_ATP__Linkup_Osko__Relation__XRange__iff__1__1_type,type,
c_ATP__Linkup_Osko__Relation__XRange__iff__1__1: $i > $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1_type,type,
c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1: $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Complete__Lattice__XUnionE__1__1_type,type,
c_ATP__Linkup_Osko__Complete__Lattice__XUnionE__1__1: $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Relation__XRangeE__1__1_type,type,
c_ATP__Linkup_Osko__Relation__XRangeE__1__1: $i > $i > $i > $i > $i ).
thf(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1_type,type,
v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1: $i ).
thf(299,axiom,
! [A: $i] :
( ( c_in @ A @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ~ ( c_in @ ( c_Relation_Oconverse @ A @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_converse__in__Lin_0) ).
thf(1036,plain,
! [A: $i] :
( ( c_in @ A @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ~ ( c_in @ ( c_Relation_Oconverse @ A @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(103,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Complete__Lattice_OInf__class_OInf @ A @ ( tc_fun @ B @ tc_bool ) ) @ C @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_in @ C @ A @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Inter__lower_0) ).
thf(629,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Complete__Lattice_OInf__class_OInf @ A @ ( tc_fun @ B @ tc_bool ) ) @ C @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_in @ C @ A @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(293,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ~ ( c_in @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ B @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntE_1) ).
thf(1024,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ~ ( c_in @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ B @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(49,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ~ ( c_lessequals @ ( c_Set_Oinsert @ A @ D @ C ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__subset_0) ).
thf(518,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ~ ( c_lessequals @ ( c_Set_Oinsert @ A @ D @ C ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(358,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( A = B )
| ~ ( c_in @ C @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( A = B )
| ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ C @ A @ B ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__below_11) ).
thf(1179,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( A = B )
| ~ ( c_in @ C @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( A = B )
| ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ C @ A @ B ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(178,axiom,
! [B: $i,A: $i] :
( ( c_Relation_Oconverse @ ( c_Relation_OId__on @ A @ B ) @ B @ B )
= ( c_Relation_OId__on @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_converse__Id__on_0) ).
thf(777,plain,
! [B: $i,A: $i] :
( ( c_Relation_Oconverse @ ( c_Relation_OId__on @ A @ B ) @ B @ B )
= ( c_Relation_OId__on @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(328,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ B @ D @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( A = D )
| ~ ( c_in @ C @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( B = D )
| ( c_in @ ( c_Pair @ A @ D @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ C @ B @ D ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__above_13) ).
thf(1110,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ B @ D @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( A = D )
| ~ ( c_in @ C @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( B = D )
| ( c_in @ ( c_Pair @ A @ D @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ C @ B @ D ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(110,axiom,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__Un__subset_0) ).
thf(645,plain,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(235,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Relation_Orel__comp @ ( c_Relation_Oconverse @ A @ B @ B ) @ A @ B @ B @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) )
| ~ ( c_Relation_Orefl__on @ C @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_refl__on__comp__subset_0) ).
thf(892,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Relation_Orel__comp @ ( c_Relation_Oconverse @ A @ B @ B ) @ A @ B @ B @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) )
| ~ ( c_Relation_Orefl__on @ C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(318,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ C @ D ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( A = B )
| ( A = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__mktop_5) ).
thf(1083,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ C @ D ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( A = B )
| ( A = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(23,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_COMBK @ A @ B @ C ) @ D )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_COMBK__def_0) ).
thf(468,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( hAPP @ ( c_COMBK @ A @ B @ C ) @ D )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(121,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_OImage @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_OImage @ A @ B @ D @ E ) @ ( c_Relation_OImage @ A @ C @ D @ E ) @ ( tc_fun @ E @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Image__Un_0) ).
thf(666,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_OImage @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_OImage @ A @ B @ D @ E ) @ ( c_Relation_OImage @ A @ C @ D @ E ) @ ( tc_fun @ E @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(405,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ C @ D @ A ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ C @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( D = A )
| ( c_in @ ( c_Pair @ D @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__above_1) ).
thf(1295,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ C @ D @ A ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ C @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( D = A )
| ( c_in @ ( c_Pair @ D @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(81,axiom,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Otrancl @ A @ B )
= ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Relation_Orel__comp @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ A @ B @ B @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trancl__unfold_0) ).
thf(582,plain,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Otrancl @ A @ B )
= ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Relation_Orel__comp @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ A @ B @ B @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(402,axiom,
! [C: $i,B: $i,A: $i] : ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) @ ( tc_prod @ B @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl_Ortrancl__refl_0) ).
thf(1290,plain,
! [C: $i,B: $i,A: $i] : ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) @ ( tc_prod @ B @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(311,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1 @ A @ B @ C @ D @ E @ F @ G ) @ B @ G @ F ) @ D @ ( tc_prod @ G @ F ) )
| ~ ( c_in @ ( c_Pair @ A @ B @ E @ F ) @ ( c_Relation_Orel__comp @ C @ D @ E @ G @ F ) @ ( tc_prod @ E @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__compEpair_1) ).
thf(1068,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1 @ A @ B @ C @ D @ E @ F @ G ) @ B @ G @ F ) @ D @ ( tc_prod @ G @ F ) )
| ~ ( c_in @ ( c_Pair @ A @ B @ E @ F ) @ ( c_Relation_Orel__comp @ C @ D @ E @ G @ F ) @ ( tc_prod @ E @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(280,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Recdef_Ocut @ A @ B @ C @ D @ E )
!= ( c_Recdef_Ocut @ F @ B @ C @ D @ E ) )
| ( ( hAPP @ A @ G )
= ( hAPP @ F @ G ) )
| ~ ( c_in @ ( c_Pair @ G @ C @ D @ D ) @ B @ ( tc_prod @ D @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cuts__eq_0) ).
thf(994,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Recdef_Ocut @ A @ B @ C @ D @ E )
!= ( c_Recdef_Ocut @ F @ B @ C @ D @ E ) )
| ( ( hAPP @ A @ G )
= ( hAPP @ F @ G ) )
| ~ ( c_in @ ( c_Pair @ G @ C @ D @ D ) @ B @ ( tc_prod @ D @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(160,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ E @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ A @ E @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__trancl__trancl_0) ).
thf(741,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ E @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ A @ E @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(218,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__mono_0) ).
thf(861,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(356,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ E @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ A @ E @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl__into__trancl_0) ).
thf(1173,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ E @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ A @ E @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(366,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ C @ D @ E ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( B = E )
| ( A = E )
| ( A = B )
| ~ ( c_in @ C @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( D = E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__above_4) ).
thf(1205,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ C @ D @ E ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( B = E )
| ( A = E )
| ( A = B )
| ~ ( c_in @ C @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( D = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(14,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_ORange @ ( c_Set_Oinsert @ ( c_Pair @ A @ B @ C @ D ) @ E @ ( tc_prod @ C @ D ) ) @ C @ D )
= ( c_Set_Oinsert @ B @ ( c_Relation_ORange @ E @ C @ D ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Range__insert_0) ).
thf(449,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_ORange @ ( c_Set_Oinsert @ ( c_Pair @ A @ B @ C @ D ) @ E @ ( tc_prod @ C @ D ) ) @ C @ D )
= ( c_Set_Oinsert @ B @ ( c_Relation_ORange @ E @ C @ D ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(227,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ A @ ( tc_fun @ B @ tc_bool ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__Un_1) ).
thf(878,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ C @ A @ ( tc_fun @ B @ tc_bool ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(115,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Relation_Oinv__image @ D @ E @ F @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ ( hAPP @ E @ A ) @ ( hAPP @ E @ B ) @ F @ F ) @ D @ ( tc_prod @ F @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__inv__image_1) ).
thf(655,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Relation_Oinv__image @ D @ E @ F @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ ( hAPP @ E @ A ) @ ( hAPP @ E @ B ) @ F @ F ) @ D @ ( tc_prod @ F @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(339,axiom,
! [C: $i,B: $i,A: $i] :
~ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ C @ A ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__mktop_0) ).
thf(1137,plain,
! [C: $i,B: $i,A: $i] :
~ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ C @ A ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(411,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__left__commute_0) ).
thf(1310,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(64,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Orel__comp @ A @ ( c_Relation_OId @ B ) @ C @ B @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_R__O__Id_0) ).
thf(550,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Orel__comp @ A @ ( c_Relation_OId @ B ) @ C @ B @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(40,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ( A = D )
| ~ ( c_in @ A @ ( c_Set_Oinsert @ D @ B @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insertE_0) ).
thf(500,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ( A = D )
| ~ ( c_in @ A @ ( c_Set_Oinsert @ D @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(148,axiom,
! [B: $i,A: $i] :
( ( ( c_Relation_Oconverse @ A @ B @ B )
!= A )
| ( c_Relation_Osym @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sym__conv__converse__eq_1) ).
thf(715,plain,
! [B: $i,A: $i] :
( ( ( c_Relation_Oconverse @ A @ B @ B )
!= A )
| ( c_Relation_Osym @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(26,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_Osym @ ( c_Relation_Oinv__image @ A @ B @ C @ D ) @ D )
| ~ ( c_Relation_Osym @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sym__inv__image_0) ).
thf(472,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_Osym @ ( c_Relation_Oinv__image @ A @ B @ C @ D ) @ D )
| ~ ( c_Relation_Osym @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(139,axiom,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ A @ ( tc_fun @ C @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__lower1_0) ).
thf(698,plain,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ A @ ( tc_fun @ C @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(163,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ C )
| ~ ( c_Finite__Set_Ofinite @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__Int_1) ).
thf(747,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ C )
| ~ ( c_Finite__Set_Ofinite @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(259,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ C @ D @ E ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ E @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( B = D )
| ( A = B )
| ~ ( c_in @ C @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( D = E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__below_8) ).
thf(945,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ C @ D @ E ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ E @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( B = D )
| ( A = B )
| ~ ( c_in @ C @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( D = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(123,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Wellfounded_Owf @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) ) @ C )
| ~ ( c_Wellfounded_Owf @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__Int2_0) ).
thf(670,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Wellfounded_Owf @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) ) @ C )
| ~ ( c_Wellfounded_Owf @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(351,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_List_Osko__Equiv__Relations__XquotientE__1__1 @ A @ B @ C @ D ) @ A @ D )
| ~ ( c_in @ B @ ( c_Equiv__Relations_Oquotient @ A @ C @ D ) @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_quotientE_1) ).
thf(1164,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_List_Osko__Equiv__Relations__XquotientE__1__1 @ A @ B @ C @ D ) @ A @ D )
| ~ ( c_in @ B @ ( c_Equiv__Relations_Oquotient @ A @ C @ D ) @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(187,axiom,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Ortrancl @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ B )
= ( c_Transitive__Closure_Ortrancl @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trancl__rtrancl__absorb_0) ).
thf(797,plain,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Ortrancl @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ B )
= ( c_Transitive__Closure_Ortrancl @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(196,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_ORange @ ( c_Relation_Oconverse @ A @ B @ C ) @ C @ B )
= ( c_Relation_ODomain @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Range__converse_0) ).
thf(814,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_ORange @ ( c_Relation_Oconverse @ A @ B @ C ) @ C @ B )
= ( c_Relation_ODomain @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(419,axiom,
! [A: $i] :
( v_thesis____
| ~ ( c_in @ A @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ~ ( c_in @ ( c_Pair @ v_a____ @ v_b____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ A @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_that_0) ).
thf(1327,plain,
! [A: $i] :
( v_thesis____
| ~ ( c_in @ A @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ~ ( c_in @ ( c_Pair @ v_a____ @ v_b____ @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ A @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(363,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Relation_OId @ C ) @ ( tc_prod @ C @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pair__in__Id__conv_0) ).
thf(1196,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Relation_OId @ C ) @ ( tc_prod @ C @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(238,axiom,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Ortrancl @ A @ B )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_OId @ B ) @ ( c_Relation_Orel__comp @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ A @ B @ B @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__unfold_0) ).
thf(898,plain,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Ortrancl @ A @ B )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_OId @ B ) @ ( c_Relation_Orel__comp @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ A @ B @ B @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(335,axiom,
! [B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ A @ ( tc_fun @ B @ tc_bool ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__absorb_0) ).
thf(1127,plain,
! [B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ A @ ( tc_fun @ B @ tc_bool ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(145,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Product__Type_OSigma @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ C @ E )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Product__Type_OSigma @ A @ D @ C @ E ) @ ( c_Product__Type_OSigma @ B @ D @ C @ E ) @ ( tc_fun @ ( tc_prod @ C @ E ) @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sigma__Int__distrib1_0) ).
thf(709,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Product__Type_OSigma @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ C @ E )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Product__Type_OSigma @ A @ D @ C @ E ) @ ( c_Product__Type_OSigma @ B @ D @ C @ E ) @ ( tc_fun @ ( tc_prod @ C @ E ) @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(271,axiom,
! [B: $i,A: $i] :
( ( A
= ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XIdE__1__1 @ A @ B ) @ ( c_ATP__Linkup_Osko__Relation__XIdE__1__1 @ A @ B ) @ B @ B ) )
| ~ ( c_in @ A @ ( c_Relation_OId @ B ) @ ( tc_prod @ B @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IdE_0) ).
thf(973,plain,
! [B: $i,A: $i] :
( ( A
= ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XIdE__1__1 @ A @ B ) @ ( c_ATP__Linkup_Osko__Relation__XIdE__1__1 @ A @ B ) @ B @ B ) )
| ~ ( c_in @ A @ ( c_Relation_OId @ B ) @ ( tc_prod @ B @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(73,axiom,
! [B: $i,A: $i] :
( ( c_Wellfounded_Owf @ ( c_Relation_Oconverse @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ B @ B ) @ B )
| ~ ( c_Wellfounded_Owf @ ( c_Relation_Oconverse @ A @ B @ B ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__converse__trancl_0) ).
thf(565,plain,
! [B: $i,A: $i] :
( ( c_Wellfounded_Owf @ ( c_Relation_Oconverse @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ B @ B ) @ B )
| ~ ( c_Wellfounded_Owf @ ( c_Relation_Oconverse @ A @ B @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(392,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__trans_0) ).
thf(1265,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(113,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) ) @ C )
| ~ ( c_lessequals @ ( c_Relation_Orel__comp @ A @ B @ C @ C @ C ) @ A @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) )
| ~ ( c_Wellfounded_Owf @ B @ C )
| ~ ( c_Wellfounded_Owf @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__union__compatible_0) ).
thf(651,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) ) @ C )
| ~ ( c_lessequals @ ( c_Relation_Orel__comp @ A @ B @ C @ C @ C ) @ A @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) )
| ~ ( c_Wellfounded_Owf @ B @ C )
| ~ ( c_Wellfounded_Owf @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(376,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Complete__Lattice__XUnionE__1__1 @ A @ B @ C ) @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_in @ A @ ( c_Complete__Lattice_OSup__class_OSup @ B @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UnionE_1) ).
thf(1228,plain,
! [C: $i,B: $i,A: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Complete__Lattice__XUnionE__1__1 @ A @ B @ C ) @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_in @ A @ ( c_Complete__Lattice_OSup__class_OSup @ B @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(387,axiom,
! [B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ A @ ( tc_fun @ B @ tc_bool ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__absorb_0) ).
thf(1254,plain,
! [B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ A @ ( tc_fun @ B @ tc_bool ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(406,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ B @ A @ C @ C ) @ D @ ( tc_prod @ C @ C ) )
| ~ ( c_Wellfounded_Owf @ D @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__asym_0) ).
thf(1298,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ B @ A @ C @ C ) @ D @ ( tc_prod @ C @ C ) )
| ~ ( c_Wellfounded_Owf @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(182,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Product__Type_OSigma @ A @ B @ C @ D ) @ ( c_Product__Type_OSigma @ E @ F @ C @ D ) @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_bool ) )
| ~ ( c_lessequals @ ( hAPP @ B @ ( c_ATP__Linkup_Osko__Product__Type__XSigma__mono__1__1 @ A @ B @ F @ C @ D ) ) @ ( hAPP @ F @ ( c_ATP__Linkup_Osko__Product__Type__XSigma__mono__1__1 @ A @ B @ F @ C @ D ) ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ A @ E @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sigma__mono_1) ).
thf(785,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Product__Type_OSigma @ A @ B @ C @ D ) @ ( c_Product__Type_OSigma @ E @ F @ C @ D ) @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_bool ) )
| ~ ( c_lessequals @ ( hAPP @ B @ ( c_ATP__Linkup_Osko__Product__Type__XSigma__mono__1__1 @ A @ B @ F @ C @ D ) ) @ ( hAPP @ F @ ( c_ATP__Linkup_Osko__Product__Type__XSigma__mono__1__1 @ A @ B @ F @ C @ D ) ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ A @ E @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(308,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Complete__Lattice_OInf__class_OInf @ B @ ( tc_fun @ C @ tc_bool ) ) @ C )
| ~ ( c_in @ A @ ( c_ATP__Linkup_Osko__Complete__Lattice__XInterI__1__1 @ A @ B @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_InterI_1) ).
thf(1059,plain,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Complete__Lattice_OInf__class_OInf @ B @ ( tc_fun @ C @ tc_bool ) ) @ C )
| ~ ( c_in @ A @ ( c_ATP__Linkup_Osko__Complete__Lattice__XInterI__1__1 @ A @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(417,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ~ ( c_in @ ( c_Pair @ D @ A @ C @ C ) @ E @ ( tc_prod @ C @ C ) )
| ~ ( c_Relation_Orefl__on @ B @ E @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_refl__onD2_0) ).
thf(1323,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ~ ( c_in @ ( c_Pair @ D @ A @ C @ C ) @ E @ ( tc_prod @ C @ C ) )
| ~ ( c_Relation_Orefl__on @ B @ E @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(207,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Oconverse @ ( c_Relation_Oconverse @ A @ B @ C ) @ C @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_converse__converse_0) ).
thf(838,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Oconverse @ ( c_Relation_Oconverse @ A @ B @ C ) @ C @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(247,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Orefl__on @ A @ B @ C )
| ~ ( c_Relation_Orefl__on @ A @ ( c_Relation_Oconverse @ B @ C @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_refl__on__converse_0) ).
thf(917,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Orefl__on @ A @ B @ C )
| ~ ( c_Relation_Orefl__on @ A @ ( c_Relation_Oconverse @ B @ C @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(165,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Wellfounded_Owf @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) ) @ C )
| ~ ( c_Wellfounded_Owf @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__Int1_0) ).
thf(751,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Wellfounded_Owf @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) ) @ C )
| ~ ( c_Wellfounded_Owf @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(413,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ A @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ B @ C @ D ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ B @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( C = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__below_0) ).
thf(1313,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ A @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ B @ C @ D ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ B @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( C = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(398,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ B @ A @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( A = B )
| ~ ( c_in @ C @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_notin__Lin__iff_1) ).
thf(1279,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ B @ A @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( A = B )
| ~ ( c_in @ C @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(240,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) )
| ~ ( c_lessequals @ A @ ( c_Transitive__Closure_Ortrancl @ C @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__subset__rtrancl_0) ).
thf(902,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) )
| ~ ( c_lessequals @ A @ ( c_Transitive__Closure_Ortrancl @ C @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(69,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Relation_ORange @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_bool ) ) @ C @ D ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_ORange @ A @ C @ D ) @ ( c_Relation_ORange @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Range__Int__subset_0) ).
thf(559,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Relation_ORange @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_bool ) ) @ C @ D ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_ORange @ A @ C @ D ) @ ( c_Relation_ORange @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(214,axiom,
! [B: $i,A: $i] :
( ( c_Wellfounded_Owf @ ( c_Relation_Orel__comp @ A @ A @ B @ B @ B ) @ B )
| ~ ( c_Wellfounded_Owf @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__comp__self_0) ).
thf(853,plain,
! [B: $i,A: $i] :
( ( c_Wellfounded_Owf @ ( c_Relation_Orel__comp @ A @ A @ B @ B @ B ) @ B )
| ~ ( c_Wellfounded_Owf @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(330,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ E @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ A @ E @ C @ C ) @ D @ ( tc_prod @ C @ C ) )
| ~ ( c_Relation_Otrans @ D @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_transD_0) ).
thf(1115,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ E @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ A @ E @ C @ C ) @ D @ ( tc_prod @ C @ C ) )
| ~ ( c_Relation_Otrans @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(324,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ B @ A @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( B = A )
| ~ ( c_in @ C @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_notin__Lin__iff_0) ).
thf(1100,plain,
! [C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( c_in @ ( c_Pair @ B @ A @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( B = A )
| ~ ( c_in @ C @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(378,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ B @ A @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ C @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Lin__irrefl_0) ).
thf(1232,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ B @ A @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ C @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(415,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Relation_OImage @ B @ C @ D @ E ) @ E )
| ~ ( c_in @ ( c_Pair @ F @ A @ D @ E ) @ B @ ( tc_prod @ D @ E ) )
| ~ ( c_in @ F @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__ImageI_0) ).
thf(1319,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Relation_OImage @ B @ C @ D @ E ) @ E )
| ~ ( c_in @ ( c_Pair @ F @ A @ D @ E ) @ B @ ( tc_prod @ D @ E ) )
| ~ ( c_in @ F @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(223,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_Orel__comp @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_bool ) ) @ E @ C @ D @ F )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ A @ E @ C @ D @ F ) @ ( c_Relation_Orel__comp @ B @ E @ C @ D @ F ) @ ( tc_fun @ ( tc_prod @ C @ F ) @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__comp__distrib2_0) ).
thf(870,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_Orel__comp @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_bool ) ) @ E @ C @ D @ F )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ A @ E @ C @ D @ F ) @ ( c_Relation_Orel__comp @ B @ E @ C @ D @ F ) @ ( tc_fun @ ( tc_prod @ C @ F ) @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(408,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( B = D )
| ( D = B )
| ~ ( c_in @ C @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( D = A )
| ( c_in @ ( c_Pair @ D @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ C @ D @ A ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__below_7) ).
thf(1302,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( B = D )
| ( D = B )
| ~ ( c_in @ C @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( D = A )
| ( c_in @ ( c_Pair @ D @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ C @ D @ A ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(184,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
= B )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__absorb1_0) ).
thf(789,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
= B )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(11,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E )
| ~ ( c_in @ B @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_imageI_0) ).
thf(443,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E )
| ~ ( c_in @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(301,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Pair @ A @ B @ C @ D )
!= ( c_Pair @ E @ F @ C @ D ) )
| ( A = E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Pair__eq_0) ).
thf(1040,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Pair @ A @ B @ C @ D )
!= ( c_Pair @ E @ F @ C @ D ) )
| ( A = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(100,axiom,
! [B: $i,A: $i] :
( ( c_Relation_ODomain @ ( c_Relation_OId__on @ A @ B ) @ B @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Domain__Id__on_0) ).
thf(623,plain,
! [B: $i,A: $i] :
( ( c_Relation_ODomain @ ( c_Relation_OId__on @ A @ B ) @ B @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(111,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Wellfounded_Owf @ ( c_Set_Oinsert @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) @ C )
| ( c_in @ ( c_Pair @ B @ A @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_Wellfounded_Owf @ D @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__insert_2) ).
thf(646,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Wellfounded_Owf @ ( c_Set_Oinsert @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) @ C )
| ( c_in @ ( c_Pair @ B @ A @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_Wellfounded_Owf @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(47,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_Oconverse @ ( c_Relation_Oinv__image @ A @ B @ C @ D ) @ D @ D )
= ( c_Relation_Oinv__image @ ( c_Relation_Oconverse @ A @ C @ C ) @ B @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_converse__inv__image_0) ).
thf(514,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_Oconverse @ ( c_Relation_Oinv__image @ A @ B @ C @ D ) @ D @ D )
= ( c_Relation_Oinv__image @ ( c_Relation_Oconverse @ A @ C @ C ) @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(77,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ B )
= ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__Un__rtrancl_0) ).
thf(574,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ B )
= ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(359,axiom,
v_a____ != v_b____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_CHAINED_0) ).
thf(1183,plain,
v_a____ != v_b____,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(30,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
| ( c_in @ B @ A @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert_1) ).
thf(480,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
| ( c_in @ B @ A @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(345,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ E @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ A @ E @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl_Ortrancl__into__rtrancl_0) ).
thf(1151,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ E @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ A @ E @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(256,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
= ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XId__onE__1__1 @ B @ A @ C ) @ ( c_ATP__Linkup_Osko__Relation__XId__onE__1__1 @ B @ A @ C ) @ C @ C ) )
| ~ ( c_in @ A @ ( c_Relation_OId__on @ B @ C ) @ ( tc_prod @ C @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Id__onE_1) ).
thf(937,plain,
! [C: $i,B: $i,A: $i] :
( ( A
= ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XId__onE__1__1 @ B @ A @ C ) @ ( c_ATP__Linkup_Osko__Relation__XId__onE__1__1 @ B @ A @ C ) @ C @ C ) )
| ~ ( c_in @ A @ ( c_Relation_OId__on @ B @ C ) @ ( tc_prod @ C @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(305,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( A = D )
| ~ ( c_in @ C @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( D = B )
| ( c_in @ ( c_Pair @ A @ D @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ C @ D @ B ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__below_9) ).
thf(1051,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( A = D )
| ~ ( c_in @ C @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( D = B )
| ( c_in @ ( c_Pair @ A @ D @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ C @ D @ B ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(199,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( hAPP @ B @ C ) @ D )
| ~ ( c_in @ ( c_Pair @ C @ A @ E @ D ) @ ( c_Product__Type_OSigma @ F @ B @ E @ D ) @ ( tc_prod @ E @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SigmaD2_0) ).
thf(821,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( hAPP @ B @ C ) @ D )
| ~ ( c_in @ ( c_Pair @ C @ A @ E @ D ) @ ( c_Product__Type_OSigma @ F @ B @ E @ D ) @ ( tc_prod @ E @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(173,axiom,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Otrancl @ A @ B )
= ( c_Relation_Orel__comp @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ A @ B @ B @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trancl__unfold__right_0) ).
thf(766,plain,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Otrancl @ A @ B )
= ( c_Relation_Orel__comp @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ A @ B @ B @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(264,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ~ ( c_in @ D @ B @ C )
| ~ ( c_in @ B @ ( c_Equiv__Relations_Oquotient @ E @ F @ C ) @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_in @ B @ ( c_Equiv__Relations_Oquotient @ E @ F @ C ) @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_Equiv__Relations_Oequiv @ E @ F @ C )
| ( c_in @ ( c_Pair @ D @ A @ C @ C ) @ F @ ( tc_prod @ C @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_quotient__eq__iff_0) ).
thf(956,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ~ ( c_in @ D @ B @ C )
| ~ ( c_in @ B @ ( c_Equiv__Relations_Oquotient @ E @ F @ C ) @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_in @ B @ ( c_Equiv__Relations_Oquotient @ E @ F @ C ) @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_Equiv__Relations_Oequiv @ E @ F @ C )
| ( c_in @ ( c_Pair @ D @ A @ C @ C ) @ F @ ( tc_prod @ C @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(221,axiom,
! [B: $i,A: $i] :
( ( c_lessequals @ ( c_Relation_Orel__comp @ ( c_Relation_Oconverse @ A @ B @ B ) @ A @ B @ B @ B ) @ A @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) )
| ~ ( c_Relation_Otrans @ A @ B )
| ~ ( c_Relation_Osym @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sym__trans__comp__subset_0) ).
thf(866,plain,
! [B: $i,A: $i] :
( ( c_lessequals @ ( c_Relation_Orel__comp @ ( c_Relation_Oconverse @ A @ B @ B ) @ A @ B @ B @ B ) @ A @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) )
| ~ ( c_Relation_Otrans @ A @ B )
| ~ ( c_Relation_Osym @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(313,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1 @ A @ B @ C ) @ B @ C @ C ) @ A @ ( tc_prod @ C @ C ) )
| ( c_in @ B @ ( c_Wellfounded_Oacc @ A @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__acc__down_0) ).
thf(1072,plain,
! [C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1 @ A @ B @ C ) @ B @ C @ C ) @ A @ ( tc_prod @ C @ C ) )
| ( c_in @ B @ ( c_Wellfounded_Oacc @ A @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(277,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_in @ A @ D @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__rev__mp_0) ).
thf(988,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_in @ A @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(4,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( c_in @ ( hAPP @ D @ A ) @ ( c_Set_Oimage @ D @ B @ C @ E ) @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__iff_2) ).
thf(428,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( c_in @ ( hAPP @ D @ A ) @ ( c_Set_Oimage @ D @ B @ C @ E ) @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(53,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
| ( c_in @ B @ A @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert__iff_2) ).
thf(527,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
| ( c_in @ B @ A @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(354,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Complete__Lattice_OInf__class_OInf @ B @ ( tc_fun @ C @ tc_bool ) ) @ C )
| ( c_in @ ( c_ATP__Linkup_Osko__Complete__Lattice__XInterI__1__1 @ A @ B @ C ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_InterI_0) ).
thf(1169,plain,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Complete__Lattice_OInf__class_OInf @ B @ ( tc_fun @ C @ tc_bool ) ) @ C )
| ( c_in @ ( c_ATP__Linkup_Osko__Complete__Lattice__XInterI__1__1 @ A @ B @ C ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(132,axiom,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__upper2_0) ).
thf(687,plain,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(370,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ E @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ A @ E @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trancl__into__trancl2_0) ).
thf(1215,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ E @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ A @ E @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(105,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ( A = B )
| ~ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__eq__or__trancl_0) ).
thf(634,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ( A = B )
| ~ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(382,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ~ ( c_in @ A @ D @ C )
| ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__iff_0) ).
thf(1242,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ~ ( c_in @ A @ D @ C )
| ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(212,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trancl__into__rtrancl_0) ).
thf(849,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(314,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ~ ( c_in @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntE_0) ).
thf(1074,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ~ ( c_in @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(127,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ E @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ B @ E @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__mono_0) ).
thf(678,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ E @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ B @ E @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(54,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_Otrans @ ( c_Relation_Oinv__image @ A @ B @ C @ D ) @ D )
| ~ ( c_Relation_Otrans @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__inv__image_0) ).
thf(529,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_Otrans @ ( c_Relation_Oinv__image @ A @ B @ C @ D ) @ D )
| ~ ( c_Relation_Otrans @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(118,axiom,
! [B: $i,A: $i] : ( c_Relation_Osym @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Relation_Oconverse @ A @ B @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sym__Un__converse_0) ).
thf(661,plain,
! [B: $i,A: $i] : ( c_Relation_Osym @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Relation_Oconverse @ A @ B @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(62,axiom,
! [B: $i,A: $i] :
( ( c_Relation_Osym @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ B )
| ~ ( c_Relation_Osym @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sym__trancl_0) ).
thf(546,plain,
! [B: $i,A: $i] :
( ( c_Relation_Osym @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ B )
| ~ ( c_Relation_Osym @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(251,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Wellfounded_Oacc @ A @ B ) @ ( c_Wellfounded_Oacc @ C @ B ) @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_lessequals @ C @ A @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acc__subset_0) ).
thf(925,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Wellfounded_Oacc @ A @ B ) @ ( c_Wellfounded_Oacc @ C @ B ) @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_lessequals @ C @ A @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(409,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Relation_OImage @ B @ C @ D @ E ) @ E )
| ~ ( c_in @ ( c_Pair @ F @ A @ D @ E ) @ B @ ( tc_prod @ D @ E ) )
| ~ ( c_in @ F @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Image__iff_2) ).
thf(1306,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Relation_OImage @ B @ C @ D @ E ) @ E )
| ~ ( c_in @ ( c_Pair @ F @ A @ D @ E ) @ B @ ( tc_prod @ D @ E ) )
| ~ ( c_in @ F @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(364,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ( B = A )
| ~ ( c_in @ C @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( B = A )
| ( c_in @ ( c_Pair @ B @ A @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ C @ B @ A ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__below_5) ).
thf(1199,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ( B = A )
| ~ ( c_in @ C @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( B = A )
| ( c_in @ ( c_Pair @ B @ A @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ C @ B @ A ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(194,axiom,
! [B: $i,A: $i] :
( ( c_Relation_Orel__comp @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ B @ B @ B )
= ( c_Transitive__Closure_Ortrancl @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__idemp__self__comp_0) ).
thf(810,plain,
! [B: $i,A: $i] :
( ( c_Relation_Orel__comp @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ B @ B @ B )
= ( c_Transitive__Closure_Ortrancl @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(303,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Relation_ORange @ B @ C @ D ) @ D )
| ~ ( c_in @ ( c_Pair @ E @ A @ C @ D ) @ B @ ( tc_prod @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_RangeI_0) ).
thf(1047,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Relation_ORange @ B @ C @ D ) @ D )
| ~ ( c_in @ ( c_Pair @ E @ A @ C @ D ) @ B @ ( tc_prod @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(46,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D )
| ~ ( c_in @ A @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__iff_2) ).
thf(512,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D )
| ~ ( c_in @ A @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(9,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D )
= ( c_Set_Oinsert @ B @ ( c_Set_Oinsert @ A @ C @ D ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__commute_0) ).
thf(439,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D )
= ( c_Set_Oinsert @ B @ ( c_Set_Oinsert @ A @ C @ D ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(346,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D )
| ~ ( c_in @ A @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UnCI_0) ).
thf(1153,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D )
| ~ ( c_in @ A @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(170,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Wellfounded_Oacc @ B @ C ) @ C )
| ~ ( c_Wellfounded_Owf @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acc__wfD_0) ).
thf(761,plain,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Wellfounded_Oacc @ B @ C ) @ C )
| ~ ( c_Wellfounded_Owf @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(396,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Recdef_Ocut @ A @ B @ C @ D @ E ) @ F )
= ( hAPP @ A @ F ) )
| ~ ( c_in @ ( c_Pair @ F @ C @ D @ D ) @ B @ ( tc_prod @ D @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cut__apply_0) ).
thf(1274,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Recdef_Ocut @ A @ B @ C @ D @ E ) @ F )
= ( hAPP @ A @ F ) )
| ~ ( c_in @ ( c_Pair @ F @ C @ D @ D ) @ B @ ( tc_prod @ D @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(244,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Relation__XImageE__1__1 @ A @ B @ C @ D @ E ) @ A @ D )
| ~ ( c_in @ B @ ( c_Relation_OImage @ C @ A @ D @ E ) @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ImageE_1) ).
thf(910,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Relation__XImageE__1__1 @ A @ B @ C @ D @ E ) @ A @ D )
| ~ ( c_in @ B @ ( c_Relation_OImage @ C @ A @ D @ E ) @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(236,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ B @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__subset__iff_2) ).
thf(894,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ B @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(292,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( c_in @ ( c_Pair @ C @ D @ E @ E ) @ F @ ( tc_prod @ E @ E ) )
| ~ ( c_in @ D @ B @ E )
| ~ ( c_in @ C @ A @ E )
| ~ ( c_in @ B @ ( c_Equiv__Relations_Oquotient @ G @ F @ E ) @ ( tc_fun @ E @ tc_bool ) )
| ~ ( c_in @ A @ ( c_Equiv__Relations_Oquotient @ G @ F @ E ) @ ( tc_fun @ E @ tc_bool ) )
| ~ ( c_Equiv__Relations_Oequiv @ G @ F @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_quotient__eqI_0) ).
thf(1021,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( c_in @ ( c_Pair @ C @ D @ E @ E ) @ F @ ( tc_prod @ E @ E ) )
| ~ ( c_in @ D @ B @ E )
| ~ ( c_in @ C @ A @ E )
| ~ ( c_in @ B @ ( c_Equiv__Relations_Oquotient @ G @ F @ E ) @ ( tc_fun @ E @ tc_bool ) )
| ~ ( c_in @ A @ ( c_Equiv__Relations_Oquotient @ G @ F @ E ) @ ( tc_fun @ E @ tc_bool ) )
| ~ ( c_Equiv__Relations_Oequiv @ G @ F @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(262,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ E @ ( tc_prod @ C @ D ) )
| ~ ( c_in @ ( c_Pair @ B @ A @ D @ C ) @ ( c_Relation_Oconverse @ E @ C @ D ) @ ( tc_prod @ D @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_converseD_0) ).
thf(952,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ E @ ( tc_prod @ C @ D ) )
| ~ ( c_in @ ( c_Pair @ B @ A @ D @ C ) @ ( c_Relation_Oconverse @ E @ C @ D ) @ ( tc_prod @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(333,axiom,
! [B: $i,A: $i] :
( ( c_in @ ( c_Arrow__Order__Mirabelle_Omktop @ A @ B ) @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ~ ( c_in @ A @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mktop__Lin_0) ).
thf(1123,plain,
! [B: $i,A: $i] :
( ( c_in @ ( c_Arrow__Order__Mirabelle_Omktop @ A @ B ) @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ~ ( c_in @ A @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(136,axiom,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Otrancl @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ B )
= ( c_Transitive__Closure_Ortrancl @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__trancl__absorb_0) ).
thf(693,plain,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Otrancl @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ B )
= ( c_Transitive__Closure_Ortrancl @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(154,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ E @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ A @ E @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trancl__rtrancl__trancl_0) ).
thf(729,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ E @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ A @ E @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(371,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trancl_Or__into__trancl_0) ).
thf(1217,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(89,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ( A = B )
| ~ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtranclD_0) ).
thf(598,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ( A = B )
| ~ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(297,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__left__commute_0) ).
thf(1032,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(101,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ C )
| ~ ( c_Finite__Set_Ofinite @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__Int_0) ).
thf(625,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ C )
| ~ ( c_Finite__Set_Ofinite @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(233,axiom,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__upper1_0) ).
thf(889,plain,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(37,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Wellfounded_Owf @ A @ B )
| ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__XwfI__1__1 @ C @ D @ A @ B ) @ D @ B )
| ~ ( c_lessequals @ A @ ( c_Product__Type_OSigma @ C @ ( c_COMBK @ D @ ( tc_fun @ B @ tc_bool ) @ B ) @ B @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wfI_3) ).
thf(493,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Wellfounded_Owf @ A @ B )
| ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__XwfI__1__1 @ C @ D @ A @ B ) @ D @ B )
| ~ ( c_lessequals @ A @ ( c_Product__Type_OSigma @ C @ ( c_COMBK @ D @ ( tc_fun @ B @ tc_bool ) @ B ) @ B @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(316,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ ( c_Relation_Oconverse @ E @ D @ C ) @ ( tc_prod @ C @ D ) )
| ~ ( c_in @ ( c_Pair @ B @ A @ D @ C ) @ E @ ( tc_prod @ D @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_converseI_0) ).
thf(1079,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ ( c_Relation_Oconverse @ E @ D @ C ) @ ( tc_prod @ C @ D ) )
| ~ ( c_in @ ( c_Pair @ B @ A @ D @ C ) @ E @ ( tc_prod @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(168,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Product__Type_OSigma @ B @ ( c_COMBK @ B @ ( tc_fun @ C @ tc_bool ) @ C ) @ C @ C ) @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) )
| ~ ( c_Equiv__Relations_Oequiv @ B @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equiv__type_0) ).
thf(757,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Product__Type_OSigma @ B @ ( c_COMBK @ B @ ( tc_fun @ C @ tc_bool ) @ C ) @ C @ C ) @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) )
| ~ ( c_Equiv__Relations_Oequiv @ B @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(129,axiom,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Ortrancl @ ( c_Relation_Oconverse @ A @ B @ B ) @ B )
= ( c_Relation_Oconverse @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ B @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__converse_0) ).
thf(682,plain,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Ortrancl @ ( c_Relation_Oconverse @ A @ B @ B ) @ B )
= ( c_Relation_Oconverse @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ B @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(403,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ~ ( c_in @ B @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_in @ A @ ( c_Complete__Lattice_OInf__class_OInf @ D @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_InterD_0) ).
thf(1291,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ~ ( c_in @ B @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_in @ A @ ( c_Complete__Lattice_OInf__class_OInf @ D @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(209,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ E @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ B @ E @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__mono_0) ).
thf(842,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ E @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ B @ E @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(288,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ~ ( c_in @ A @ D @ C )
| ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__mp_0) ).
thf(1012,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ~ ( c_in @ A @ D @ C )
| ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(326,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1 @ A @ B @ C @ D ) @ C @ D @ D ) @ ( c_Transitive__Closure_Otrancl @ A @ D ) @ ( tc_prod @ D @ D ) )
| ( c_in @ ( c_Pair @ B @ C @ D @ D ) @ A @ ( tc_prod @ D @ D ) )
| ~ ( c_in @ ( c_Pair @ B @ C @ D @ D ) @ ( c_Transitive__Closure_Otrancl @ A @ D ) @ ( tc_prod @ D @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_converse__tranclE_1) ).
thf(1106,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1 @ A @ B @ C @ D ) @ C @ D @ D ) @ ( c_Transitive__Closure_Otrancl @ A @ D ) @ ( tc_prod @ D @ D ) )
| ( c_in @ ( c_Pair @ B @ C @ D @ D ) @ A @ ( tc_prod @ D @ D ) )
| ~ ( c_in @ ( c_Pair @ B @ C @ D @ D ) @ ( c_Transitive__Closure_Otrancl @ A @ D ) @ ( tc_prod @ D @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(211,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ ( c_Relation_Oconverse @ D @ C @ C ) @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ B @ A @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__converseI_0) ).
thf(847,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ ( c_Relation_Oconverse @ D @ C @ C ) @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ B @ A @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(32,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_Finite__Set_Ofinite @ ( c_Set_Oinsert @ C @ A @ B ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__insert_0) ).
thf(484,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_Finite__Set_Ofinite @ ( c_Set_Oinsert @ C @ A @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(51,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ B @ C )
= B )
| ~ ( c_in @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__absorb_0) ).
thf(522,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ B @ C )
= B )
| ~ ( c_in @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(204,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Relation_OField @ A @ B ) @ ( c_Relation_OField @ C @ B ) @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mono__Field_0) ).
thf(830,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Relation_OField @ A @ B ) @ ( c_Relation_OField @ C @ B ) @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(349,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ C @ D ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( B = D )
| ( A = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__mktop_3) ).
thf(1159,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ C @ D ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( B = D )
| ( A = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(19,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Wellfounded_Owf @ A @ B )
| ~ ( c_Wellfounded_Owf @ ( c_Set_Oinsert @ ( c_Pair @ C @ D @ B @ B ) @ A @ ( tc_prod @ B @ B ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__insert_0) ).
thf(461,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Wellfounded_Owf @ A @ B )
| ~ ( c_Wellfounded_Owf @ ( c_Set_Oinsert @ ( c_Pair @ C @ D @ B @ B ) @ A @ ( tc_prod @ B @ B ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(79,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ D @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__Un__distrib_0) ).
thf(578,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ D @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(379,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ~ ( c_in @ ( c_Pair @ A @ D @ C @ C ) @ E @ ( tc_prod @ C @ C ) )
| ~ ( c_Equiv__Relations_Oequiv @ B @ E @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equiv__class__eq__iff_1) ).
thf(1234,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ~ ( c_in @ ( c_Pair @ A @ D @ C @ C ) @ E @ ( tc_prod @ C @ C ) )
| ~ ( c_Equiv__Relations_Oequiv @ B @ E @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(260,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__left__absorb_0) ).
thf(948,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(310,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ( B = A )
| ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ C @ A ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__mkbot_4) ).
thf(1064,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ( B = A )
| ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ C @ A ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(152,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Osym @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) ) @ C )
| ~ ( c_Relation_Osym @ B @ C )
| ~ ( c_Relation_Osym @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sym__Un_0) ).
thf(725,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Osym @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) ) @ C )
| ~ ( c_Relation_Osym @ B @ C )
| ~ ( c_Relation_Osym @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(274,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Wellfounded_Oacc @ B @ C ) @ C )
| ~ ( c_in @ ( c_Pair @ A @ D @ C @ C ) @ B @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ D @ ( c_Wellfounded_Oacc @ B @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acc__downward_0) ).
thf(980,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Wellfounded_Oacc @ B @ C ) @ C )
| ~ ( c_in @ ( c_Pair @ A @ D @ C @ C ) @ B @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ D @ ( c_Wellfounded_Oacc @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(322,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__left__absorb_0) ).
thf(1096,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(285,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D )
| ~ ( c_in @ A @ B @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UnCI_1) ).
thf(1006,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D )
| ~ ( c_in @ A @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(216,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__subset__iff_0) ).
thf(857,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(225,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_OImage @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_bool ) ) @ E @ C @ D )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_OImage @ A @ E @ C @ D ) @ ( c_Relation_OImage @ B @ E @ C @ D ) @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Image_0) ).
thf(874,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_OImage @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_bool ) ) @ E @ C @ D )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_OImage @ A @ E @ C @ D ) @ ( c_Relation_OImage @ B @ E @ C @ D ) @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(342,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( A = D )
| ~ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ C @ D ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__mkbot_2) ).
thf(1143,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( A = D )
| ~ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ C @ D ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(395,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Pair @ A @ B @ C @ D )
!= ( c_Pair @ E @ F @ C @ D ) )
| ( B = F ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Pair__eq_1) ).
thf(1270,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Pair @ A @ B @ C @ D )
!= ( c_Pair @ E @ F @ C @ D ) )
| ( B = F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(390,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D )
| ~ ( c_in @ A @ C @ D )
| ~ ( c_in @ A @ B @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__iff_2) ).
thf(1259,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D )
| ~ ( c_in @ A @ C @ D )
| ~ ( c_in @ A @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(181,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ A @ A @ B @ B @ B ) @ ( c_Relation_Orel__comp @ C @ A @ B @ B @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ C @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ B )
| ~ ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__union__merge_0) ).
thf(783,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ A @ A @ B @ B @ B ) @ ( c_Relation_Orel__comp @ C @ A @ B @ B @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ C @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ B )
| ~ ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(1,negated_conjecture,
~ v_thesis____,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(420,plain,
~ v_thesis____,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(25,axiom,
! [C: $i,B: $i,A: $i] : ( c_in @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__iff_1) ).
thf(471,plain,
! [C: $i,B: $i,A: $i] : ( c_in @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(230,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Otrans @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) ) @ C )
| ~ ( c_Relation_Otrans @ B @ C )
| ~ ( c_Relation_Otrans @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__Int_0) ).
thf(884,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Otrans @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) ) @ C )
| ~ ( c_Relation_Otrans @ B @ C )
| ~ ( c_Relation_Otrans @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(295,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ~ ( c_in @ ( c_Pair @ A @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 @ B @ D @ C ) @ C @ C ) @ D @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ E @ B @ C )
| ~ ( c_Wellfounded_Owf @ D @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__eq__minimal_1) ).
thf(1028,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ~ ( c_in @ ( c_Pair @ A @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 @ B @ D @ C ) @ C @ C ) @ D @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ E @ B @ C )
| ~ ( c_Wellfounded_Owf @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(34,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D )
| ~ ( c_in @ A @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insertCI_0) ).
thf(488,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D )
| ~ ( c_in @ A @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(58,axiom,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Ortrancl @ A @ B )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ ( c_Relation_OId @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nitpick_Ortrancl__def_0) ).
thf(537,plain,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Ortrancl @ A @ B )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ ( c_Relation_OId @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(106,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Int__crazy_0) ).
thf(637,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ A @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(369,axiom,
! [B: $i,A: $i] : ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ ( c_Relation_OId @ B ) @ ( tc_prod @ B @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IdI_0) ).
thf(1214,plain,
! [B: $i,A: $i] : ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ ( c_Relation_OId @ B ) @ ( tc_prod @ B @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(270,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ D @ A @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( D = B )
| ~ ( c_in @ C @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( D = A )
| ( c_in @ ( c_Pair @ D @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ C @ D @ A ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__below_13) ).
thf(970,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ D @ A @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( D = B )
| ~ ( c_in @ C @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( D = A )
| ( c_in @ ( c_Pair @ D @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ C @ D @ A ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(347,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ ( c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1 @ A @ B @ C @ D ) @ C @ D ) @ B @ ( tc_prod @ C @ D ) )
| ~ ( c_in @ A @ ( c_Relation_ODomain @ B @ C @ D ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Domain__iff_0) ).
thf(1155,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ ( c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1 @ A @ B @ C @ D ) @ C @ D ) @ B @ ( tc_prod @ C @ D ) )
| ~ ( c_in @ A @ ( c_Relation_ODomain @ B @ C @ D ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(66,axiom,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Ortrancl @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ B )
= ( c_Transitive__Closure_Ortrancl @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__idemp_0) ).
thf(554,plain,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Ortrancl @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ B )
= ( c_Transitive__Closure_Ortrancl @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(166,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_Oconverse @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_bool ) ) @ C @ D )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_Oconverse @ A @ C @ D ) @ ( c_Relation_Oconverse @ B @ C @ D ) @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_converse__Int_0) ).
thf(753,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_Oconverse @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_bool ) ) @ C @ D )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_Oconverse @ A @ C @ D ) @ ( c_Relation_Oconverse @ B @ C @ D ) @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(131,axiom,
! [B: $i,A: $i] : ( c_Relation_Orefl__on @ A @ ( c_Relation_OId__on @ A @ B ) @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_refl__on__Id__on_0) ).
thf(686,plain,
! [B: $i,A: $i] : ( c_Relation_Orefl__on @ A @ ( c_Relation_OId__on @ A @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(28,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oimage @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ A @ B @ D @ E ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ ( tc_fun @ E @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__Un_0) ).
thf(476,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oimage @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oimage @ A @ B @ D @ E ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ ( tc_fun @ E @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(290,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XImageE__1__1 @ A @ B @ C @ D @ E ) @ B @ D @ E ) @ C @ ( tc_prod @ D @ E ) )
| ~ ( c_in @ B @ ( c_Relation_OImage @ C @ A @ D @ E ) @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_ImageE_0) ).
thf(1016,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XImageE__1__1 @ A @ B @ C @ D @ E ) @ B @ D @ E ) @ C @ ( tc_prod @ D @ E ) )
| ~ ( c_in @ B @ ( c_Relation_OImage @ C @ A @ D @ E ) @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(85,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ B @ tc_bool ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__Un_0) ).
thf(590,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ B @ tc_bool ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(281,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Arrow__Order__Mirabelle_Obelow @ A @ B @ C ) @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ~ ( c_in @ A @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_below__Lin_0) ).
thf(997,plain,
! [C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Arrow__Order__Mirabelle_Obelow @ A @ B @ C ) @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ~ ( c_in @ A @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(276,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ C @ D @ E ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ E @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ A @ E @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( A = B )
| ~ ( c_in @ C @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( D = E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__below_14) ).
thf(985,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ C @ D @ E ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ E @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ A @ E @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( A = B )
| ~ ( c_in @ C @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( D = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(141,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Relation_Oconverse @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ C @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ ( c_Relation_Oconverse @ D @ C @ C ) @ C ) @ ( tc_prod @ C @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trancl__converseD_0) ).
thf(701,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Relation_Oconverse @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ C @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ ( c_Relation_Oconverse @ D @ C @ C ) @ C ) @ ( tc_prod @ C @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(385,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) )
| ( c_in @ ( c_Pair @ B @ A @ C @ C ) @ D @ ( tc_prod @ C @ C ) )
| ( B = A )
| ~ ( c_in @ A @ E @ C )
| ~ ( c_in @ B @ E @ C )
| ~ ( c_Relation_Ototal__on @ E @ D @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_total__on__def_0) ).
thf(1249,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) )
| ( c_in @ ( c_Pair @ B @ A @ C @ C ) @ D @ ( tc_prod @ C @ C ) )
| ( B = A )
| ~ ( c_in @ A @ E @ C )
| ~ ( c_in @ B @ E @ C )
| ~ ( c_Relation_Ototal__on @ E @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(159,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
= A )
| ~ ( c_lessequals @ B @ A @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__absorb2_0) ).
thf(738,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
= A )
| ~ ( c_lessequals @ B @ A @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(337,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( c_lessequals @ B @ A @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equalityI_0) ).
thf(1131,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( c_lessequals @ B @ A @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(17,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ( c_in @ D @ A @ C )
| ~ ( c_lessequals @ A @ ( c_Set_Oinsert @ D @ B @ C ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert__iff_1) ).
thf(457,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ( c_in @ D @ A @ C )
| ~ ( c_lessequals @ A @ ( c_Set_Oinsert @ D @ B @ C ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(75,axiom,
! [B: $i,A: $i] :
( ( ( c_Relation_Oconverse @ A @ B @ B )
= A )
| ~ ( c_Relation_Osym @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sym__conv__converse__eq_0) ).
thf(569,plain,
! [B: $i,A: $i] :
( ( ( c_Relation_Oconverse @ A @ B @ B )
= A )
| ~ ( c_Relation_Osym @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(384,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ C @ D @ E ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( A = D )
| ( B = D )
| ( A = B )
| ~ ( c_in @ C @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( D = E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__below_4) ).
thf(1246,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ C @ D @ E ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( A = D )
| ( B = D )
| ( A = B )
| ~ ( c_in @ C @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( D = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(179,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Product__Type_OSigma @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_COMBK @ D @ ( tc_fun @ E @ tc_bool ) @ C ) @ C @ E )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Product__Type_OSigma @ A @ ( c_COMBK @ D @ ( tc_fun @ E @ tc_bool ) @ C ) @ C @ E ) @ ( c_Product__Type_OSigma @ B @ ( c_COMBK @ D @ ( tc_fun @ E @ tc_bool ) @ C ) @ C @ E ) @ ( tc_fun @ ( tc_prod @ C @ E ) @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Times__Un__distrib1_0) ).
thf(779,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Product__Type_OSigma @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_COMBK @ D @ ( tc_fun @ E @ tc_bool ) @ C ) @ C @ E )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Product__Type_OSigma @ A @ ( c_COMBK @ D @ ( tc_fun @ E @ tc_bool ) @ C ) @ C @ E ) @ ( c_Product__Type_OSigma @ B @ ( c_COMBK @ D @ ( tc_fun @ E @ tc_bool ) @ C ) @ C @ E ) @ ( tc_fun @ ( tc_prod @ C @ E ) @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(41,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C )
= ( c_Set_Oinsert @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__absorb2_0) ).
thf(503,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Set_Oinsert @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C )
= ( c_Set_Oinsert @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(92,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_Orefl__on @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ E @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) ) @ C )
| ~ ( c_Relation_Orefl__on @ B @ E @ C )
| ~ ( c_Relation_Orefl__on @ A @ D @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_refl__on__Int_0) ).
thf(605,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_Orefl__on @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ E @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) ) @ C )
| ~ ( c_Relation_Orefl__on @ B @ E @ C )
| ~ ( c_Relation_Orefl__on @ A @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(185,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
!= B )
| ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__Un__eq_1) ).
thf(792,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
!= B )
| ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(319,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( A = D )
| ( A = D )
| ~ ( c_in @ C @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( B = D )
| ( c_in @ ( c_Pair @ A @ D @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ C @ B @ D ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__above_7) ).
thf(1086,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( A = D )
| ( A = D )
| ~ ( c_in @ C @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( B = D )
| ( c_in @ ( c_Pair @ A @ D @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ C @ B @ D ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(191,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Relation_OImage @ A @ B @ C @ D ) @ E @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ A @ ( c_Product__Type_OSigma @ F @ ( c_COMBK @ E @ ( tc_fun @ D @ tc_bool ) @ C ) @ C @ D ) @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Image__subset_0) ).
thf(805,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Relation_OImage @ A @ B @ C @ D ) @ E @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ A @ ( c_Product__Type_OSigma @ F @ ( c_COMBK @ E @ ( tc_fun @ D @ tc_bool ) @ C ) @ C @ D ) @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(44,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Set_Oimage @ A @ B @ C @ D ) @ D )
| ~ ( c_Finite__Set_Ofinite @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__imageI_0) ).
thf(508,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Set_Oimage @ A @ B @ C @ D ) @ D )
| ~ ( c_Finite__Set_Ofinite @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(249,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Product__Type_OSigma @ B @ ( c_COMBK @ B @ ( tc_fun @ C @ tc_bool ) @ C ) @ C @ C ) @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) )
| ~ ( c_Relation_Orefl__on @ B @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_refl__on__def_0) ).
thf(921,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Product__Type_OSigma @ B @ ( c_COMBK @ B @ ( tc_fun @ C @ tc_bool ) @ C ) @ C @ C ) @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) )
| ~ ( c_Relation_Orefl__on @ B @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(60,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ ( hAPP @ A @ B ) @ ( hAPP @ A @ C ) @ D @ D ) @ E @ ( tc_prod @ D @ D ) )
| ~ ( c_in @ ( c_Pair @ B @ C @ F @ F ) @ ( c_Relation_Oinv__image @ E @ A @ D @ F ) @ ( tc_prod @ F @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__inv__image_0) ).
thf(541,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ ( hAPP @ A @ B ) @ ( hAPP @ A @ C ) @ D @ D ) @ E @ ( tc_prod @ D @ D ) )
| ~ ( c_in @ ( c_Pair @ B @ C @ F @ F ) @ ( c_Relation_Oinv__image @ E @ A @ D @ F ) @ ( tc_prod @ F @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(116,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ A @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__subset__iff_1) ).
thf(657,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ A @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(400,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Complete__Lattice_OSup__class_OSup @ B @ ( tc_fun @ C @ tc_bool ) ) @ C )
| ~ ( c_in @ A @ D @ C )
| ~ ( c_in @ D @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UnionI_0) ).
thf(1286,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Complete__Lattice_OSup__class_OSup @ B @ ( tc_fun @ C @ tc_bool ) ) @ C )
| ~ ( c_in @ A @ D @ C )
| ~ ( c_in @ D @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(125,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 @ A @ B @ C ) @ A @ C )
| ~ ( c_in @ D @ A @ C )
| ~ ( c_Wellfounded_Owf @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__eq__minimal_0) ).
thf(674,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 @ A @ B @ C ) @ A @ C )
| ~ ( c_in @ D @ A @ C )
| ~ ( c_Wellfounded_Owf @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(83,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ D @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Int__distrib_0) ).
thf(586,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ D @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(172,axiom,
! [B: $i,A: $i] : ( c_Relation_Otrans @ ( c_Relation_OId__on @ A @ B ) @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__Id__on_0) ).
thf(765,plain,
! [B: $i,A: $i] : ( c_Relation_Otrans @ ( c_Relation_OId__on @ A @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(306,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ ( c_ATP__Linkup_Osko__Relation__XDomainE__1__1 @ A @ B @ C @ D ) @ C @ D ) @ B @ ( tc_prod @ C @ D ) )
| ~ ( c_in @ A @ ( c_Relation_ODomain @ B @ C @ D ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_DomainE_0) ).
thf(1054,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ ( c_ATP__Linkup_Osko__Relation__XDomainE__1__1 @ A @ B @ C @ D ) @ C @ D ) @ B @ ( tc_prod @ C @ D ) )
| ~ ( c_in @ A @ ( c_Relation_ODomain @ B @ C @ D ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(294,axiom,
! [C: $i,B: $i,A: $i] :
~ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ C @ B ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__mkbot_0) ).
thf(1026,plain,
! [C: $i,B: $i,A: $i] :
~ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ C @ B ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(353,axiom,
! [B: $i,A: $i] :
~ ( c_in @ ( c_Pair @ A @ A @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ B @ A ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__mkbot_1) ).
thf(1167,plain,
! [B: $i,A: $i] :
~ ( c_in @ ( c_Pair @ A @ A @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ B @ A ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(119,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_Oconverse @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_bool ) ) @ C @ D )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Oconverse @ A @ C @ D ) @ ( c_Relation_Oconverse @ B @ C @ D ) @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_converse__Un_0) ).
thf(662,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_Oconverse @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_bool ) ) @ C @ D )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Oconverse @ A @ C @ D ) @ ( c_Relation_Oconverse @ B @ C @ D ) @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(149,axiom,
! [B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ ( c_Relation_OId @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) )
= ( c_Transitive__Closure_Ortrancl @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__reflcl__absorb_0) ).
thf(718,plain,
! [B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ ( c_Relation_OId @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) )
= ( c_Transitive__Closure_Ortrancl @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(242,axiom,
! [B: $i,A: $i] :
( ( c_Relation_Osym @ ( c_Relation_Oconverse @ A @ B @ B ) @ B )
| ~ ( c_Relation_Osym @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sym__converse_1) ).
thf(906,plain,
! [B: $i,A: $i] :
( ( c_Relation_Osym @ ( c_Relation_Oconverse @ A @ B @ B ) @ B )
| ~ ( c_Relation_Osym @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(268,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ~ ( c_in @ ( c_Pair @ A @ D @ C @ C ) @ ( c_Relation_OId__on @ B @ C ) @ ( tc_prod @ C @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Id__on__iff_1) ).
thf(965,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ~ ( c_in @ ( c_Pair @ A @ D @ C @ C ) @ ( c_Relation_OId__on @ B @ C ) @ ( tc_prod @ C @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(98,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Equiv__Relations_Oquotient @ A @ B @ C ) @ ( tc_fun @ C @ tc_bool ) )
= A )
| ~ ( c_Equiv__Relations_Oequiv @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Union__quotient_0) ).
thf(618,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Complete__Lattice_OSup__class_OSup @ ( c_Equiv__Relations_Oquotient @ A @ B @ C ) @ ( tc_fun @ C @ tc_bool ) )
= A )
| ~ ( c_Equiv__Relations_Oequiv @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(3,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Set_Oinsert @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ D ) )
| ~ ( c_in @ B @ A @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__insert__right_0) ).
thf(425,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Set_Oinsert @ B @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ D ) )
| ~ ( c_in @ B @ A @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(325,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( c_lessequals @ B @ A @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_set__eq__subset_2) ).
thf(1103,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( c_lessequals @ B @ A @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(162,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__Un__distrib2_0) ).
thf(745,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(134,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Orel__comp @ ( c_Relation_OId @ A ) @ B @ A @ A @ C )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Id__O__R_0) ).
thf(689,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Orel__comp @ ( c_Relation_OId @ A ) @ B @ A @ A @ C )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(156,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Orefl__on @ A @ B @ C )
| ~ ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__Xrefl__on__def__1__1 @ A @ B @ C ) @ ( c_ATP__Linkup_Osko__Relation__Xrefl__on__def__1__1 @ A @ B @ C ) @ C @ C ) @ B @ ( tc_prod @ C @ C ) )
| ~ ( c_lessequals @ B @ ( c_Product__Type_OSigma @ A @ ( c_COMBK @ A @ ( tc_fun @ C @ tc_bool ) @ C ) @ C @ C ) @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_refl__on__def_3) ).
thf(733,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Orefl__on @ A @ B @ C )
| ~ ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__Xrefl__on__def__1__1 @ A @ B @ C ) @ ( c_ATP__Linkup_Osko__Relation__Xrefl__on__def__1__1 @ A @ B @ C ) @ C @ C ) @ B @ ( tc_prod @ C @ C ) )
| ~ ( c_lessequals @ B @ ( c_Product__Type_OSigma @ A @ ( c_COMBK @ A @ ( tc_fun @ C @ tc_bool ) @ C ) @ C @ C ) @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(90,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ B @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__least_0) ).
thf(601,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ B @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(343,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( B = D )
| ( A = D )
| ~ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ C @ E @ D ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ C @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( E = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__above_3) ).
thf(1146,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( B = D )
| ( A = D )
| ~ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ C @ E @ D ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ C @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( E = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(5,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Orefl__on @ A @ B @ C )
| ( c_in @ ( c_ATP__Linkup_Osko__Relation__Xrefl__onI__1__1 @ A @ B @ C ) @ A @ C )
| ~ ( c_lessequals @ B @ ( c_Product__Type_OSigma @ A @ ( c_COMBK @ A @ ( tc_fun @ C @ tc_bool ) @ C ) @ C @ C ) @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_refl__onI_0) ).
thf(430,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Orefl__on @ A @ B @ C )
| ( c_in @ ( c_ATP__Linkup_Osko__Relation__Xrefl__onI__1__1 @ A @ B @ C ) @ A @ C )
| ~ ( c_lessequals @ B @ ( c_Product__Type_OSigma @ A @ ( c_COMBK @ A @ ( tc_fun @ C @ tc_bool ) @ C ) @ C @ C ) @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(372,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ ( c_Relation_Orel__comp @ E @ F @ C @ G @ D ) @ ( tc_prod @ C @ D ) )
| ~ ( c_in @ ( c_Pair @ H @ B @ G @ D ) @ F @ ( tc_prod @ G @ D ) )
| ~ ( c_in @ ( c_Pair @ A @ H @ C @ G ) @ E @ ( tc_prod @ C @ G ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__compI_0) ).
thf(1219,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ ( c_Relation_Orel__comp @ E @ F @ C @ G @ D ) @ ( tc_prod @ C @ D ) )
| ~ ( c_in @ ( c_Pair @ H @ B @ G @ D ) @ F @ ( tc_prod @ G @ D ) )
| ~ ( c_in @ ( c_Pair @ A @ H @ C @ G ) @ E @ ( tc_prod @ C @ G ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(201,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Osym @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) ) @ C )
| ~ ( c_Relation_Osym @ B @ C )
| ~ ( c_Relation_Osym @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sym__Int_0) ).
thf(824,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Osym @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) ) @ C )
| ~ ( c_Relation_Osym @ B @ C )
| ~ ( c_Relation_Osym @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(82,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Ototal__on @ A @ ( c_Relation_Oconverse @ B @ C @ C ) @ C )
| ~ ( c_Relation_Ototal__on @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_total__on__converse_1) ).
thf(584,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Ototal__on @ A @ ( c_Relation_Oconverse @ B @ C @ C ) @ C )
| ~ ( c_Relation_Ototal__on @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(334,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ E @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ A @ E @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trancl__trans_0) ).
thf(1125,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ E @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ A @ E @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(176,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) )
= A )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__absorb2_0) ).
thf(772,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) )
= A )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(161,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_Orel__comp @ ( c_Relation_Orel__comp @ A @ B @ C @ D @ E ) @ F @ C @ E @ G )
= ( c_Relation_Orel__comp @ A @ ( c_Relation_Orel__comp @ B @ F @ D @ E @ G ) @ C @ D @ G ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_O__assoc_0) ).
thf(743,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_Orel__comp @ ( c_Relation_Orel__comp @ A @ B @ C @ D @ E ) @ F @ C @ E @ G )
= ( c_Relation_Orel__comp @ A @ ( c_Relation_Orel__comp @ B @ F @ D @ E @ G ) @ C @ D @ G ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(71,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ E @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ A @ E @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__into__trancl1_0) ).
thf(562,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ E @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ A @ E @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(241,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Int__distrib2_0) ).
thf(904,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(202,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_Oconverse @ ( c_Relation_Orel__comp @ A @ B @ C @ D @ E ) @ C @ E )
= ( c_Relation_Orel__comp @ ( c_Relation_Oconverse @ B @ D @ E ) @ ( c_Relation_Oconverse @ A @ C @ D ) @ E @ D @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_converse__rel__comp_0) ).
thf(826,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_Oconverse @ ( c_Relation_Orel__comp @ A @ B @ C @ D @ E ) @ C @ E )
= ( c_Relation_Orel__comp @ ( c_Relation_Oconverse @ B @ D @ E ) @ ( c_Relation_Oconverse @ A @ C @ D ) @ E @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(146,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Relation_Orel__comp @ A @ B @ C @ D @ E ) @ ( c_Relation_Orel__comp @ F @ G @ C @ D @ E ) @ ( tc_fun @ ( tc_prod @ C @ E ) @ tc_bool ) )
| ~ ( c_lessequals @ B @ G @ ( tc_fun @ ( tc_prod @ D @ E ) @ tc_bool ) )
| ~ ( c_lessequals @ A @ F @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__comp__mono_0) ).
thf(711,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Relation_Orel__comp @ A @ B @ C @ D @ E ) @ ( c_Relation_Orel__comp @ F @ G @ C @ D @ E ) @ ( tc_fun @ ( tc_prod @ C @ E ) @ tc_bool ) )
| ~ ( c_lessequals @ B @ G @ ( tc_fun @ ( tc_prod @ D @ E ) @ tc_bool ) )
| ~ ( c_lessequals @ A @ F @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(388,axiom,
! [B: $i,A: $i] : ( c_lessequals @ A @ A @ ( tc_fun @ B @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__refl_0) ).
thf(1256,plain,
! [B: $i,A: $i] : ( c_lessequals @ A @ A @ ( tc_fun @ B @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(375,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ E @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ A @ E @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_converse__rtrancl__into__rtrancl_0) ).
thf(1226,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ E @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ A @ E @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(108,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1 @ A @ B @ C @ D ) @ C @ D @ D ) @ ( c_Transitive__Closure_Ortrancl @ A @ D ) @ ( tc_prod @ D @ D ) )
| ~ ( c_in @ ( c_Pair @ B @ C @ D @ D ) @ ( c_Transitive__Closure_Otrancl @ A @ D ) @ ( tc_prod @ D @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_tranclD_1) ).
thf(641,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1 @ A @ B @ C @ D ) @ C @ D @ D ) @ ( c_Transitive__Closure_Ortrancl @ A @ D ) @ ( tc_prod @ D @ D ) )
| ~ ( c_in @ ( c_Pair @ B @ C @ D @ D ) @ ( c_Transitive__Closure_Otrancl @ A @ D ) @ ( tc_prod @ D @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(340,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ~ ( c_in @ ( c_Pair @ A @ ( c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 @ B @ D @ C ) @ C @ C ) @ D @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ E @ B @ C )
| ~ ( c_Wellfounded_Owf @ D @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wfE__min_1) ).
thf(1139,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ~ ( c_in @ ( c_Pair @ A @ ( c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 @ B @ D @ C ) @ C @ C ) @ D @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ E @ B @ C )
| ~ ( c_Wellfounded_Owf @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(12,axiom,
! [B: $i,A: $i] :
( ( c_Relation_OField @ ( c_Relation_Oconverse @ A @ B @ B ) @ B )
= ( c_Relation_OField @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Field__converse_0) ).
thf(445,plain,
! [B: $i,A: $i] :
( ( c_Relation_OField @ ( c_Relation_Oconverse @ A @ B @ B ) @ B )
= ( c_Relation_OField @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(76,axiom,
! [B: $i,A: $i] :
( ( c_Wellfounded_Owf @ A @ B )
| ~ ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__acc__iff__1__1 @ A @ B ) @ ( c_Wellfounded_Oacc @ A @ B ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__acc__iff_1) ).
thf(572,plain,
! [B: $i,A: $i] :
( ( c_Wellfounded_Owf @ A @ B )
| ~ ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xwf__acc__iff__1__1 @ A @ B ) @ ( c_Wellfounded_Oacc @ A @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(412,axiom,
! [C: $i,B: $i,A: $i] : ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) @ ( tc_prod @ B @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__eq__or__trancl_1) ).
thf(1312,plain,
! [C: $i,B: $i,A: $i] : ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ ( c_Transitive__Closure_Ortrancl @ C @ B ) @ ( tc_prod @ B @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(147,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_Wellfounded_Owf @ ( c_Set_Oinsert @ ( c_Pair @ B @ A @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__insert_1) ).
thf(713,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_Wellfounded_Owf @ ( c_Set_Oinsert @ ( c_Pair @ B @ A @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(381,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ C @ D ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( A = D )
| ( B = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__mkbot_3) ).
thf(1239,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ C @ D ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( A = D )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(22,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Wellfounded_Owf @ A @ B )
| ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__XwfI__1__1 @ C @ D @ A @ B ) @ C @ B )
| ~ ( c_lessequals @ A @ ( c_Product__Type_OSigma @ C @ ( c_COMBK @ D @ ( tc_fun @ B @ tc_bool ) @ B ) @ B @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wfI_2) ).
thf(466,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Wellfounded_Owf @ A @ B )
| ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__XwfI__1__1 @ C @ D @ A @ B ) @ C @ B )
| ~ ( c_lessequals @ A @ ( c_Product__Type_OSigma @ C @ ( c_COMBK @ D @ ( tc_fun @ B @ tc_bool ) @ B ) @ B @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(320,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( B = D )
| ~ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ C @ D ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__mktop_2) ).
thf(1090,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( B = D )
| ~ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ C @ D ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(248,axiom,
! [B: $i,A: $i] :
( ( c_Relation_Otrans @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Relation_OId @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ B )
| ~ ( c_Relation_Otrans @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__reflclI_0) ).
thf(919,plain,
! [B: $i,A: $i] :
( ( c_Relation_Otrans @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Relation_OId @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ B )
| ~ ( c_Relation_Otrans @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(374,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ C @ ( tc_prod @ B @ B ) )
| ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1 @ C @ B ) @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1 @ C @ B ) @ B @ B ) @ ( c_Transitive__Closure_Otrancl @ C @ B ) @ ( tc_prod @ B @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_irrefl__trancl__rD_0) ).
thf(1224,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ C @ ( tc_prod @ B @ B ) )
| ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1 @ C @ B ) @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1 @ C @ B ) @ B @ B ) @ ( c_Transitive__Closure_Otrancl @ C @ B ) @ ( tc_prod @ B @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(124,axiom,
! [B: $i,A: $i] :
( ( c_Relation_OImage @ ( c_Relation_OId @ A ) @ B @ A @ A )
= B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Image__Id_0) ).
thf(672,plain,
! [B: $i,A: $i] :
( ( c_Relation_OImage @ ( c_Relation_OId @ A ) @ B @ A @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(95,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( hAPP @ A @ B ) @ C @ D )
| ~ ( c_in @ B @ E @ F )
| ~ ( c_lessequals @ ( c_Set_Oimage @ A @ E @ F @ D ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__subset__iff_0) ).
thf(611,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( hAPP @ A @ B ) @ C @ D )
| ~ ( c_in @ B @ E @ F )
| ~ ( c_lessequals @ ( c_Set_Oimage @ A @ E @ F @ D ) @ C @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(183,axiom,
! [B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ ( c_Relation_OId @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) )
= ( c_Transitive__Closure_Ortrancl @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_reflcl__trancl_0) ).
thf(787,plain,
! [B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ ( c_Relation_OId @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) )
= ( c_Transitive__Closure_Ortrancl @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(239,axiom,
! [B: $i,A: $i] :
( ( c_Relation_Osym @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ B )
| ~ ( c_Relation_Osym @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sym__rtrancl_0) ).
thf(900,plain,
! [B: $i,A: $i] :
( ( c_Relation_Osym @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ B )
| ~ ( c_Relation_Osym @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(399,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( A = B )
| ~ ( c_in @ C @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( A = D )
| ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ C @ A @ D ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__above_12) ).
thf(1282,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( A = B )
| ~ ( c_in @ C @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( A = D )
| ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ C @ A @ D ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(331,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ C @ D ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( A = B )
| ( B = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__mkbot_5) ).
thf(1117,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omkbot @ C @ D ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( A = B )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(158,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ D @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__subset__iff_0) ).
thf(736,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ D @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(278,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Wellfounded_Oacc @ B @ C ) @ C )
| ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1 @ B @ A @ C ) @ A @ C @ C ) @ B @ ( tc_prod @ C @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acc_OaccI_0) ).
thf(990,plain,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Wellfounded_Oacc @ B @ C ) @ C )
| ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1 @ B @ A @ C ) @ A @ C @ C ) @ B @ ( tc_prod @ C @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(97,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Wellfounded_Oacc @ B @ C ) @ C )
| ~ ( c_in @ D @ ( c_Wellfounded_Oacc @ B @ C ) @ C )
| ~ ( c_in @ ( c_Pair @ A @ D @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ B @ C ) @ ( tc_prod @ C @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acc__downwards__aux_0) ).
thf(616,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Wellfounded_Oacc @ B @ C ) @ C )
| ~ ( c_in @ D @ ( c_Wellfounded_Oacc @ B @ C ) @ C )
| ~ ( c_in @ ( c_Pair @ A @ D @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ B @ C ) @ ( tc_prod @ C @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(15,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) )
| ( c_in @ A @ D @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__insert__left_1) ).
thf(451,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) )
| ( c_in @ A @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(74,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ ( c_Product__Type_OSigma @ C @ ( c_COMBK @ C @ ( tc_fun @ B @ tc_bool ) @ B ) @ B @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) )
| ~ ( c_lessequals @ A @ ( c_Product__Type_OSigma @ C @ ( c_COMBK @ C @ ( tc_fun @ B @ tc_bool ) @ B ) @ B @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trancl__subset__Sigma_0) ).
thf(567,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ ( c_Product__Type_OSigma @ C @ ( c_COMBK @ C @ ( tc_fun @ B @ tc_bool ) @ B ) @ B @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) )
| ~ ( c_lessequals @ A @ ( c_Product__Type_OSigma @ C @ ( c_COMBK @ C @ ( tc_fun @ B @ tc_bool ) @ B ) @ B @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(228,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_OImage @ ( c_Relation_OId__on @ A @ B ) @ C @ B @ B )
= ( c_Lattices_Olower__semilattice__class_Oinf @ A @ C @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Image__Id__on_0) ).
thf(880,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_OImage @ ( c_Relation_OId__on @ A @ B ) @ C @ B @ B )
= ( c_Lattices_Olower__semilattice__class_Oinf @ A @ C @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(7,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ A @ C @ ( tc_fun @ D @ tc_bool ) ) )
| ( c_in @ B @ A @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__insert__right_1) ).
thf(434,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ A @ C @ ( tc_fun @ D @ tc_bool ) ) )
| ( c_in @ B @ A @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(219,axiom,
! [B: $i,A: $i] :
( ( c_Relation_ORange @ ( c_Relation_OId__on @ A @ B ) @ B @ B )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Range__Id__on_0) ).
thf(863,plain,
! [B: $i,A: $i] :
( ( c_Relation_ORange @ ( c_Relation_OId__on @ A @ B ) @ B @ B )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(357,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ( A = C )
| ~ ( c_in @ D @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( A = B )
| ( c_in @ ( c_Pair @ A @ C @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ D @ A @ B ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ A @ C @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__above_6) ).
thf(1175,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ( A = C )
| ~ ( c_in @ D @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( A = B )
| ( c_in @ ( c_Pair @ A @ C @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ D @ A @ B ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ A @ C @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(234,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_ODomain @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_bool ) ) @ C @ D )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_ODomain @ A @ C @ D ) @ ( c_Relation_ODomain @ B @ C @ D ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Domain__Un__eq_0) ).
thf(890,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_ODomain @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_bool ) ) @ C @ D )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_ODomain @ A @ C @ D ) @ ( c_Relation_ODomain @ B @ C @ D ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(104,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ( A = D )
| ~ ( c_lessequals @ E @ ( c_Product__Type_OSigma @ B @ ( c_COMBK @ B @ ( tc_fun @ C @ tc_bool ) @ C ) @ C @ C ) @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) )
| ~ ( c_in @ ( c_Pair @ A @ D @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ E @ C ) @ ( tc_prod @ C @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trancl__subset__Sigma__aux_0) ).
thf(631,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ( A = D )
| ~ ( c_lessequals @ E @ ( c_Product__Type_OSigma @ B @ ( c_COMBK @ B @ ( tc_fun @ C @ tc_bool ) @ C ) @ C @ C ) @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) )
| ~ ( c_in @ ( c_Pair @ A @ D @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ E @ C ) @ ( tc_prod @ C @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(65,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ ( c_Product__Type_OSigma @ E @ F @ C @ D ) @ ( tc_prod @ C @ D ) )
| ~ ( c_in @ B @ ( hAPP @ F @ A ) @ D )
| ~ ( c_in @ A @ E @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SigmaI_0) ).
thf(552,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ ( c_Product__Type_OSigma @ E @ F @ C @ D ) @ ( tc_prod @ C @ D ) )
| ~ ( c_in @ B @ ( hAPP @ F @ A ) @ D )
| ~ ( c_in @ A @ E @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(57,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ ( c_Set_Oinsert @ D @ B @ C ) @ ( tc_fun @ C @ tc_bool ) )
| ( c_in @ D @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insert_0) ).
thf(535,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ ( c_Set_Oinsert @ D @ B @ C ) @ ( tc_fun @ C @ tc_bool ) )
| ( c_in @ D @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(197,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Osym @ A @ B )
| ~ ( c_Equiv__Relations_Oequiv @ C @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equiv_Osym_0) ).
thf(816,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Osym @ A @ B )
| ~ ( c_Equiv__Relations_Oequiv @ C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(94,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Relation_ODomain @ A @ B @ C ) @ ( c_Relation_ODomain @ D @ B @ C ) @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ ( tc_prod @ B @ C ) @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Domain__mono_0) ).
thf(609,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Relation_ODomain @ A @ B @ C ) @ ( c_Relation_ODomain @ D @ B @ C ) @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_lessequals @ A @ D @ ( tc_fun @ ( tc_prod @ B @ C ) @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(87,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_ORange @ A @ B @ C )
= ( c_Relation_ODomain @ ( c_Relation_Oconverse @ A @ B @ C ) @ C @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Range__def_0) ).
thf(594,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_ORange @ A @ B @ C )
= ( c_Relation_ODomain @ ( c_Relation_Oconverse @ A @ B @ C ) @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(99,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ C )
| ~ ( c_Finite__Set_Ofinite @ B @ C )
| ~ ( c_Finite__Set_Ofinite @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__Un_2) ).
thf(621,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ C )
| ~ ( c_Finite__Set_Ofinite @ B @ C )
| ~ ( c_Finite__Set_Ofinite @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(50,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_ODomain @ ( c_Set_Oinsert @ ( c_Pair @ A @ B @ C @ D ) @ E @ ( tc_prod @ C @ D ) ) @ C @ D )
= ( c_Set_Oinsert @ A @ ( c_Relation_ODomain @ E @ C @ D ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Domain__insert_0) ).
thf(520,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_ODomain @ ( c_Set_Oinsert @ ( c_Pair @ A @ B @ C @ D ) @ E @ ( tc_prod @ C @ D ) ) @ C @ D )
= ( c_Set_Oinsert @ A @ ( c_Relation_ODomain @ E @ C @ D ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(418,axiom,
! [A: $i] :
( ( c_in @ ( c_Relation_Oconverse @ A @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ~ ( c_in @ A @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_converse__in__Lin_1) ).
thf(1325,plain,
! [A: $i] :
( ( c_in @ ( c_Relation_Oconverse @ A @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ~ ( c_in @ A @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(344,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ~ ( c_in @ A @ D @ C )
| ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subsetD_0) ).
thf(1149,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ~ ( c_in @ A @ D @ C )
| ~ ( c_lessequals @ D @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(246,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Relation__XId__onE__1__1 @ A @ B @ C ) @ A @ C )
| ~ ( c_in @ B @ ( c_Relation_OId__on @ A @ C ) @ ( tc_prod @ C @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Id__onE_0) ).
thf(915,plain,
! [C: $i,B: $i,A: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Relation__XId__onE__1__1 @ A @ B @ C ) @ A @ C )
| ~ ( c_in @ B @ ( c_Relation_OId__on @ A @ C ) @ ( tc_prod @ C @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(175,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ A @ B @ C @ D @ E @ F ) )
!= ( hAPP @ B @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ A @ B @ C @ D @ E @ F ) ) )
| ( ( c_Recdef_Ocut @ A @ C @ D @ E @ F )
= ( c_Recdef_Ocut @ B @ C @ D @ E @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cuts__eq_2) ).
thf(769,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ A @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ A @ B @ C @ D @ E @ F ) )
!= ( hAPP @ B @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ A @ B @ C @ D @ E @ F ) ) )
| ( ( c_Recdef_Ocut @ A @ C @ D @ E @ F )
= ( c_Recdef_Ocut @ B @ C @ D @ E @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(258,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ B @ A @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__commute_0) ).
thf(943,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ B @ A @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(309,axiom,
! [B: $i,A: $i] :
( ( c_in @ ( v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1 @ A @ B ) @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__Lin_0) ).
thf(1061,plain,
! [B: $i,A: $i] :
( ( c_in @ ( v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1 @ A @ B ) @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(188,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__subset__iff_2) ).
thf(799,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(350,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ C @ ( tc_prod @ B @ B ) )
| ~ ( c_in @ A @ D @ B )
| ~ ( c_Relation_Orefl__on @ D @ C @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_refl__on__def_1) ).
thf(1162,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ C @ ( tc_prod @ B @ B ) )
| ~ ( c_in @ A @ D @ B )
| ~ ( c_Relation_Orefl__on @ D @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(404,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ( c_in @ A @ D @ C )
| ~ ( c_in @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ B @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UnE_0) ).
thf(1293,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ( c_in @ A @ D @ C )
| ~ ( c_in @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ B @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(122,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ ( c_Relation_Oconverse @ D @ C @ C ) @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Relation_Oconverse @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ C @ C ) @ ( tc_prod @ C @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trancl__converseI_0) ).
thf(668,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ ( c_Relation_Oconverse @ D @ C @ C ) @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Relation_Oconverse @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ C @ C ) @ ( tc_prod @ C @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(265,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__assoc_0) ).
thf(959,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(174,axiom,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__lower2_0) ).
thf(768,plain,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ B @ ( tc_fun @ C @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(222,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Wellfounded_Owf @ A @ B )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) )
| ~ ( c_Wellfounded_Owf @ C @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__subset_0) ).
thf(868,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Wellfounded_Owf @ A @ B )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) )
| ~ ( c_Wellfounded_Owf @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(329,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ E @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ A @ E @ C @ C ) @ D @ ( tc_prod @ C @ C ) )
| ~ ( c_Relation_Otrans @ D @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__def_0) ).
thf(1113,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ E @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ A @ E @ C @ C ) @ D @ ( tc_prod @ C @ C ) )
| ~ ( c_Relation_Otrans @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(282,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ C @ D @ E ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ A @ D @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( A = E )
| ( A = B )
| ~ ( c_in @ C @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( D = E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__above_8) ).
thf(1000,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ C @ D @ E ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ A @ D @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( A = E )
| ( A = B )
| ~ ( c_in @ C @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( D = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(213,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_ODomain @ ( c_Relation_Oconverse @ A @ B @ C ) @ C @ B )
= ( c_Relation_ORange @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Domain__converse_0) ).
thf(851,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_ODomain @ ( c_Relation_Oconverse @ A @ B @ C ) @ C @ B )
= ( c_Relation_ORange @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(42,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Set_Oimage @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oimage @ A @ B @ D @ E ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ ( tc_fun @ E @ tc_bool ) ) @ ( tc_fun @ E @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__Int__subset_0) ).
thf(505,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Set_Oimage @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oimage @ A @ B @ D @ E ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ ( tc_fun @ E @ tc_bool ) ) @ ( tc_fun @ E @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(114,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Product__Type_OSigma @ A @ B @ C @ D ) @ ( c_Product__Type_OSigma @ E @ F @ C @ D ) @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_bool ) )
| ( c_in @ ( c_ATP__Linkup_Osko__Product__Type__XSigma__mono__1__1 @ A @ B @ F @ C @ D ) @ A @ C )
| ~ ( c_lessequals @ A @ E @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sigma__mono_0) ).
thf(653,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Product__Type_OSigma @ A @ B @ C @ D ) @ ( c_Product__Type_OSigma @ E @ F @ C @ D ) @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_bool ) )
| ( c_in @ ( c_ATP__Linkup_Osko__Product__Type__XSigma__mono__1__1 @ A @ B @ F @ C @ D ) @ A @ C )
| ~ ( c_lessequals @ A @ E @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(245,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Relation_Orel__comp @ ( c_Relation_Oconverse @ A @ B @ B ) @ A @ B @ B @ B )
= A )
| ~ ( c_Equiv__Relations_Oequiv @ C @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equiv__comp__eq_0) ).
thf(912,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Relation_Orel__comp @ ( c_Relation_Oconverse @ A @ B @ B ) @ A @ B @ B @ B )
= A )
| ~ ( c_Equiv__Relations_Oequiv @ C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(355,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XImage__iff__1__1 @ A @ B @ C @ D @ E ) @ B @ D @ E ) @ C @ ( tc_prod @ D @ E ) )
| ~ ( c_in @ B @ ( c_Relation_OImage @ C @ A @ D @ E ) @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Image__iff_1) ).
thf(1171,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XImage__iff__1__1 @ A @ B @ C @ D @ E ) @ B @ D @ E ) @ C @ ( tc_prod @ D @ E ) )
| ~ ( c_in @ B @ ( c_Relation_OImage @ C @ A @ D @ E ) @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(302,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ C @ D @ E ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( A = D )
| ~ ( c_in @ ( c_Pair @ A @ E @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( A = B )
| ~ ( c_in @ C @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( D = E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__below_10) ).
thf(1044,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ C @ D @ E ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( A = D )
| ~ ( c_in @ ( c_Pair @ A @ E @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( A = B )
| ~ ( c_in @ C @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( D = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(137,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Relation_OImage @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_OImage @ A @ B @ D @ E ) @ ( c_Relation_OImage @ A @ C @ D @ E ) @ ( tc_fun @ E @ tc_bool ) ) @ ( tc_fun @ E @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Image__Int__subset_0) ).
thf(695,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Relation_OImage @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D @ E ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_OImage @ A @ B @ D @ E ) @ ( c_Relation_OImage @ A @ C @ D @ E ) @ ( tc_fun @ E @ tc_bool ) ) @ ( tc_fun @ E @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(315,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ C @ B @ D ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ C @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( B = D )
| ( c_in @ ( c_Pair @ A @ D @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__below_1) ).
thf(1076,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ C @ B @ D ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ C @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( B = D )
| ( c_in @ ( c_Pair @ A @ D @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(298,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Transitive__Closure_Ortrancl @ B @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ A @ B @ ( tc_prod @ C @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_r__into__rtrancl_0) ).
thf(1034,plain,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Transitive__Closure_Ortrancl @ B @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ A @ B @ ( tc_prod @ C @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(35,axiom,
! [C: $i,B: $i,A: $i] : ( c_in @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insertI1_0) ).
thf(490,plain,
! [C: $i,B: $i,A: $i] : ( c_in @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(352,axiom,
! [B: $i,A: $i] : ( c_lessequals @ A @ A @ ( tc_fun @ B @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equalityE_0) ).
thf(1166,plain,
! [B: $i,A: $i] : ( c_lessequals @ A @ A @ ( tc_fun @ B @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(55,axiom,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ A @ C ) @ ( tc_fun @ C @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insertI_0) ).
thf(531,plain,
! [C: $i,B: $i,A: $i] : ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ A @ C ) @ ( tc_fun @ C @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(63,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ C @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Relation_Orel__comp @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ C @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ A @ B @ B @ B ) @ C @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trancl__Int__subset_0) ).
thf(548,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ C @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Relation_Orel__comp @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ C @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ A @ B @ B @ B ) @ C @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(252,axiom,
! [B: $i,A: $i] :
( ( c_Relation_Orel__comp @ A @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ B @ B @ B )
= ( c_Relation_Orel__comp @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ A @ B @ B @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_r__comp__rtrancl__eq_0) ).
thf(927,plain,
! [B: $i,A: $i] :
( ( c_Relation_Orel__comp @ A @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ B @ B @ B )
= ( c_Relation_Orel__comp @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ A @ B @ B @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(397,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1 @ B @ A @ C @ D ) @ D @ D ) @ B @ ( tc_prod @ D @ D ) )
| ( c_in @ ( c_Pair @ A @ C @ D @ D ) @ B @ ( tc_prod @ D @ D ) )
| ~ ( c_in @ ( c_Pair @ A @ C @ D @ D ) @ ( c_Transitive__Closure_Otrancl @ B @ D ) @ ( tc_prod @ D @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_converse__tranclE_0) ).
thf(1277,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ ( c_ATP__Linkup_Osko__Transitive__Closure__Xconverse__tranclE__1__1 @ B @ A @ C @ D ) @ D @ D ) @ B @ ( tc_prod @ D @ D ) )
| ( c_in @ ( c_Pair @ A @ C @ D @ D ) @ B @ ( tc_prod @ D @ D ) )
| ~ ( c_in @ ( c_Pair @ A @ C @ D @ D ) @ ( c_Transitive__Closure_Otrancl @ B @ D ) @ ( tc_prod @ D @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(195,axiom,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Relation_OId @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ B )
= ( c_Transitive__Closure_Ortrancl @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__reflcl_0) ).
thf(812,plain,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Relation_OId @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ B )
= ( c_Transitive__Closure_Ortrancl @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(48,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E )
| ~ ( c_in @ B @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__eqI_0) ).
thf(516,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E )
| ~ ( c_in @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(291,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Recdef_Ocut @ A @ B @ C @ D @ E ) @ F )
= ( hAPP @ A @ F ) )
| ~ ( c_in @ ( c_Pair @ F @ C @ D @ D ) @ B @ ( tc_prod @ D @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_tfl__cut__apply_0) ).
thf(1018,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( hAPP @ ( c_Recdef_Ocut @ A @ B @ C @ D @ E ) @ F )
= ( hAPP @ A @ F ) )
| ~ ( c_in @ ( c_Pair @ F @ C @ D @ D ) @ B @ ( tc_prod @ D @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(200,axiom,
! [B: $i,A: $i] : ( c_Relation_Otrans @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__rtrancl_0) ).
thf(823,plain,
! [B: $i,A: $i] : ( c_Relation_Otrans @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(304,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Transitive__Closure_Otrancl @ B @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_lessequals @ D @ B @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) )
| ~ ( c_in @ A @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trancl__mono_0) ).
thf(1049,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Transitive__Closure_Otrancl @ B @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_lessequals @ D @ B @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) )
| ~ ( c_in @ A @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(365,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Wellfounded_Oacc @ B @ C ) @ C )
| ~ ( c_in @ ( c_Pair @ A @ D @ C @ C ) @ B @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ D @ ( c_Wellfounded_Oacc @ B @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acc_Ocases_0) ).
thf(1203,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Wellfounded_Oacc @ B @ C ) @ C )
| ~ ( c_in @ ( c_Pair @ A @ D @ C @ C ) @ B @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ D @ ( c_Wellfounded_Oacc @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(367,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ( C = A )
| ~ ( c_in @ D @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( B = A )
| ( c_in @ ( c_Pair @ C @ A @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ D @ B @ A ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ C @ A @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__below_6) ).
thf(1208,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ( C = A )
| ~ ( c_in @ D @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( B = A )
| ( c_in @ ( c_Pair @ C @ A @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ D @ B @ A ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ C @ A @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ D @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(186,axiom,
! [B: $i,A: $i] :
( ( c_Relation_Osym @ A @ B )
| ~ ( c_Relation_Osym @ ( c_Relation_Oconverse @ A @ B @ B ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sym__converse_0) ).
thf(795,plain,
! [B: $i,A: $i] :
( ( c_Relation_Osym @ A @ B )
| ~ ( c_Relation_Osym @ ( c_Relation_Oconverse @ A @ B @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(128,axiom,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Otrancl @ ( c_Relation_Oconverse @ A @ B @ B ) @ B )
= ( c_Relation_Oconverse @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ B @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trancl__converse_0) ).
thf(680,plain,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Otrancl @ ( c_Relation_Oconverse @ A @ B @ B ) @ B )
= ( c_Relation_Oconverse @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ B @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(338,axiom,
! [B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1 @ A @ B ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_complete__Lin_1) ).
thf(1134,plain,
! [B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( v_sko__Arrow__Order__Mirabelle__Xcomplete__Lin__1 @ A @ B ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(112,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ( c_in @ A @ ( c_Relation_ODomain @ D @ C @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Not__Domain__rtrancl_0) ).
thf(648,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ( c_in @ A @ ( c_Relation_ODomain @ D @ C @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(317,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ B @ A @ C @ C ) @ D @ ( tc_prod @ C @ C ) )
| ~ ( c_Relation_Osym @ D @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_symD_0) ).
thf(1081,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ B @ A @ C @ C ) @ D @ ( tc_prod @ C @ C ) )
| ~ ( c_Relation_Osym @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(164,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Orefl__on @ A @ ( c_Relation_Oconverse @ B @ C @ C ) @ C )
| ~ ( c_Relation_Orefl__on @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_refl__on__converse_1) ).
thf(749,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Orefl__on @ A @ ( c_Relation_Oconverse @ B @ C @ C ) @ C )
| ~ ( c_Relation_Orefl__on @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(52,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Product__Type_OSigma @ ( c_Set_Oinsert @ A @ B @ C ) @ ( c_COMBK @ ( c_Set_Oinsert @ D @ E @ F ) @ ( tc_fun @ F @ tc_bool ) @ C ) @ C @ F )
= ( c_Set_Oinsert @ ( c_Pair @ A @ D @ C @ F ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Product__Type_OSigma @ B @ ( c_COMBK @ ( c_Set_Oinsert @ D @ E @ F ) @ ( tc_fun @ F @ tc_bool ) @ C ) @ C @ F ) @ ( c_Product__Type_OSigma @ ( c_Set_Oinsert @ A @ B @ C ) @ ( c_COMBK @ E @ ( tc_fun @ F @ tc_bool ) @ C ) @ C @ F ) @ ( tc_fun @ ( tc_prod @ C @ F ) @ tc_bool ) ) @ ( tc_prod @ C @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__times__insert_0) ).
thf(525,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Product__Type_OSigma @ ( c_Set_Oinsert @ A @ B @ C ) @ ( c_COMBK @ ( c_Set_Oinsert @ D @ E @ F ) @ ( tc_fun @ F @ tc_bool ) @ C ) @ C @ F )
= ( c_Set_Oinsert @ ( c_Pair @ A @ D @ C @ F ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Product__Type_OSigma @ B @ ( c_COMBK @ ( c_Set_Oinsert @ D @ E @ F ) @ ( tc_fun @ F @ tc_bool ) @ C ) @ C @ F ) @ ( c_Product__Type_OSigma @ ( c_Set_Oinsert @ A @ B @ C ) @ ( c_COMBK @ E @ ( tc_fun @ F @ tc_bool ) @ C ) @ C @ F ) @ ( tc_fun @ ( tc_prod @ C @ F ) @ tc_bool ) ) @ ( tc_prod @ C @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(143,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_ORange @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_bool ) ) @ C @ D )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_ORange @ A @ C @ D ) @ ( c_Relation_ORange @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Range__Un__eq_0) ).
thf(705,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_ORange @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_bool ) ) @ C @ D )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_ORange @ A @ C @ D ) @ ( c_Relation_ORange @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(144,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Otrans @ A @ B )
| ~ ( c_Equiv__Relations_Oequiv @ C @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equiv_Otrans_0) ).
thf(707,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Otrans @ A @ B )
| ~ ( c_Equiv__Relations_Oequiv @ C @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(232,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) ) @ C )
| ~ ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ A @ A @ C @ C @ C ) @ ( c_Relation_Orel__comp @ B @ A @ C @ C @ C ) @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) ) @ B @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__union__merge_1) ).
thf(887,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) ) @ C )
| ~ ( c_Wellfounded_Owf @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ A @ A @ C @ C @ C ) @ ( c_Relation_Orel__comp @ B @ A @ C @ C @ C ) @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) ) @ B @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(393,axiom,
c_in @ v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_linear__alt_0) ).
thf(1267,plain,
c_in @ v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1 @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(377,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XRangeE__1__1 @ A @ B @ C @ D ) @ A @ D @ C ) @ B @ ( tc_prod @ D @ C ) )
| ~ ( c_in @ A @ ( c_Relation_ORange @ B @ D @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_RangeE_0) ).
thf(1230,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XRangeE__1__1 @ A @ B @ C @ D ) @ A @ D @ C ) @ B @ ( tc_prod @ D @ C ) )
| ~ ( c_in @ A @ ( c_Relation_ORange @ B @ D @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(323,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_bool ) ) @ D ) @ ( tc_prod @ D @ D ) )
| ~ ( c_in @ A @ ( c_Transitive__Closure_Ortrancl @ B @ D ) @ ( tc_prod @ D @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__rtrancl__UnI_0) ).
thf(1098,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_bool ) ) @ D ) @ ( tc_prod @ D @ D ) )
| ~ ( c_in @ A @ ( c_Transitive__Closure_Ortrancl @ B @ D ) @ ( tc_prod @ D @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(68,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Wellfounded_Oacc @ B @ C ) @ C )
| ~ ( c_in @ ( c_Pair @ A @ D @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ B @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ D @ ( c_Wellfounded_Oacc @ B @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acc__downwards_0) ).
thf(557,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Wellfounded_Oacc @ B @ C ) @ C )
| ~ ( c_in @ ( c_Pair @ A @ D @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ B @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ D @ ( c_Wellfounded_Oacc @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(283,axiom,
! [B: $i,A: $i] : ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ ( c_Relation_OId @ B ) @ ( tc_prod @ B @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_pair__in__Id__conv_1) ).
thf(1003,plain,
! [B: $i,A: $i] : ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ ( c_Relation_OId @ B ) @ ( tc_prod @ B @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(80,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_Orel__comp @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ ( tc_prod @ D @ E ) @ tc_bool ) ) @ F @ D @ E )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ A @ B @ F @ D @ E ) @ ( c_Relation_Orel__comp @ A @ C @ F @ D @ E ) @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__comp__distrib_0) ).
thf(580,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_Orel__comp @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ ( tc_prod @ D @ E ) @ tc_bool ) ) @ F @ D @ E )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_Orel__comp @ A @ B @ F @ D @ E ) @ ( c_Relation_Orel__comp @ A @ C @ F @ D @ E ) @ ( tc_fun @ ( tc_prod @ F @ E ) @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(215,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Wellfounded_Oacc @ B @ C ) @ C )
| ~ ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1 @ B @ A @ C ) @ ( c_Wellfounded_Oacc @ B @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acc_OaccI_1) ).
thf(855,plain,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Wellfounded_Oacc @ B @ C ) @ C )
| ~ ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1 @ B @ A @ C ) @ ( c_Wellfounded_Oacc @ B @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(312,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Relation_ORange @ B @ C @ D ) @ D )
| ~ ( c_in @ ( c_Pair @ E @ A @ C @ D ) @ B @ ( tc_prod @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Range__iff_1) ).
thf(1070,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Relation_ORange @ B @ C @ D ) @ D )
| ~ ( c_in @ ( c_Pair @ E @ A @ C @ D ) @ B @ ( tc_prod @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(224,axiom,
! [B: $i,A: $i] :
( ( c_Relation_OField @ A @ B )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_ODomain @ A @ B @ B ) @ ( c_Relation_ORange @ A @ B @ B ) @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Field__def_0) ).
thf(872,plain,
! [B: $i,A: $i] :
( ( c_Relation_OField @ A @ B )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_ODomain @ A @ B @ B ) @ ( c_Relation_ORange @ A @ B @ B ) @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(263,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Relation_ODomain @ B @ C @ D ) @ C )
| ~ ( c_in @ ( c_Pair @ A @ E @ C @ D ) @ B @ ( tc_prod @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Domain__iff_1) ).
thf(954,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Relation_ODomain @ B @ C @ D ) @ C )
| ~ ( c_in @ ( c_Pair @ A @ E @ C @ D ) @ B @ ( tc_prod @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(386,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ ( c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1 @ A @ B @ C @ D @ E @ F @ G ) @ E @ G ) @ C @ ( tc_prod @ E @ G ) )
| ~ ( c_in @ ( c_Pair @ A @ B @ E @ F ) @ ( c_Relation_Orel__comp @ C @ D @ E @ G @ F ) @ ( tc_prod @ E @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__compEpair_0) ).
thf(1252,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ ( c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1 @ A @ B @ C @ D @ E @ F @ G ) @ E @ G ) @ C @ ( tc_prod @ E @ G ) )
| ~ ( c_in @ ( c_Pair @ A @ B @ E @ F ) @ ( c_Relation_Orel__comp @ C @ D @ E @ G @ F ) @ ( tc_prod @ E @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(407,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ ( c_Relation_OId__on @ C @ B ) @ ( tc_prod @ B @ B ) )
| ~ ( c_in @ A @ C @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Id__on__eqI_0) ).
thf(1300,plain,
! [C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ ( c_Relation_OId__on @ C @ B ) @ ( tc_prod @ B @ B ) )
| ~ ( c_in @ A @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(360,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Relation_OId__on @ D @ C ) @ ( tc_prod @ C @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Id__on__iff_0) ).
thf(1186,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Relation_OId__on @ D @ C ) @ ( tc_prod @ C @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(10,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Set_Oinsert @ A @ B @ C ) @ ( c_Set_Oinsert @ A @ D @ C ) @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ B @ D @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__mono_0) ).
thf(441,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Set_Oinsert @ A @ B @ C ) @ ( c_Set_Oinsert @ A @ D @ C ) @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ B @ D @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(300,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__assoc_0) ).
thf(1038,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(208,axiom,
! [B: $i,A: $i] :
( ( c_lessequals @ ( c_Relation_Orel__comp @ A @ A @ B @ B @ B ) @ A @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) )
| ~ ( c_Relation_Otrans @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__O__subset_0) ).
thf(840,plain,
! [B: $i,A: $i] :
( ( c_lessequals @ ( c_Relation_Orel__comp @ A @ A @ B @ B @ B ) @ A @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) )
| ~ ( c_Relation_Otrans @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(20,axiom,
! [C: $i,B: $i,A: $i] : ( c_in @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insertCI_1) ).
thf(463,plain,
! [C: $i,B: $i,A: $i] : ( c_in @ A @ ( c_Set_Oinsert @ A @ B @ C ) @ C ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(193,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Relation__XImage__iff__1__1 @ A @ B @ C @ D @ E ) @ A @ D )
| ~ ( c_in @ B @ ( c_Relation_OImage @ C @ A @ D @ E ) @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Image__iff_0) ).
thf(808,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Relation__XImage__iff__1__1 @ A @ B @ C @ D @ E ) @ A @ D )
| ~ ( c_in @ B @ ( c_Relation_OImage @ C @ A @ D @ E ) @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(109,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Product__Type_OSigma @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_COMBK @ D @ ( tc_fun @ E @ tc_bool ) @ C ) @ C @ E )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Product__Type_OSigma @ A @ ( c_COMBK @ D @ ( tc_fun @ E @ tc_bool ) @ C ) @ C @ E ) @ ( c_Product__Type_OSigma @ B @ ( c_COMBK @ D @ ( tc_fun @ E @ tc_bool ) @ C ) @ C @ E ) @ ( tc_fun @ ( tc_prod @ C @ E ) @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Times__Int__distrib1_0) ).
thf(643,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Product__Type_OSigma @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_COMBK @ D @ ( tc_fun @ E @ tc_bool ) @ C ) @ C @ E )
= ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Product__Type_OSigma @ A @ ( c_COMBK @ D @ ( tc_fun @ E @ tc_bool ) @ C ) @ C @ E ) @ ( c_Product__Type_OSigma @ B @ ( c_COMBK @ D @ ( tc_fun @ E @ tc_bool ) @ C ) @ C @ E ) @ ( tc_fun @ ( tc_prod @ C @ E ) @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(24,axiom,
! [B: $i,A: $i] : ( c_lessequals @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ ( c_Product__Type_OSigma @ ( c_Relation_OField @ A @ B ) @ ( c_COMBK @ ( c_Relation_OField @ A @ B ) @ ( tc_fun @ B @ tc_bool ) @ B ) @ B @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trancl__subset__Field2_0) ).
thf(470,plain,
! [B: $i,A: $i] : ( c_lessequals @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ ( c_Product__Type_OSigma @ ( c_Relation_OField @ A @ B ) @ ( c_COMBK @ ( c_Relation_OField @ A @ B ) @ ( tc_fun @ B @ tc_bool ) @ B ) @ B @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(78,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Relation_ODomain @ B @ C @ C ) @ C )
| ( c_in @ ( c_Pair @ A @ A @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ B @ C ) @ ( tc_prod @ C @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Not__Domain__rtrancl_1) ).
thf(576,plain,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Relation_ODomain @ B @ C @ C ) @ C )
| ( c_in @ ( c_Pair @ A @ A @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ B @ C ) @ ( tc_prod @ C @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(389,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_bool ) ) @ D ) @ ( tc_prod @ D @ D ) )
| ~ ( c_in @ A @ ( c_Transitive__Closure_Ortrancl @ C @ D ) @ ( tc_prod @ D @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__rtrancl__UnI_1) ).
thf(1257,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Transitive__Closure_Ortrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ C @ ( tc_fun @ ( tc_prod @ D @ D ) @ tc_bool ) ) @ D ) @ ( tc_prod @ D @ D ) )
| ~ ( c_in @ A @ ( c_Transitive__Closure_Ortrancl @ C @ D ) @ ( tc_prod @ D @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(142,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__greatest_0) ).
thf(703,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ A @ B @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(341,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ~ ( c_in @ ( c_Pair @ A @ D @ C @ C ) @ E @ ( tc_prod @ C @ C ) )
| ~ ( c_Relation_Orefl__on @ B @ E @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_refl__onD1_0) ).
thf(1141,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ~ ( c_in @ ( c_Pair @ A @ D @ C @ C ) @ E @ ( tc_prod @ C @ C ) )
| ~ ( c_Relation_Orefl__on @ B @ E @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(96,axiom,
! [B: $i,A: $i] :
( ( ( c_Transitive__Closure_Otrancl @ A @ B )
= A )
| ~ ( c_Relation_Otrans @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trancl__id_0) ).
thf(613,plain,
! [B: $i,A: $i] :
( ( ( c_Transitive__Closure_Otrancl @ A @ B )
= A )
| ~ ( c_Relation_Otrans @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(373,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ C @ D @ E ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( B = E )
| ~ ( c_in @ ( c_Pair @ D @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( A = B )
| ~ ( c_in @ C @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( D = E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__above_10) ).
thf(1221,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ C @ D @ E ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( B = E )
| ~ ( c_in @ ( c_Pair @ D @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( A = B )
| ~ ( c_in @ C @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( D = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(153,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__subset__iff_1) ).
thf(727,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ D @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(273,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ E @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ A @ E @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__trans_0) ).
thf(978,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ E @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ A @ E @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(286,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1 @ A @ B @ C @ D ) @ C @ D @ D ) @ A @ ( tc_prod @ D @ D ) )
| ~ ( c_in @ ( c_Pair @ B @ C @ D @ D ) @ ( c_Transitive__Closure_Otrancl @ A @ D ) @ ( tc_prod @ D @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_tranclD2_1) ).
thf(1008,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1 @ A @ B @ C @ D ) @ C @ D @ D ) @ A @ ( tc_prod @ D @ D ) )
| ~ ( c_in @ ( c_Pair @ B @ C @ D @ D ) @ ( c_Transitive__Closure_Otrancl @ A @ D ) @ ( tc_prod @ D @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(217,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Relation_Orel__comp @ A @ B @ C @ D @ E ) @ ( c_Product__Type_OSigma @ F @ ( c_COMBK @ G @ ( tc_fun @ E @ tc_bool ) @ C ) @ C @ E ) @ ( tc_fun @ ( tc_prod @ C @ E ) @ tc_bool ) )
| ~ ( c_lessequals @ B @ ( c_Product__Type_OSigma @ H @ ( c_COMBK @ G @ ( tc_fun @ E @ tc_bool ) @ D ) @ D @ E ) @ ( tc_fun @ ( tc_prod @ D @ E ) @ tc_bool ) )
| ~ ( c_lessequals @ A @ ( c_Product__Type_OSigma @ F @ ( c_COMBK @ H @ ( tc_fun @ D @ tc_bool ) @ C ) @ C @ D ) @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rel__comp__subset__Sigma_0) ).
thf(859,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Relation_Orel__comp @ A @ B @ C @ D @ E ) @ ( c_Product__Type_OSigma @ F @ ( c_COMBK @ G @ ( tc_fun @ E @ tc_bool ) @ C ) @ C @ E ) @ ( tc_fun @ ( tc_prod @ C @ E ) @ tc_bool ) )
| ~ ( c_lessequals @ B @ ( c_Product__Type_OSigma @ H @ ( c_COMBK @ G @ ( tc_fun @ E @ tc_bool ) @ D ) @ D @ E ) @ ( tc_fun @ ( tc_prod @ D @ E ) @ tc_bool ) )
| ~ ( c_lessequals @ A @ ( c_Product__Type_OSigma @ F @ ( c_COMBK @ H @ ( tc_fun @ D @ tc_bool ) @ C ) @ C @ D ) @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(39,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ B @ C )
!= ( c_Set_Oinsert @ A @ D @ C ) )
| ( c_in @ A @ D @ C )
| ( c_in @ A @ B @ C )
| ( B = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__ident_0) ).
thf(497,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ A @ B @ C )
!= ( c_Set_Oinsert @ A @ D @ C ) )
| ( c_in @ A @ D @ C )
| ( c_in @ A @ B @ C )
| ( B = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(226,axiom,
! [B: $i,A: $i] :
( ( c_Relation_Otrans @ ( c_Relation_Oconverse @ A @ B @ B ) @ B )
| ~ ( c_Relation_Otrans @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__converse_1) ).
thf(876,plain,
! [B: $i,A: $i] :
( ( c_Relation_Otrans @ ( c_Relation_Oconverse @ A @ B @ B ) @ B )
| ~ ( c_Relation_Otrans @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(102,axiom,
! [B: $i,A: $i] :
( ( c_Wellfounded_Owf @ A @ B )
| ~ ( c_Wellfounded_Owf @ ( c_Relation_Orel__comp @ A @ A @ B @ B @ B ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__comp__self_1) ).
thf(627,plain,
! [B: $i,A: $i] :
( ( c_Wellfounded_Owf @ A @ B )
| ~ ( c_Wellfounded_Owf @ ( c_Relation_Orel__comp @ A @ A @ B @ B @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(414,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Arrow__Order__Mirabelle_Oabove @ A @ B @ C ) @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ~ ( c_in @ A @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( B = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_above__Lin_0) ).
thf(1316,plain,
! [C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Arrow__Order__Mirabelle_Oabove @ A @ B @ C ) @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ~ ( c_in @ A @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( B = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(67,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Relation_ODomain @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_bool ) ) @ C @ D ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_ODomain @ A @ C @ D ) @ ( c_Relation_ODomain @ B @ C @ D ) @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Domain__Int__subset_0) ).
thf(556,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( c_lessequals @ ( c_Relation_ODomain @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_bool ) ) @ C @ D ) @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Relation_ODomain @ A @ C @ D ) @ ( c_Relation_ODomain @ B @ C @ D ) @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(31,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Set_Oinsert @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__insert__left_0) ).
thf(482,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Set_Oinsert @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(38,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oimage @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D @ E )
= ( c_Set_Oinsert @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__insert_0) ).
thf(495,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Set_Oimage @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ D @ E )
= ( c_Set_Oinsert @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(169,axiom,
! [B: $i,A: $i] :
( ( c_Wellfounded_Owf @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ B )
| ~ ( c_Wellfounded_Owf @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__trancl_0) ).
thf(759,plain,
! [B: $i,A: $i] :
( ( c_Wellfounded_Owf @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ B )
| ~ ( c_Wellfounded_Owf @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(361,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( A = B )
| ~ ( c_in @ C @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( A = B )
| ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ C @ A @ B ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__above_11) ).
thf(1189,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( A = B )
| ~ ( c_in @ C @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( A = B )
| ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ C @ A @ B ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(287,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ E @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ A @ E @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_r__r__into__trancl_0) ).
thf(1010,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ E @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ A @ E @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(210,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
!= ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) )
| ( c_lessequals @ D @ A @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Int__assoc__eq_0) ).
thf(844,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
!= ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) )
| ( c_lessequals @ D @ A @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(327,axiom,
! [B: $i,A: $i] :
~ ( c_in @ ( c_Pair @ A @ A @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ B @ A ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__mktop_1) ).
thf(1108,plain,
! [B: $i,A: $i] :
~ ( c_in @ ( c_Pair @ A @ A @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ B @ A ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(254,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ( A = B )
| ~ ( c_in @ C @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( A = B )
| ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ C @ A @ B ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__above_5) ).
thf(931,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( c_in @ C @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( A = B )
| ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ C @ A @ B ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(59,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_in @ A @ ( c_Equiv__Relations_Oquotient @ C @ D @ B ) @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_lessequals @ D @ ( c_Product__Type_OSigma @ C @ ( c_COMBK @ C @ ( tc_fun @ B @ tc_bool ) @ B ) @ B @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ C @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__equiv__class_0) ).
thf(539,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_in @ A @ ( c_Equiv__Relations_Oquotient @ C @ D @ B ) @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_lessequals @ D @ ( c_Product__Type_OSigma @ C @ ( c_COMBK @ C @ ( tc_fun @ B @ tc_bool ) @ B ) @ B @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(348,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__commute_0) ).
thf(1157,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Oupper__semilattice__class_Osup @ B @ A @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(416,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ C @ ( tc_prod @ B @ B ) )
| ~ ( c_Wellfounded_Owf @ C @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__irrefl_0) ).
thf(1321,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ C @ ( tc_prod @ B @ B ) )
| ~ ( c_Wellfounded_Owf @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(272,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Transitive__Closure_Otrancl @ B @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ A @ B @ ( tc_prod @ C @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_r__into__trancl_H_0) ).
thf(976,plain,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Transitive__Closure_Otrancl @ B @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ A @ B @ ( tc_prod @ C @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(133,axiom,
! [B: $i,A: $i] : ( c_Relation_Osym @ ( c_Relation_OId__on @ A @ B ) @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sym__Id__on_0) ).
thf(688,plain,
! [B: $i,A: $i] : ( c_Relation_Osym @ ( c_Relation_OId__on @ A @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(266,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Relation_ODomain @ B @ C @ D ) @ C )
| ~ ( c_in @ ( c_Pair @ A @ E @ C @ D ) @ B @ ( tc_prod @ C @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_DomainI_0) ).
thf(961,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Relation_ODomain @ B @ C @ D ) @ C )
| ~ ( c_in @ ( c_Pair @ A @ E @ C @ D ) @ B @ ( tc_prod @ C @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(267,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D )
| ~ ( c_in @ A @ C @ D )
| ~ ( c_in @ A @ B @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_IntI_0) ).
thf(963,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ C @ ( tc_fun @ D @ tc_bool ) ) @ D )
| ~ ( c_in @ A @ C @ D )
| ~ ( c_in @ A @ B @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(237,axiom,
! [B: $i,A: $i] :
( ( c_Relation_Otrans @ A @ B )
| ~ ( c_Relation_Otrans @ ( c_Relation_Oconverse @ A @ B @ B ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__converse_0) ).
thf(896,plain,
! [B: $i,A: $i] :
( ( c_Relation_Otrans @ A @ B )
| ~ ( c_Relation_Otrans @ ( c_Relation_Oconverse @ A @ B @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(383,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ~ ( c_in @ ( c_Pair @ D @ A @ C @ C ) @ E @ ( tc_prod @ C @ C ) )
| ~ ( c_Equiv__Relations_Oequiv @ B @ E @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equiv__class__eq__iff_2) ).
thf(1244,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ~ ( c_in @ ( c_Pair @ D @ A @ C @ C ) @ E @ ( tc_prod @ C @ C ) )
| ~ ( c_Equiv__Relations_Oequiv @ B @ E @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(155,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Orefl__on @ A @ B @ C )
| ~ ( c_Equiv__Relations_Oequiv @ A @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_equiv_Orefl__on_0) ).
thf(731,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Orefl__on @ A @ B @ C )
| ~ ( c_Equiv__Relations_Oequiv @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(180,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ ( c_Product__Type_OSigma @ E @ F @ C @ D ) @ ( tc_prod @ C @ D ) )
| ~ ( c_in @ B @ ( hAPP @ F @ A ) @ D )
| ~ ( c_in @ A @ E @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mem__Sigma__iff_2) ).
thf(781,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ ( c_Product__Type_OSigma @ E @ F @ C @ D ) @ ( tc_prod @ C @ D ) )
| ~ ( c_in @ B @ ( hAPP @ F @ A ) @ D )
| ~ ( c_in @ A @ E @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(84,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 @ A @ B @ C ) @ A @ C )
| ~ ( c_in @ D @ A @ C )
| ~ ( c_Wellfounded_Owf @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wfE__min_0) ).
thf(588,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 @ A @ B @ C ) @ A @ C )
| ~ ( c_in @ D @ A @ C )
| ~ ( c_Wellfounded_Owf @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(140,axiom,
! [B: $i,A: $i] :
( ( c_Wellfounded_Owf @ A @ B )
| ~ ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1 @ A @ B ) @ ( c_Wellfounded_Oacc @ A @ B ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_acc__wfI_0) ).
thf(699,plain,
! [B: $i,A: $i] :
( ( c_Wellfounded_Owf @ A @ B )
| ~ ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1 @ A @ B ) @ ( c_Wellfounded_Oacc @ A @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(296,axiom,
! [B: $i,A: $i] :
( ( c_Nitpick_Orefl_H @ A @ B )
| ~ ( c_in @ ( c_Pair @ ( c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1 @ A @ B ) @ ( c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1 @ A @ B ) @ B @ B ) @ A @ ( tc_prod @ B @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nitpick_Orefl_H__def_1) ).
thf(1030,plain,
! [B: $i,A: $i] :
( ( c_Nitpick_Orefl_H @ A @ B )
| ~ ( c_in @ ( c_Pair @ ( c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1 @ A @ B ) @ ( c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1 @ A @ B ) @ B @ B ) @ A @ ( tc_prod @ B @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(45,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Wellfounded_Owf @ ( c_Relation_Oinv__image @ A @ B @ C @ D ) @ D )
| ~ ( c_Wellfounded_Owf @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_wf__inv__image_0) ).
thf(510,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Wellfounded_Owf @ ( c_Relation_Oinv__image @ A @ B @ C @ D ) @ D )
| ~ ( c_Wellfounded_Owf @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(253,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Product__Type_OSigma @ A @ ( c_COMBK @ D @ ( tc_fun @ E @ tc_bool ) @ C ) @ C @ E ) @ ( c_Product__Type_OSigma @ B @ ( c_COMBK @ D @ ( tc_fun @ E @ tc_bool ) @ C ) @ C @ E ) @ ( tc_fun @ ( tc_prod @ C @ E ) @ tc_bool ) )
| ~ ( c_in @ F @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Times__subset__cancel2_0) ).
thf(929,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Product__Type_OSigma @ A @ ( c_COMBK @ D @ ( tc_fun @ E @ tc_bool ) @ C ) @ C @ E ) @ ( c_Product__Type_OSigma @ B @ ( c_COMBK @ D @ ( tc_fun @ E @ tc_bool ) @ C ) @ C @ E ) @ ( tc_fun @ ( tc_prod @ C @ E ) @ tc_bool ) )
| ~ ( c_in @ F @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(410,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_ATP__Linkup_Osko__Complete__Lattice__XUnionE__1__1 @ A @ B @ C ) @ C )
| ~ ( c_in @ A @ ( c_Complete__Lattice_OSup__class_OSup @ B @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_UnionE_0) ).
thf(1308,plain,
! [C: $i,B: $i,A: $i] :
( ( c_in @ A @ ( c_ATP__Linkup_Osko__Complete__Lattice__XUnionE__1__1 @ A @ B @ C ) @ C )
| ~ ( c_in @ A @ ( c_Complete__Lattice_OSup__class_OSup @ B @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(362,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ C @ D @ B ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ C @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( D = B )
| ( c_in @ ( c_Pair @ A @ D @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( A = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__above_2) ).
thf(1193,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ C @ D @ B ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ C @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( D = B )
| ( c_in @ ( c_Pair @ A @ D @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( A = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(29,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Set_Oinsert @ A @ B @ C ) @ C )
| ~ ( c_Finite__Set_Ofinite @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__insert_1) ).
thf(478,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Set_Oinsert @ A @ B @ C ) @ C )
| ~ ( c_Finite__Set_Ofinite @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(368,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XRange__iff__1__1 @ A @ B @ C @ D ) @ A @ D @ C ) @ B @ ( tc_prod @ D @ C ) )
| ~ ( c_in @ A @ ( c_Relation_ORange @ B @ D @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Range__iff_0) ).
thf(1212,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__XRange__iff__1__1 @ A @ B @ C @ D ) @ A @ D @ C ) @ B @ ( tc_prod @ D @ C ) )
| ~ ( c_in @ A @ ( c_Relation_ORange @ B @ D @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(171,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Product__Type_OSigma @ A @ ( c_COMBK @ B @ ( tc_fun @ C @ tc_bool ) @ D ) @ D @ C ) @ ( c_Product__Type_OSigma @ E @ ( c_COMBK @ B @ ( tc_fun @ C @ tc_bool ) @ D ) @ D @ C ) @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_bool ) )
| ~ ( c_lessequals @ A @ E @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_in @ F @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Times__subset__cancel2_1) ).
thf(763,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Product__Type_OSigma @ A @ ( c_COMBK @ B @ ( tc_fun @ C @ tc_bool ) @ D ) @ D @ C ) @ ( c_Product__Type_OSigma @ E @ ( c_COMBK @ B @ ( tc_fun @ C @ tc_bool ) @ D ) @ D @ C ) @ ( tc_fun @ ( tc_prod @ D @ C ) @ tc_bool ) )
| ~ ( c_lessequals @ A @ E @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_in @ F @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(205,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__eq__or__trancl_2) ).
thf(832,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(130,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Product__Type_OSigma @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ C @ E )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Product__Type_OSigma @ A @ D @ C @ E ) @ ( c_Product__Type_OSigma @ B @ D @ C @ E ) @ ( tc_fun @ ( tc_prod @ C @ E ) @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Sigma__Un__distrib1_0) ).
thf(684,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Product__Type_OSigma @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ C @ E )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Product__Type_OSigma @ A @ D @ C @ E ) @ ( c_Product__Type_OSigma @ B @ D @ C @ E ) @ ( tc_fun @ ( tc_prod @ C @ E ) @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(13,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Orefl__on @ A @ B @ C )
| ( c_in @ ( c_ATP__Linkup_Osko__Relation__Xrefl__on__def__1__1 @ A @ B @ C ) @ A @ C )
| ~ ( c_lessequals @ B @ ( c_Product__Type_OSigma @ A @ ( c_COMBK @ A @ ( tc_fun @ C @ tc_bool ) @ C ) @ C @ C ) @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_refl__on__def_2) ).
thf(447,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Orefl__on @ A @ B @ C )
| ( c_in @ ( c_ATP__Linkup_Osko__Relation__Xrefl__on__def__1__1 @ A @ B @ C ) @ A @ C )
| ~ ( c_lessequals @ B @ ( c_Product__Type_OSigma @ A @ ( c_COMBK @ A @ ( tc_fun @ C @ tc_bool ) @ C ) @ C @ C ) @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(6,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ( c_lessequals @ ( c_Set_Oimage @ D @ A @ C @ E ) @ ( c_Set_Oimage @ D @ B @ C @ E ) @ ( tc_fun @ E @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__image__iff_2) ).
thf(432,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ( c_lessequals @ ( c_Set_Oimage @ D @ A @ C @ E ) @ ( c_Set_Oimage @ D @ B @ C @ E ) @ ( tc_fun @ E @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(269,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ C @ D @ E ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ A @ D @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ D @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( A = B )
| ~ ( c_in @ C @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( D = E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__above_14) ).
thf(967,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ C @ D @ E ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ A @ D @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ D @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( A = B )
| ~ ( c_in @ C @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( D = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(198,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Transitive__Closure_Ortrancl @ A @ B )
= ( c_Transitive__Closure_Ortrancl @ C @ B ) )
| ~ ( c_lessequals @ A @ ( c_Transitive__Closure_Ortrancl @ C @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) )
| ~ ( c_lessequals @ C @ A @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__subset_0) ).
thf(818,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Transitive__Closure_Ortrancl @ A @ B )
= ( c_Transitive__Closure_Ortrancl @ C @ B ) )
| ~ ( c_lessequals @ A @ ( c_Transitive__Closure_Ortrancl @ C @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) )
| ~ ( c_lessequals @ C @ A @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(2,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E )
= ( c_Set_Oimage @ A @ C @ D @ E ) )
| ~ ( c_in @ B @ C @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__image_0) ).
thf(422,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Set_Oinsert @ ( hAPP @ A @ B ) @ ( c_Set_Oimage @ A @ C @ D @ E ) @ E )
= ( c_Set_Oimage @ A @ C @ D @ E ) )
| ~ ( c_in @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(220,axiom,
! [B: $i,A: $i] : ( c_Relation_Osym @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Relation_Oconverse @ A @ B @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sym__Int__converse_0) ).
thf(865,plain,
! [B: $i,A: $i] : ( c_Relation_Osym @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Relation_Oconverse @ A @ B @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(91,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_lessequals @ A @ ( c_Set_Oimage @ C @ D @ E @ B ) @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ D @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__surj_0) ).
thf(603,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_lessequals @ A @ ( c_Set_Oimage @ C @ D @ E @ B ) @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ D @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(157,axiom,
! [B: $i,A: $i] : ( c_Relation_Otrans @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__trancl_0) ).
thf(735,plain,
! [B: $i,A: $i] : ( c_Relation_Otrans @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(261,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1 @ B @ A @ C @ D ) @ D @ D ) @ B @ ( tc_prod @ D @ D ) )
| ~ ( c_in @ ( c_Pair @ A @ C @ D @ D ) @ ( c_Transitive__Closure_Otrancl @ B @ D ) @ ( tc_prod @ D @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_tranclD_0) ).
thf(950,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1 @ B @ A @ C @ D ) @ D @ D ) @ B @ ( tc_prod @ D @ D ) )
| ~ ( c_in @ ( c_Pair @ A @ C @ D @ D ) @ ( c_Transitive__Closure_Otrancl @ B @ D ) @ ( tc_prod @ D @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(206,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) )
| ~ ( c_lessequals @ D @ A @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__Int__assoc__eq_1) ).
thf(835,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Lattices_Olower__semilattice__class_Oinf @ A @ ( c_Lattices_Oupper__semilattice__class_Osup @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) ) )
| ~ ( c_lessequals @ D @ A @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(72,axiom,
! [A: $i] : ( c_Relation_Otrans @ ( c_Relation_OId @ A ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trans__Id_0) ).
thf(564,plain,
! [A: $i] : ( c_Relation_Otrans @ ( c_Relation_OId @ A ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(189,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ C @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Relation_Orel__comp @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ C @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ A @ B @ B @ B ) @ C @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Relation_OId @ B ) @ C @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__Int__subset_0) ).
thf(801,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ C @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Relation_Orel__comp @ ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ C @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ A @ B @ B @ B ) @ C @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Relation_OId @ B ) @ C @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(43,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_subset__insertI2_0) ).
thf(506,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ D @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(192,axiom,
! [A: $i] : ( c_Relation_Osym @ ( c_Relation_OId @ A ) @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sym__Id_0) ).
thf(807,plain,
! [A: $i] : ( c_Relation_Osym @ ( c_Relation_OId @ A ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(8,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( c_in @ ( hAPP @ D @ A ) @ ( c_Set_Oimage @ D @ B @ C @ E ) @ E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__image__eqI_0) ).
thf(437,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ A @ B @ C )
| ( c_in @ ( hAPP @ D @ A ) @ ( c_Set_Oimage @ D @ B @ C @ E ) @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(27,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Set_Oimage @ A @ B @ C @ D ) @ ( c_Set_Oimage @ A @ E @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ B @ E @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_image__mono_0) ).
thf(474,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Set_Oimage @ A @ B @ C @ D ) @ ( c_Set_Oimage @ A @ E @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ B @ E @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(401,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ~ ( c_in @ ( c_Pair @ A @ D @ C @ E ) @ ( c_Product__Type_OSigma @ B @ F @ C @ E ) @ ( tc_prod @ C @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SigmaD1_0) ).
thf(1288,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ A @ B @ C )
| ~ ( c_in @ ( c_Pair @ A @ D @ C @ E ) @ ( c_Product__Type_OSigma @ B @ F @ C @ E ) @ ( tc_prod @ C @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(203,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Complete__Lattice_OSup__class_OSup @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_in @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Union__upper_0) ).
thf(828,plain,
! [C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ ( c_Complete__Lattice_OSup__class_OSup @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_in @ A @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(56,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Set_Oinsert @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ C ) )
| ~ ( c_in @ A @ D @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__insert__left_0) ).
thf(532,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
= ( c_Set_Oinsert @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ C ) )
| ~ ( c_in @ A @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(138,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ C )
| ~ ( c_Finite__Set_Ofinite @ B @ C )
| ~ ( c_Finite__Set_Ofinite @ A @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__UnI_0) ).
thf(696,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ C )
| ~ ( c_Finite__Set_Ofinite @ B @ C )
| ~ ( c_Finite__Set_Ofinite @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(150,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) )
= B )
| ~ ( c_lessequals @ B @ A @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Int__absorb1_0) ).
thf(720,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c_Lattices_Olower__semilattice__class_Oinf @ A @ B @ ( tc_fun @ C @ tc_bool ) )
= B )
| ~ ( c_lessequals @ B @ A @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(231,axiom,
! [B: $i,A: $i] : ( c_lessequals @ ( c_Relation_OId__on @ A @ B ) @ ( c_Product__Type_OSigma @ A @ ( c_COMBK @ A @ ( tc_fun @ B @ tc_bool ) @ B ) @ B @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Id__on__subset__Times_0) ).
thf(886,plain,
! [B: $i,A: $i] : ( c_lessequals @ ( c_Relation_OId__on @ A @ B ) @ ( c_Product__Type_OSigma @ A @ ( c_COMBK @ A @ ( tc_fun @ B @ tc_bool ) @ B ) @ B @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(307,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( D = B )
| ~ ( c_in @ C @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( A = D )
| ( c_in @ ( c_Pair @ D @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ C @ A @ D ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__above_9) ).
thf(1056,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( D = B )
| ~ ( c_in @ C @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( A = D )
| ( c_in @ ( c_Pair @ D @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ C @ A @ D ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(120,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_Finite__Set_Ofinite @ C @ B )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__subset_0) ).
thf(664,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_Finite__Set_Ofinite @ C @ B )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(321,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ( A = B )
| ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ C @ B ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__mktop_4) ).
thf(1093,plain,
! [C: $i,B: $i,A: $i] :
( ( A = B )
| ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Omktop @ C @ B ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(380,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ A @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ B @ C @ D ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ B @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( C = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__above_0) ).
thf(1236,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ A @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Oabove @ B @ C @ D ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ B @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( C = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(21,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Set_Oinsert @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Un__insert__right_0) ).
thf(464,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Set_Oinsert @ B @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
= ( c_Set_Oinsert @ B @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ C @ ( tc_fun @ D @ tc_bool ) ) @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(336,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ ( c_Relation_Oconverse @ E @ D @ C ) @ ( tc_prod @ C @ D ) )
| ~ ( c_in @ ( c_Pair @ B @ A @ D @ C ) @ E @ ( tc_prod @ D @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_converse__iff_1) ).
thf(1129,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ D ) @ ( c_Relation_Oconverse @ E @ D @ C ) @ ( tc_prod @ C @ D ) )
| ~ ( c_in @ ( c_Pair @ B @ A @ D @ C ) @ E @ ( tc_prod @ D @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(391,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( A = B )
| ~ ( c_in @ C @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( D = B )
| ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ C @ D @ B ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__below_12) ).
thf(1261,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( A = B )
| ~ ( c_in @ C @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( D = B )
| ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ C @ D @ B ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(394,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Complete__Lattice_OInf__class_OInf @ A @ ( tc_fun @ B @ tc_bool ) ) @ B )
| ~ ( c_Finite__Set_Ofinite @ C @ B )
| ~ ( c_in @ C @ A @ ( tc_fun @ B @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_finite__Inter_0) ).
thf(1268,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ ( c_Complete__Lattice_OInf__class_OInf @ A @ ( tc_fun @ B @ tc_bool ) ) @ B )
| ~ ( c_Finite__Set_Ofinite @ C @ B )
| ~ ( c_in @ C @ A @ ( tc_fun @ B @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(88,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1 @ A @ B @ C ) @ ( c_Wellfounded_Oacc @ A @ C ) @ C )
| ( c_in @ B @ ( c_Wellfounded_Oacc @ A @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_not__acc__down_1) ).
thf(596,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( c_in @ ( c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1 @ A @ B @ C ) @ ( c_Wellfounded_Oacc @ A @ C ) @ C )
| ( c_in @ B @ ( c_Wellfounded_Oacc @ A @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(18,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ A @ B @ C ) @ ( c_Set_Oinsert @ A @ D @ C ) @ ( tc_fun @ C @ tc_bool ) )
= ( c_Set_Oinsert @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__inter__insert_0) ).
thf(459,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_Lattices_Olower__semilattice__class_Oinf @ ( c_Set_Oinsert @ A @ B @ C ) @ ( c_Set_Oinsert @ A @ D @ C ) @ ( tc_fun @ C @ tc_bool ) )
= ( c_Set_Oinsert @ A @ ( c_Lattices_Olower__semilattice__class_Oinf @ B @ D @ ( tc_fun @ C @ tc_bool ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(151,axiom,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Otrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Relation_OId @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ B )
= ( c_Transitive__Closure_Ortrancl @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trancl__reflcl_0) ).
thf(723,plain,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Otrancl @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ ( c_Relation_OId @ B ) @ ( tc_fun @ ( tc_prod @ B @ B ) @ tc_bool ) ) @ B )
= ( c_Transitive__Closure_Ortrancl @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(135,axiom,
! [B: $i,A: $i] :
( ( c_Relation_ODomain @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ B @ B )
= ( c_Relation_ODomain @ A @ B @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trancl__domain_0) ).
thf(691,plain,
! [B: $i,A: $i] :
( ( c_Relation_ODomain @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ B @ B )
= ( c_Relation_ODomain @ A @ B @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(332,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( c_in @ ( c_Pair @ B @ A @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ C @ B @ D ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ C @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( B = D )
| ( c_in @ ( c_Pair @ D @ A @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( A = D ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__below_2) ).
thf(1120,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( c_in @ ( c_Pair @ B @ A @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ C @ B @ D ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ C @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( B = D )
| ( c_in @ ( c_Pair @ D @ A @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( A = D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(93,axiom,
! [A: $i] :
( ( c_Relation_Oconverse @ ( c_Relation_OId @ A ) @ A @ A )
= ( c_Relation_OId @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_converse__Id_0) ).
thf(607,plain,
! [A: $i] :
( ( c_Relation_Oconverse @ ( c_Relation_OId @ A ) @ A @ A )
= ( c_Relation_OId @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(243,axiom,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Otrancl @ A @ B )
= ( c_Relation_Orel__comp @ A @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ B @ B @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trancl__unfold__left_0) ).
thf(908,plain,
! [B: $i,A: $i] :
( ( c_Transitive__Closure_Otrancl @ A @ B )
= ( c_Relation_Orel__comp @ A @ ( c_Transitive__Closure_Ortrancl @ A @ B ) @ B @ B @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(279,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ C @ ( tc_prod @ B @ B ) )
| ~ ( c_Nitpick_Orefl_H @ C @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Nitpick_Orefl_H__def_0) ).
thf(992,plain,
! [C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ C @ ( tc_prod @ B @ B ) )
| ~ ( c_Nitpick_Orefl_H @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(275,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( A = D )
| ( B = D )
| ~ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ C @ D @ E ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ C @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( D = E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_in__below_3) ).
thf(982,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ C @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ( A = D )
| ( B = D )
| ~ ( c_in @ ( c_Pair @ A @ B @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ ( c_Arrow__Order__Mirabelle_Obelow @ C @ D @ E ) @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) )
| ~ ( c_in @ C @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ( D = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(284,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ C @ ( tc_prod @ B @ B ) )
| ~ ( c_in @ A @ D @ B )
| ~ ( c_Relation_Orefl__on @ D @ C @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_refl__onD_0) ).
thf(1004,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ A @ B @ B ) @ C @ ( tc_prod @ B @ B ) )
| ~ ( c_in @ A @ D @ B )
| ~ ( c_Relation_Orefl__on @ D @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(33,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Set_Oinsert @ D @ A @ C ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__subset_1) ).
thf(486,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ A @ B @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ ( c_Set_Oinsert @ D @ A @ C ) @ B @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(190,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Ototal__on @ A @ B @ C )
| ~ ( c_Relation_Ototal__on @ A @ ( c_Relation_Oconverse @ B @ C @ C ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_total__on__converse_0) ).
thf(803,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Ototal__on @ A @ B @ C )
| ~ ( c_Relation_Ototal__on @ A @ ( c_Relation_Oconverse @ B @ C @ C ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(257,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Recdef_Ocut @ A @ B @ C @ D @ E )
= ( c_Recdef_Ocut @ F @ B @ C @ D @ E ) )
| ( c_in @ ( c_Pair @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ A @ F @ B @ C @ D @ E ) @ C @ D @ D ) @ B @ ( tc_prod @ D @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_cuts__eq_1) ).
thf(940,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Recdef_Ocut @ A @ B @ C @ D @ E )
= ( c_Recdef_Ocut @ F @ B @ C @ D @ E ) )
| ( c_in @ ( c_Pair @ ( c_List_Osko__Recdef__Xcuts__eq__1__1 @ A @ F @ B @ C @ D @ E ) @ C @ D @ D ) @ B @ ( tc_prod @ D @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(255,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ B @ A @ C @ C ) @ D @ ( tc_prod @ C @ C ) )
| ~ ( c_Relation_Osym @ D @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_sym__def_0) ).
thf(935,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ D @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ B @ A @ C @ C ) @ D @ ( tc_prod @ C @ C ) )
| ~ ( c_Relation_Osym @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(250,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_OField @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) ) @ C )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_OField @ A @ C ) @ ( c_Relation_OField @ B @ C ) @ ( tc_fun @ C @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Field__Un_0) ).
thf(923,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_OField @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) ) @ C )
= ( c_Lattices_Oupper__semilattice__class_Osup @ ( c_Relation_OField @ A @ C ) @ ( c_Relation_OField @ B @ C ) @ ( tc_fun @ C @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(117,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_Orefl__on @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ E @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) ) @ C )
| ~ ( c_Relation_Orefl__on @ B @ E @ C )
| ~ ( c_Relation_Orefl__on @ A @ D @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_refl__on__Un_0) ).
thf(659,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_Relation_Orefl__on @ ( c_Lattices_Oupper__semilattice__class_Osup @ A @ B @ ( tc_fun @ C @ tc_bool ) ) @ ( c_Lattices_Oupper__semilattice__class_Osup @ D @ E @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) ) @ C )
| ~ ( c_Relation_Orefl__on @ B @ E @ C )
| ~ ( c_Relation_Orefl__on @ A @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(61,axiom,
! [B: $i,A: $i] :
( ( ( c_Relation_Orel__comp @ ( c_Relation_Oconverse @ A @ B @ B ) @ A @ B @ B @ B )
!= A )
| ( c_Equiv__Relations_Oequiv @ ( c_Relation_ODomain @ A @ B @ B ) @ A @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_comp__equivI_0) ).
thf(543,plain,
! [B: $i,A: $i] :
( ( ( c_Relation_Orel__comp @ ( c_Relation_Oconverse @ A @ B @ B ) @ A @ B @ B @ B )
!= A )
| ( c_Equiv__Relations_Oequiv @ ( c_Relation_ODomain @ A @ B @ B ) @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(107,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Orefl__on @ A @ B @ C )
| ~ ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__Xrefl__onI__1__1 @ A @ B @ C ) @ ( c_ATP__Linkup_Osko__Relation__Xrefl__onI__1__1 @ A @ B @ C ) @ C @ C ) @ B @ ( tc_prod @ C @ C ) )
| ~ ( c_lessequals @ B @ ( c_Product__Type_OSigma @ A @ ( c_COMBK @ A @ ( tc_fun @ C @ tc_bool ) @ C ) @ C @ C ) @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_refl__onI_1) ).
thf(639,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Relation_Orefl__on @ A @ B @ C )
| ~ ( c_in @ ( c_Pair @ ( c_ATP__Linkup_Osko__Relation__Xrefl__onI__1__1 @ A @ B @ C ) @ ( c_ATP__Linkup_Osko__Relation__Xrefl__onI__1__1 @ A @ B @ C ) @ C @ C ) @ B @ ( tc_prod @ C @ C ) )
| ~ ( c_lessequals @ B @ ( c_Product__Type_OSigma @ A @ ( c_COMBK @ A @ ( tc_fun @ C @ tc_bool ) @ C ) @ C @ C ) @ ( tc_fun @ ( tc_prod @ C @ C ) @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(36,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ B @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_in @ A @ D @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_insert__subset_2) ).
thf(491,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Set_Oinsert @ A @ B @ C ) @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ B @ D @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_in @ A @ D @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(86,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Relation_OImage @ A @ B @ C @ D ) @ ( c_Relation_OImage @ E @ F @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ B @ F @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ E @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Image__mono_0) ).
thf(592,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_lessequals @ ( c_Relation_OImage @ A @ B @ C @ D ) @ ( c_Relation_OImage @ E @ F @ C @ D ) @ ( tc_fun @ D @ tc_bool ) )
| ~ ( c_lessequals @ B @ F @ ( tc_fun @ C @ tc_bool ) )
| ~ ( c_lessequals @ A @ E @ ( tc_fun @ ( tc_prod @ C @ D ) @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(16,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Product__Type_OSigma @ A @ ( c_COMBK @ B @ ( tc_fun @ C @ tc_bool ) @ D ) @ D @ C )
!= ( c_Product__Type_OSigma @ E @ ( c_COMBK @ B @ ( tc_fun @ C @ tc_bool ) @ D ) @ D @ C ) )
| ~ ( c_in @ F @ B @ C )
| ( A = E ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Times__eq__cancel2_0) ).
thf(454,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( c_Product__Type_OSigma @ A @ ( c_COMBK @ B @ ( tc_fun @ C @ tc_bool ) @ D ) @ D @ C )
!= ( c_Product__Type_OSigma @ E @ ( c_COMBK @ B @ ( tc_fun @ C @ tc_bool ) @ D ) @ D @ C ) )
| ~ ( c_in @ F @ B @ C )
| ( A = E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(229,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1 @ B @ A @ C @ D ) @ D @ D ) @ ( c_Transitive__Closure_Ortrancl @ B @ D ) @ ( tc_prod @ D @ D ) )
| ~ ( c_in @ ( c_Pair @ A @ C @ D @ D ) @ ( c_Transitive__Closure_Otrancl @ B @ D ) @ ( tc_prod @ D @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_tranclD2_0) ).
thf(882,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ ( c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1 @ B @ A @ C @ D ) @ D @ D ) @ ( c_Transitive__Closure_Ortrancl @ B @ D ) @ ( tc_prod @ D @ D ) )
| ~ ( c_in @ ( c_Pair @ A @ C @ D @ D ) @ ( c_Transitive__Closure_Otrancl @ B @ D ) @ ( tc_prod @ D @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(289,axiom,
! [B: $i,A: $i] :
( ( c_in @ ( c_Arrow__Order__Mirabelle_Omkbot @ A @ B ) @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ~ ( c_in @ A @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_mkbot__Lin_0) ).
thf(1014,plain,
! [B: $i,A: $i] :
( ( c_in @ ( c_Arrow__Order__Mirabelle_Omkbot @ A @ B ) @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) )
| ~ ( c_in @ A @ c_Arrow__Order__Mirabelle_OLin @ ( tc_fun @ ( tc_prod @ tc_Arrow__Order__Mirabelle_Oalt @ tc_Arrow__Order__Mirabelle_Oalt ) @ tc_bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(177,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ E @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ A @ E @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__into__trancl2_0) ).
thf(775,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Otrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ E @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ A @ E @ C @ C ) @ D @ ( tc_prod @ C @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(70,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ B @ A @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ ( c_Relation_Oconverse @ D @ C @ C ) @ C ) @ ( tc_prod @ C @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rtrancl__converseD_0) ).
thf(560,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( c_in @ ( c_Pair @ A @ B @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ D @ C ) @ ( tc_prod @ C @ C ) )
| ~ ( c_in @ ( c_Pair @ B @ A @ C @ C ) @ ( c_Transitive__Closure_Ortrancl @ ( c_Relation_Oconverse @ D @ C @ C ) @ C ) @ ( tc_prod @ C @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(167,axiom,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ C @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_rev__finite__subset_0) ).
thf(755,plain,
! [C: $i,B: $i,A: $i] :
( ( c_Finite__Set_Ofinite @ A @ B )
| ~ ( c_lessequals @ A @ C @ ( tc_fun @ B @ tc_bool ) )
| ~ ( c_Finite__Set_Ofinite @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(126,axiom,
! [B: $i,A: $i] :
( ( c_Relation_ORange @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ B @ B )
= ( c_Relation_ORange @ A @ B @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_trancl__range_0) ).
thf(676,plain,
! [B: $i,A: $i] :
( ( c_Relation_ORange @ ( c_Transitive__Closure_Otrancl @ A @ B ) @ B @ B )
= ( c_Relation_ORange @ A @ B @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(1329,plain,
$false,
inference(e,[status(thm)],[1036,629,1024,518,1179,777,1110,645,892,1083,468,666,1295,582,1290,1068,994,741,861,1173,1205,449,878,655,1137,1310,550,500,715,472,698,747,945,670,1164,797,814,1327,1196,898,1127,709,973,565,1265,651,1228,1254,1298,785,1059,1323,838,917,751,1313,1279,902,559,853,1115,1100,1232,1319,870,1302,789,443,1040,623,646,514,574,1183,480,1151,937,1051,821,766,956,866,1072,988,428,527,1169,687,1215,634,1242,849,1074,678,529,661,546,925,1306,1199,810,1047,512,439,1153,761,1274,910,894,1021,952,1123,693,729,1217,598,1032,625,889,493,1079,757,682,1291,842,1012,1106,847,484,522,830,1159,461,578,1234,948,1064,725,980,1096,1006,857,874,1143,1270,1259,783,420,471,884,1028,488,537,637,1214,970,1155,554,753,686,476,1016,590,997,985,701,1249,738,1131,457,569,1246,779,503,605,792,1086,805,508,921,541,657,1286,674,586,765,1054,1026,1167,662,718,906,965,618,425,1103,745,689,733,601,1146,430,1219,824,584,1125,772,743,562,904,826,711,1256,1226,641,1139,445,572,1312,713,1239,466,1090,919,1224,672,611,787,900,1282,1117,736,990,616,451,567,880,434,863,1175,890,631,552,535,816,609,594,621,520,1325,1149,915,769,943,1061,799,1162,1293,668,959,768,868,1113,1000,851,505,653,912,1171,1044,695,1076,1034,490,1166,531,548,927,1277,812,516,1018,823,1049,1203,1208,795,680,1134,648,1081,749,525,705,707,887,1267,1230,1098,557,1003,580,855,1070,872,954,1252,1300,1186,441,1038,840,463,808,643,470,576,1257,703,1141,613,1221,727,978,1008,859,497,876,627,1316,556,482,495,759,1189,1010,844,1108,931,539,1157,1321,976,688,961,963,896,1244,731,781,588,699,1030,510,929,1308,1193,478,1212,763,832,684,447,432,967,818,422,865,603,735,950,835,564,801,506,807,437,474,1288,828,532,696,720,886,1056,664,1093,1236,464,1129,1261,1268,596,459,723,691,1120,607,908,992,982,1004,486,803,940,935,923,659,543,639,491,592,454,882,1014,775,560,755,676]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.11 % Problem : SCT073-1 : TPTP v8.1.2. Released v4.1.0.
% 0.04/0.14 % Command : run_Leo-III %s %d
% 0.14/0.34 % Computer : n003.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Thu May 18 15:34:01 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.93/0.85 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.60/1.07 % [INFO] Parsing done (224ms).
% 1.60/1.08 % [INFO] Running in sequential loop mode.
% 2.20/1.30 % [INFO] eprover registered as external prover.
% 2.20/1.30 % [INFO] cvc4 registered as external prover.
% 2.20/1.30 % [INFO] Scanning for conjecture ...
% 2.57/1.43 % [INFO] Found a conjecture and 548 axioms. Running axiom selection ...
% 3.30/1.56 % [INFO] Axiom selection finished. Selected 418 axioms (removed 130 axioms).
% 3.75/1.74 % [INFO] Problem is propositional (TPTP CNF).
% 3.75/1.75 % [INFO] Type checking passed.
% 3.75/1.76 % [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 ...
% 10.06/3.20 % External prover 'e' found a proof!
% 10.06/3.20 % [INFO] Killing All external provers ...
% 10.06/3.20 % Time passed: 2703ms (effective reasoning time: 2120ms)
% 10.06/3.20 % 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)>
% 10.06/3.21 % Axioms used in derivation (418): cls_trancl__converseD_0, cls_in__mktop_1, cls_subset__insert_1, cls_rtrancl__idemp_0, cls_Inter__lower_0, cls_sym__conv__converse__eq_1, cls_cuts__eq_1, cls_Int__Un__distrib_0, cls_Range__Un__eq_0, cls_converse__tranclE_1, cls_wfI_3, cls_Int__absorb2_0, cls_sym__Int__converse_0, cls_in__above_11, cls_insertE_0, cls_Un__subset__iff_0, cls_wf__subset_0, cls_insert__inter__insert_0, cls_rtrancl__converseD_0, cls_in__below_14, cls_total__on__def_0, cls_converseI_0, cls_InterI_1, cls_equalityI_0, cls_Id__onE_0, cls_subset__image__iff_2, cls_trancl__subset__Sigma__aux_0, cls_finite__insert_0, cls_wfE__min_0, cls_image__mono_0, cls_tranclD2_0, cls_Int__mono_0, cls_Un__commute_0, cls_finite__Un_2, cls_COMBK__def_0, cls_acc__wfD_0, cls_in__below_3, cls_Id__O__R_0, cls_mkbot__Lin_0, cls_CHAINED_0, cls_Range__def_0, cls_Id__on__eqI_0, cls_finite__Inter_0, cls_Un__upper1_0, cls_UnCI_1, cls_tranclD_0, cls_Int__insert__left_0, cls_insert__absorb_0, cls_comp__equivI_0, cls_in__above_7, cls_Domain__iff_0, cls_wf__inv__image_0, cls_Int__subset__iff_2, cls_in__below_2, cls_Int__Un__distrib2_0, cls_rtrancl__trans_0, cls_insert__iff_1, cls_wf__union__compatible_0, cls_insert__subset_0, cls_Int__absorb1_0, cls_in__above_4, cls_Field__converse_0, cls_refl__on__converse_0, cls_in__below_7, cls_set__rev__mp_0, cls_Times__subset__cancel2_1, cls_Image__Un_0, cls_in__mkbot_4, cls_trans__converse_1, cls_DomainE_0, cls_subset__insert__iff_2, cls_Range__Id__on_0, cls_refl__on__Id__on_0, cls_rtrancl__trancl__absorb_0, cls_Un__left__commute_0, cls_rtrancl__into__trancl1_0, cls_finite__insert_1, cls_trancl__subset__Field2_0, cls_set__mp_0, cls_cut__apply_0, cls_wf__converse__trancl_0, cls_wfI_2, cls_Un__Int__distrib2_0, cls_finite__Int_1, cls_trans__Int_0, cls_Image__iff_0, cls_in__below_11, cls_sym__Id__on_0, cls_rel__compEpair_0, cls_sym__Id_0, cls_rtrancl__mono_0, cls_Un__subset__iff_1, cls_Image__subset_0, cls_rtrancl__unfold_0, cls_wf__insert_0, cls_converse__rtrancl__into__rtrancl_0, cls_wfE__min_1, cls_Image__iff_1, cls_rtrancl__reflcl_0, cls_rev__image__eqI_0, cls_in__mktop_3, cls_rel__comp__distrib2_0, cls_in__below_9, cls_notin__Lin__iff_0, cls_insert__ident_0, cls_wf__acc__iff_1, cls_sym__trancl_0, cls_r__into__trancl_H_0, cls_cuts__eq_0, cls_acc__wfI_0, cls_SigmaI_0, cls_Union__upper_0, cls_finite__Int_0, cls_Un__absorb2_0, cls_trancl__into__trancl2_0, cls_Image__Id__on_0, cls_Range__converse_0, cls_rtrancl__eq__or__trancl_0, cls_in__above_6, cls_Range__Int__subset_0, cls_RangeE_0, cls_UnCI_0, cls_Int__insert__right_1, cls_sym__Un_0, cls_r__r__into__trancl_0, cls_wf__trancl_0, cls_rtrancl__converse_0, cls_trans__rtrancl_0, cls_refl__on__def_1, cls_in__below_6, cls_Lin__irrefl_0, cls_not__acc__down_1, cls_Un__upper2_0, cls_r__comp__rtrancl__eq_0, cls_subset__iff_0, cls_wf__comp__self_0, cls_trans__O__subset_0, cls_Field__Un_0, cls_in__mkbot_3, cls_rel__comp__distrib_0, cls_sym__converse_1, cls_wf__eq__minimal_0, cls_UnionE_1, cls_converse__Un_0, cls_image__insert_0, cls_equiv_Otrans_0, cls_acc__downwards__aux_0, cls_Range__iff_1, cls_Domain__Int__subset_0, cls_wf__comp__self_1, cls_tranclD_1, cls_Range__iff_0, cls_Un__insert__left_0, cls_wf__irrefl_0, cls_rtrancl__Un__rtrancl_0, cls_Id__on__iff_0, cls_IdE_0, cls_finite__surj_0, cls_trancl__reflcl_0, cls_set__eq__subset_2, cls_Un__mono_0, cls_Int__insert__left_1, cls_insert__subset_1, cls_Int__subset__iff_1, cls_pair__in__Id__conv_0, cls_Field__def_0, cls_Range__insert_0, cls_sym__inv__image_0, cls_SigmaD2_0, cls_finite__UnI_0, cls_trancl__domain_0, cls_converse__Id__on_0, cls_in__above_1, cls_rtrancl__reflcl__absorb_0, cls_DomainI_0, cls_Un__subset__iff_2, cls_in__below_10, cls_in__below_1, cls_refl__on__def_2, cls_wf__asym_0, cls_in__mktop_5, cls_Int__assoc_0, cls_acc__downwards_0, cls_wf__eq__minimal_1, cls_Times__subset__cancel2_0, cls_mktop__Lin_0, cls_sym__rtrancl_0, cls_subset__trans_0, cls_in__mktop_0, cls_trans__converse_0, cls_refl__onD2_0, cls_acc_Ocases_0, cls_transD_0, cls_mono__Field_0, cls_SigmaD1_0, cls_Domain__Un__eq_0, cls_Image__iff_2, cls_rtrancl__eq__or__trancl_1, cls_trans__Id__on_0, cls_Image__Int__subset_0, cls_in__mkbot_2, cls_Id__on__subset__Times_0, cls_insertI1_0, cls_Id__onE_1, cls_Un__Int__crazy_0, cls_trans__inv__image_0, cls_in__mktop_4, cls_Int__commute_0, cls_finite__equiv__class_0, cls_rev__ImageI_0, cls_Pair__eq_0, cls_Domain__converse_0, cls_trancl__converseI_0, cls_trans__Id_0, cls_Un__absorb1_0, cls_sym__converse_0, cls_in__inv__image_1, cls_in__above_5, cls_converse__iff_1, cls_refl__onD_0, cls_subset__refl_0, cls_converse__in__Lin_0, cls_Nitpick_Ortrancl__def_0, cls_image__Un_0, cls_Image__mono_0, cls_in__below_12, cls_R__O__Id_0, cls_image__iff_2, cls_insertCI_0, cls_UnionE_0, cls_image__Int__subset_0, cls_pair__in__Id__conv_1, cls_in__above_12, cls_tranclD2_1, cls_trancl__into__rtrancl_0, cls_reflcl__trancl_0, cls_Sigma__mono_1, cls_rtrancl__Int__subset_0, cls_above__Lin_0, cls_ImageE_1, cls_trancl__unfold__left_0, cls_in__above_9, cls_rtrancl__trancl__trancl_0, cls_Int__lower2_0, cls_rel__compI_0, cls_insert__mono_0, cls_Un__assoc_0, cls_linear__alt_0, cls_trancl__id_0, cls_in__rtrancl__UnI_1, cls_Sigma__Un__distrib1_0, cls_Int__absorb_0, cls_converse__Id_0, cls_refl__on__Un_0, cls_complete__Lin_0, cls_Int__left__absorb_0, cls_wf__union__merge_0, cls_in__above_13, cls_total__on__converse_1, cls_acc__subset_0, cls_converse__inv__image_0, cls_Un__absorb_0, cls_ImageE_0, cls_trancl__rtrancl__absorb_0, cls_in__below_5, cls_equiv_Osym_0, cls_UnE_0, cls_subset__insertI2_0, cls_converseD_0, cls_acc_OaccI_0, cls_Int__lower1_0, cls_InterD_0, cls_Int__subset__iff_0, cls_trancl__range_0, cls_Union__quotient_0, cls_refl__on__converse_1, cls_refl__onI_1, cls_refl__onD1_0, cls_Nitpick_Orefl_H__def_0, cls_Domain__Id__on_0, cls_equiv__type_0, cls_rtrancl__subset_0, cls_rtrancl__into__trancl2_0, cls_Un__Int__distrib_0, cls_Not__Domain__rtrancl_0, cls_finite__subset_0, cls_converse__rel__comp_0, cls_insert__subset_2, cls_equiv_Orefl__on_0, cls_rtrancl__converseI_0, cls_subsetD_0, cls_symD_0, cls_sym__def_0, cls_Image__Id_0, cls_finite__Un_0, cls_Int__left__commute_0, cls_in__above_2, cls_trancl__Int__subset_0, cls_insert__absorb2_0, cls_IdI_0, cls_irrefl__trancl__rD_0, cls_notin__Lin__iff_1, cls_Un__Int__assoc__eq_1, cls_trans__reflclI_0, cls_converse__converse_0, cls_RangeI_0, cls_Int__iff_2, cls_rtrancl_Ortrancl__refl_0, cls_Id__on__iff_1, cls_equiv__class__eq__iff_1, cls_cuts__eq_2, cls_in__mkbot_1, cls_Times__Un__distrib1_0, cls_in__mktop_2, cls_IntI_0, cls_in__inv__image_0, cls_Un__left__absorb_0, cls_converse__tranclE_0, cls_rtrancl__eq__or__trancl_2, cls_subset__insert_0, cls_InterI_0, cls_insert__times__insert_0, cls_in__below_0, cls_trancl_Or__into__trancl_0, cls_in__above_10, cls_Times__eq__cancel2_0, cls_rtrancl_Ortrancl__into__rtrancl_0, cls_converse__in__Lin_1, cls_IntE_1, cls_rtrancl__subset__rtrancl_0, cls_trancl__unfold__right_0, cls_trancl__rtrancl__trancl_0, cls_Int__greatest_0, cls_Domain__insert_0, cls_in__above_8, cls_subset__Un__eq_1, cls_sym__Un__converse_0, cls_sym__conv__converse__eq_0, cls_IntE_0, cls_in__mkbot_5, cls_Un__least_0, cls_in__rtrancl__UnI_0, cls_rel__comp__subset__Sigma_0, cls_wf__insert_2, cls_sym__trans__comp__subset_0, cls_refl__on__Int_0, cls_trancl__mono_0, cls_wf__Int1_0, cls_trans__trancl_0, cls_r__into__rtrancl_0, cls_rel__comp__mono_0, cls_insertCI_1, cls_refl__on__comp__subset_0, cls_in__below_13, cls_rtranclD_0, cls_mem__Sigma__iff_2, cls_image__eqI_0, cls_acc__downward_0, cls_in__below_4, cls_rtrancl__Un__subset_0, cls_image__subset__iff_0, cls_finite__imageI_0, cls_rtrancl__idemp__self__comp_0, cls_UnionI_0, cls_acc_OaccI_1, cls_subset__insertI_0, cls_trancl__unfold_0, cls_Domain__mono_0, cls_total__on__converse_0, cls_Sigma__Int__distrib1_0, cls_trancl__trans_0, cls_Un__Image_0, cls_Transitive__Closure_Otrancl__into__trancl_0, cls_quotient__eqI_0, cls_below__Lin_0, cls_that_0, cls_equiv__comp__eq_0, cls_converse__Int_0, cls_Domain__iff_1, cls_insert__image_0, cls_rev__finite__subset_0, cls_finite__Un_1, cls_Not__Domain__rtrancl_1, cls_wf__insert_1, cls_Nitpick_Orefl_H__def_1, cls_refl__on__def_0, cls_refl__on__def_3, cls_in__below_8, cls_Un__Int__assoc__eq_0, cls_Sigma__mono_0, cls_insert__commute_0, cls_trancl__subset__Sigma_0, cls_complete__Lin_1, cls_insert__iff_2, cls_equiv__class__eq__iff_2, cls_quotient__eq__iff_0, cls_Un__insert__right_0, cls_Pair__eq_1, cls_refl__onI_0, cls_sym__Int_0, cls_trancl__converse_0, cls_imageI_0, cls_Times__Int__distrib1_0, cls_quotientE_1, cls_equalityE_0, cls_wf__Int2_0, cls_wf__union__merge_1, cls_trans__def_0, cls_O__assoc_0, cls_not__acc__down_0, cls_rel__compEpair_1, cls_in__above_3, cls_in__mkbot_0, cls_Int__insert__right_0, cls_tfl__cut__apply_0, cls_subset__insert__iff_1, cls_in__above_14, cls_in__above_0
% 10.06/3.21 % No. of inferences in proof: 839
% 10.06/3.21 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2703 ms resp. 2120 ms w/o parsing
% 11.10/3.43 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 11.10/3.43 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------