%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SCT026-1 : TPTP v9.3.1. Released v4.1.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:27:03 AM UTC 2026
% Result : Unsatisfiable 23.72s 7.01s
% Output : Refutation 25.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 530
% Syntax : Number of formulae : 1061 ( 239 unt; 0 typ; 0 def)
% Number of atoms : 2579 ( 548 equ; 0 cnn)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 19738 (1288 ~;1518 |; 0 &;16932 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 11 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 100 ( 98 usr; 10 con; 0-7 aty)
% Number of variables : 3776 ( 0 ^;3776 !; 0 ?;3776 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_in_decl,type,
c_in: $i > $i > $i > $o ).
thf(c_Pair_decl,type,
c_Pair: $i > $i > $i > $i > $i ).
thf(v_a_decl,type,
v_a: $i ).
thf(v_b_decl,type,
v_b: $i ).
thf(tc_Arrow__Order__Mirabelle_Oalt_decl,type,
tc_Arrow__Order__Mirabelle_Oalt: $i ).
thf(tc_prod_decl,type,
tc_prod: $i > $i > $i ).
thf(c_Arrow__Order__Mirabelle_OLin_decl,type,
c_Arrow__Order__Mirabelle_OLin: $i ).
thf(tc_fun_decl,type,
tc_fun: $i > $i > $i ).
thf(tc_bool_decl,type,
tc_bool: $i ).
thf(hBOOL_decl,type,
hBOOL: $i > $o ).
thf(hAPP_decl,type,
hAPP: $i > $i > $i ).
thf(c_Set_Oinsert_decl,type,
c_Set_Oinsert: $i > $i > $i > $i ).
thf(class_Lattices_Olower__semilattice_decl,type,
class_Lattices_Olower__semilattice: $i > $o ).
thf(c_lessequals_decl,type,
c_lessequals: $i > $i > $i > $o ).
thf(c_Lattices_Olower__semilattice__class_Oinf_decl,type,
c_Lattices_Olower__semilattice__class_Oinf: $i > $i > $i > $i ).
thf(c_Relation_Orel__comp_decl,type,
c_Relation_Orel__comp: $i > $i > $i > $i > $i > $i ).
thf(c_Relation_Oconverse_decl,type,
c_Relation_Oconverse: $i > $i > $i > $i ).
thf(c_Equiv__Relations_Oequiv_decl,type,
c_Equiv__Relations_Oequiv: $i > $i > $i > $o ).
thf(c_Relation_ODomain_decl,type,
c_Relation_ODomain: $i > $i > $i > $i ).
thf(class_Lattices_Obounded__lattice_decl,type,
class_Lattices_Obounded__lattice: $i > $o ).
thf(c_Orderings_Obot__class_Obot_decl,type,
c_Orderings_Obot__class_Obot: $i > $i ).
thf(c_Relation_Osym_decl,type,
c_Relation_Osym: $i > $i > $o ).
thf(c_Transitive__Closure_Otrancl_decl,type,
c_Transitive__Closure_Otrancl: $i > $i > $i ).
thf(c_Relation_OId_decl,type,
c_Relation_OId: $i > $i ).
thf(c_Wellfounded_Owf_decl,type,
c_Wellfounded_Owf: $i > $i > $o ).
thf(c_Relation_Otrans_decl,type,
c_Relation_Otrans: $i > $i > $o ).
thf(class_Orderings_Obot_decl,type,
class_Orderings_Obot: $i > $o ).
thf(class_Lattices_Olattice_decl,type,
class_Lattices_Olattice: $i > $o ).
thf(c_Relation_Ototal__on_decl,type,
c_Relation_Ototal__on: $i > $i > $i > $o ).
thf(c_Relation_ORange_decl,type,
c_Relation_ORange: $i > $i > $i > $i ).
thf(class_Complete__Lattice_Ocomplete__lattice_decl,type,
class_Complete__Lattice_Ocomplete__lattice: $i > $o ).
thf(c_Complete__Lattice_OInf__class_OInf_decl,type,
c_Complete__Lattice_OInf__class_OInf: $i > $i > $i ).
thf(c_Relation_OField_decl,type,
c_Relation_OField: $i > $i > $i ).
thf(c_Relation_Oantisym_decl,type,
c_Relation_Oantisym: $i > $i > $o ).
thf(c_Relation_OId__on_decl,type,
c_Relation_OId__on: $i > $i > $i ).
thf(class_Orderings_Opreorder_decl,type,
class_Orderings_Opreorder: $i > $o ).
thf(class_Orderings_Oorder_decl,type,
class_Orderings_Oorder: $i > $o ).
thf(c_Transitive__Closure_Ortrancl_decl,type,
c_Transitive__Closure_Ortrancl: $i > $i > $i ).
thf(c_Relation_Orefl__on_decl,type,
c_Relation_Orefl__on: $i > $i > $i > $o ).
thf(c_Relation_OImage_decl,type,
c_Relation_OImage: $i > $i > $i > $i > $i ).
thf(c_COMBK_decl,type,
c_COMBK: $i > $i > $i > $i ).
thf(c_Relation_Oinv__image_decl,type,
c_Relation_Oinv__image: $i > $i > $i > $i > $i ).
thf(c_Finite__Set_Ofinite_decl,type,
c_Finite__Set_Ofinite: $i > $i > $o ).
thf(c_List_Osko__Recdef__Xcuts__eq__1__1_decl,type,
c_List_Osko__Recdef__Xcuts__eq__1__1: $i > $i > $i > $i > $i > $i > $i ).
thf(c_Recdef_Ocut_decl,type,
c_Recdef_Ocut: $i > $i > $i > $i > $i > $i ).
thf(class_Finite__Set_Ofinite_Ofinite_decl,type,
class_Finite__Set_Ofinite_Ofinite: $i > $o ).
thf(c_Set_Oimage_decl,type,
c_Set_Oimage: $i > $i > $i > $i > $i ).
thf(v_r_decl,type,
v_r: $i ).
thf(t_a_decl,type,
t_a: $i ).
thf(t_b_decl,type,
t_b: $i ).
thf(class_Orderings_Olinorder_decl,type,
class_Orderings_Olinorder: $i > $o ).
thf(c_Arrow__Order__Mirabelle_Oabove_decl,type,
c_Arrow__Order__Mirabelle_Oabove: $i > $i > $i > $i ).
thf(c_Equiv__Relations_Oquotient_decl,type,
c_Equiv__Relations_Oquotient: $i > $i > $i > $i ).
thf(c_Product__Type_OSigma_decl,type,
c_Product__Type_OSigma: $i > $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Relation__XId__onE__1__1_decl,type,
c_ATP__Linkup_Osko__Relation__XId__onE__1__1: $i > $i > $i > $i ).
thf(c_Arrow__Order__Mirabelle_Obelow_decl,type,
c_Arrow__Order__Mirabelle_Obelow: $i > $i > $i > $i ).
thf(c_Equiv__Relations_Ocongruent2_decl,type,
c_Equiv__Relations_Ocongruent2: $i > $i > $i > $i > $i > $i > $o ).
thf(c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1_decl,type,
c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1: $i > $i > $i > $i > $i ).
thf(c_Wellfounded_Oacc_decl,type,
c_Wellfounded_Oacc: $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Wellfounded__Xwf__acc__iff__1__1_decl,type,
c_ATP__Linkup_Osko__Wellfounded__Xwf__acc__iff__1__1: $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Relation__Xrefl__onI__1__1_decl,type,
c_ATP__Linkup_Osko__Relation__Xrefl__onI__1__1: $i > $i > $i > $i ).
thf(c_FuncSet_OPi_decl,type,
c_FuncSet_OPi: $i > $i > $i > $i > $i ).
thf(c_FuncSet_Osko__FuncSet__XPi__I__1__1_decl,type,
c_FuncSet_Osko__FuncSet__XPi__I__1__1: $i > $i > $i > $i > $i > $i ).
thf(c_Complete__Lattice_OSup__class_OSup_decl,type,
c_Complete__Lattice_OSup__class_OSup: $i > $i > $i ).
thf(c_FuncSet_Osko__FuncSet__XPi__I_H__1__1_decl,type,
c_FuncSet_Osko__FuncSet__XPi__I_H__1__1: $i > $i > $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Relation__XIdE__1__1_decl,type,
c_ATP__Linkup_Osko__Relation__XIdE__1__1: $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1_decl,type,
c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1: $i > $i > $i > $i ).
thf(c_List_Osko__Equiv__Relations__XquotientE__1__1_decl,type,
c_List_Osko__Equiv__Relations__XquotientE__1__1: $i > $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1_decl,type,
c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1: $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1_decl,type,
c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1: $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1_decl,type,
c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1: $i > $i > $i > $i ).
thf(c_Nitpick_Orefl_H_decl,type,
c_Nitpick_Orefl_H: $i > $i > $o ).
thf(c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1_decl,type,
c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1: $i > $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Relation__Xrefl__on__def__1__1_decl,type,
c_ATP__Linkup_Osko__Relation__Xrefl__on__def__1__1: $i > $i > $i > $i ).
thf(c_Arrow__Order__Mirabelle_Omkbot_decl,type,
c_Arrow__Order__Mirabelle_Omkbot: $i > $i > $i ).
thf(class_HOL_Oord_decl,type,
class_HOL_Oord: $i > $o ).
thf(c_ATP__Linkup_Osko__Relation__XImageE__1__1_decl,type,
c_ATP__Linkup_Osko__Relation__XImageE__1__1: $i > $i > $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1_decl,type,
c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1: $i > $i > $i > $i ).
thf(c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1_decl,type,
c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1: $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Product__Type__XSigma__mono__1__1_decl,type,
c_ATP__Linkup_Osko__Product__Type__XSigma__mono__1__1: $i > $i > $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Relation__XDomainE__1__1_decl,type,
c_ATP__Linkup_Osko__Relation__XDomainE__1__1: $i > $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Complete__Lattice__XInterI__1__1_decl,type,
c_ATP__Linkup_Osko__Complete__Lattice__XInterI__1__1: $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1_decl,type,
c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1: $i > $i > $i > $i > $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Wellfounded__XwfI__1__1_decl,type,
c_ATP__Linkup_Osko__Wellfounded__XwfI__1__1: $i > $i > $i > $i > $i ).
thf(c_Arrow__Order__Mirabelle_Omktop_decl,type,
c_Arrow__Order__Mirabelle_Omktop: $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1_decl,type,
c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1: $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1_decl,type,
c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1: $i > $i > $i > $i ).
thf(v_sko__Wellfounded__Xacc__Xinduct__1_decl,type,
v_sko__Wellfounded__Xacc__Xinduct__1: $i > $i > $i ).
thf(c_Equiv__Relations_Ocongruent_decl,type,
c_Equiv__Relations_Ocongruent: $i > $i > $i > $i > $o ).
thf(v_sko__Wellfounded__Xacc__Xinducts__1_decl,type,
v_sko__Wellfounded__Xacc__Xinducts__1: $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1_decl,type,
c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1: $i > $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Relation__XImage__iff__1__1_decl,type,
c_ATP__Linkup_Osko__Relation__XImage__iff__1__1: $i > $i > $i > $i > $i > $i ).
thf(c_FuncSet_Osko__FuncSet__XfuncsetI__1__1_decl,type,
c_FuncSet_Osko__FuncSet__XfuncsetI__1__1: $i > $i > $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Relation__XRange__iff__1__1_decl,type,
c_ATP__Linkup_Osko__Relation__XRange__iff__1__1: $i > $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1_decl,type,
c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1: $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Relation__XRangeE__1__1_decl,type,
c_ATP__Linkup_Osko__Relation__XRangeE__1__1: $i > $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Wellfounded__XwfI__1__2_decl,type,
c_ATP__Linkup_Osko__Wellfounded__XwfI__1__2: $i > $i > $i > $i > $i > $o ).
thf(v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1_decl,type,
v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1: $i ).
thf(514,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_in ) ) )
| ( A @ ( A @ ( C @ c_Complete__Lattice_OSup__class_OSup ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sup__upper_0) ).
thf(1665,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_in ) ) )
| ( A @ ( A @ ( C @ c_Complete__Lattice_OSup__class_OSup ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).
thf(427,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
!= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__not__empty_0) ).
thf(1469,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
!= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(387,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( A @ ( C @ c_lessequals ) ) )
| ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( A @ c_lessequals ) ) )
| ( ( B @ ( A @ c_Transitive__Closure_Ortrancl ) )
= ( B @ ( C @ c_Transitive__Closure_Ortrancl ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__subset_0) ).
thf(1369,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( A @ ( C @ c_lessequals ) ) )
| ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( A @ c_lessequals ) ) )
| ( ( B @ ( A @ c_Transitive__Closure_Ortrancl ) )
= ( B @ ( C @ c_Transitive__Closure_Ortrancl ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(262,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( D @ ( C @ c_Pair ) ) ) @ c_Set_Oinsert ) ) @ c_Wellfounded_Owf ) )
| ( B @ ( A @ c_Wellfounded_Owf ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__insert_0) ).
thf(1105,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( D @ ( C @ c_Pair ) ) ) @ c_Set_Oinsert ) ) @ c_Wellfounded_Owf ) )
| ( B @ ( A @ c_Wellfounded_Owf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(146,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) )
| ( A
= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( A
= ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__singletonD_0) ).
thf(846,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) )
| ( A
= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( A
= ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(47,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_Equiv__Relations_Oequiv ) ) )
| ( B @ ( A @ c_Relation_Otrans ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv_Otrans_0) ).
thf(628,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_Equiv__Relations_Oequiv ) ) )
| ( B @ ( A @ c_Relation_Otrans ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(167,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D = E )
| ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
| ( A = B )
| ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( D @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( E @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__above_14) ).
thf(893,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D = E )
| ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
| ( A = B )
| ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( D @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( E @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(361,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( D @ c_Relation_Orefl__on ) ) )
| ~ ( B @ ( D @ ( A @ c_in ) ) )
| ( B @ ( B @ tc_prod ) @ ( C @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__def_1) ).
thf(1315,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( D @ c_Relation_Orefl__on ) ) )
| ~ ( B @ ( D @ ( A @ c_in ) ) )
| ( B @ ( B @ tc_prod ) @ ( C @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(297,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( C @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Product__Type_OSigma ) ) ) )
= ( tc_bool @ ( E @ ( C @ tc_prod ) @ tc_fun ) @ ( E @ ( C @ ( D @ ( B @ c_Product__Type_OSigma ) ) ) @ ( E @ ( C @ ( D @ ( A @ c_Product__Type_OSigma ) ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sigma__Int__distrib1_0) ).
thf(1179,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( C @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Product__Type_OSigma ) ) ) )
= ( tc_bool @ ( E @ ( C @ tc_prod ) @ tc_fun ) @ ( E @ ( C @ ( D @ ( B @ c_Product__Type_OSigma ) ) ) @ ( E @ ( C @ ( D @ ( A @ c_Product__Type_OSigma ) ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(352,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E = D )
| ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
| ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( D @ ( E @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( A = D )
| ( B = D )
| ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__above_3) ).
thf(1295,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E = D )
| ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
| ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( D @ ( E @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( A = D )
| ( B = D )
| ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(480,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = F )
| ( ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) )
!= ( D @ ( C @ ( F @ ( E @ c_Pair ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Pair__eq_1) ).
thf(1586,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = F )
| ( ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) )
!= ( D @ ( C @ ( F @ ( E @ c_Pair ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).
thf(442,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( A @ ( C @ ( tc_bool @ ( B @ ( A @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Relation_Orel__comp ) ) ) ) )
= ( tc_bool @ ( D @ ( A @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__comp__empty1_0) ).
thf(1501,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( A @ ( C @ ( tc_bool @ ( B @ ( A @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Relation_Orel__comp ) ) ) ) )
= ( tc_bool @ ( D @ ( A @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).
thf(293,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Omktop ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( B = D )
| ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mktop_2) ).
thf(1168,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Omktop ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( B = D )
| ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(109,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( C @ ( B @ c_Relation_Oconverse ) ) @ ( A @ c_Relation_Orefl__on ) ) )
| ( C @ ( B @ ( A @ c_Relation_Orefl__on ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__converse_0) ).
thf(760,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( C @ ( B @ c_Relation_Oconverse ) ) @ ( A @ c_Relation_Orefl__on ) ) )
| ( C @ ( B @ ( A @ c_Relation_Orefl__on ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(116,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( B @ ( B @ ( B @ ( A @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Relation_Orel__comp ) ) ) ) @ c_lessequals ) ) )
| ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__Int__subset_0) ).
thf(777,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( B @ ( B @ ( B @ ( A @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Relation_Orel__comp ) ) ) ) @ c_lessequals ) ) )
| ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(12,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I2_J_0) ).
thf(555,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(465,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_Relation_Osym ) )
| ~ ( B @ ( A @ c_Relation_Otrans ) )
| ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( A @ ( B @ ( B @ ( B @ ( A @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_Orel__comp ) ) ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__trans__comp__subset_0) ).
thf(1554,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_Relation_Osym ) )
| ~ ( B @ ( A @ c_Relation_Otrans ) )
| ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( A @ ( B @ ( B @ ( B @ ( A @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_Orel__comp ) ) ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(265,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( A @ ( C @ c_Arrow__Order__Mirabelle_Omkbot ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( B = A )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mkbot_4) ).
thf(1110,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( A @ ( C @ c_Arrow__Order__Mirabelle_Omkbot ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( B = A )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(313,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__rtrancl__trancl_0) ).
thf(1211,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[313]) ).
thf(350,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Omkbot ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( A = D )
| ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mkbot_2) ).
thf(1290,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Omkbot ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( A = D )
| ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(244,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( B @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) )
| ( C @ ( A @ ( D @ c_in ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_1) ).
thf(1068,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( B @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) )
| ( C @ ( A @ ( D @ c_in ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(415,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
!= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ~ ( C @ ( D @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_disjoint__iff__not__equal_0) ).
thf(1443,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
!= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ~ ( C @ ( D @ ( A @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[415]) ).
thf(494,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
| ( A = B )
| ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_notin__Lin__iff_1) ).
thf(1618,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
| ( A = B )
| ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[494]) ).
thf(212,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( E @ ( D @ ( A @ ( C @ ( B @ c_FuncSet_Osko__FuncSet__XPi__I__1__1 ) ) ) ) @ c_in ) ) )
| ( E @ ( D @ tc_fun ) @ ( E @ ( D @ ( C @ ( B @ c_FuncSet_OPi ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Pi__I_0) ).
thf(994,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( E @ ( D @ ( A @ ( C @ ( B @ c_FuncSet_Osko__FuncSet__XPi__I__1__1 ) ) ) ) @ c_in ) ) )
| ( E @ ( D @ tc_fun ) @ ( E @ ( D @ ( C @ ( B @ c_FuncSet_OPi ) ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(246,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( D @ ( A @ c_Set_Oinsert ) ) @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__inter__insert_0) ).
thf(1073,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( D @ ( A @ c_Set_Oinsert ) ) @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Set_Oinsert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(310,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ c_COMBK ) ) @ ( A @ c_Product__Type_OSigma ) ) ) @ ( B @ c_lessequals ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( B @ ( C @ ( C @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__Xrefl__on__def__1__1 ) ) @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__Xrefl__on__def__1__1 ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( B @ ( A @ c_Relation_Orefl__on ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__def_3) ).
thf(1205,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ c_COMBK ) ) @ ( A @ c_Product__Type_OSigma ) ) ) @ ( B @ c_lessequals ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( B @ ( C @ ( C @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__Xrefl__on__def__1__1 ) ) @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__Xrefl__on__def__1__1 ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( B @ ( A @ c_Relation_Orefl__on ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(481,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( C @ ( B @ ( A @ c_Relation_OId__on ) @ c_Relation_OImage ) ) ) )
= ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__Id__on_0) ).
thf(1591,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( C @ ( B @ ( A @ c_Relation_OId__on ) @ c_Relation_OImage ) ) ) )
= ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[481]) ).
thf(160,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_in ) ) )
| ~ ( D @ ( C @ ( A @ c_in ) ) )
| ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntI_0) ).
thf(878,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_in ) ) )
| ~ ( D @ ( C @ ( A @ c_in ) ) )
| ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(456,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( E @ c_Relation_Ototal__on ) ) )
| ~ ( C @ ( E @ ( B @ c_in ) ) )
| ~ ( C @ ( E @ ( A @ c_in ) ) )
| ( B = A )
| ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_total__on__def_0) ).
thf(1533,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( E @ c_Relation_Ototal__on ) ) )
| ~ ( C @ ( E @ ( B @ c_in ) ) )
| ~ ( C @ ( E @ ( A @ c_in ) ) )
| ( B = A )
| ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).
thf(289,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( D @ ( B @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( B = D )
| ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
| ( A = D )
| ( A = D )
| ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__above_7) ).
thf(1158,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( D @ ( B @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( B = D )
| ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
| ( A = D )
| ( A = D )
| ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(110,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_Transitive__Closure_Ortrancl ) )
= ( B @ ( A @ c_Transitive__Closure_Ortrancl ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__idemp_0) ).
thf(762,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_Transitive__Closure_Ortrancl ) )
= ( B @ ( A @ c_Transitive__Closure_Ortrancl ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(406,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( A = E )
| ( ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
!= ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ c_Set_Oinsert ) ) @ ( D @ c_Set_Oinsert ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_0) ).
thf(1422,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( A = E )
| ( ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
!= ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ c_Set_Oinsert ) ) @ ( D @ c_Set_Oinsert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(473,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_in ) ) )
| ~ ( D @ ( C @ ( A @ c_in ) ) )
| ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__iff_2) ).
thf(1569,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_in ) ) )
| ~ ( D @ ( C @ ( A @ c_in ) ) )
| ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).
thf(280,axiom,
! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__lower1_0) ).
thf(1142,plain,
! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(341,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ c_Wellfounded_Owf ) )
| ~ ( C @ ( B @ ( E @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( C @ ( D @ ( B @ c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wfE__min_1) ).
thf(1269,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ c_Wellfounded_Owf ) )
| ~ ( C @ ( B @ ( E @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( C @ ( D @ ( B @ c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[341]) ).
thf(40,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_Relation_ODomain ) ) )
= ( B @ ( B @ ( A @ c_Relation_ODomain ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__domain_0) ).
thf(614,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_Relation_ODomain ) ) )
= ( B @ ( B @ ( A @ c_Relation_ODomain ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(527,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ c_Wellfounded_Owf ) )
| ~ ( B @ ( B @ tc_prod ) @ ( C @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__irrefl_0) ).
thf(1692,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ c_Wellfounded_Owf ) )
| ~ ( B @ ( B @ tc_prod ) @ ( C @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).
thf(356,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( E @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( D @ hAPP ) @ ( C @ ( B @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_HOL_Oord ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__funD_0) ).
thf(1305,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( E @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( D @ hAPP ) @ ( C @ ( B @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_HOL_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(31,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__antisym__conv_0) ).
thf(597,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(234,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = E )
| ( ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) )
!= ( D @ ( C @ ( F @ ( E @ c_Pair ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Pair__eq_0) ).
thf(1041,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = E )
| ( ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) )
!= ( D @ ( C @ ( F @ ( E @ c_Pair ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(152,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( B @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ ( C @ c_COMBK ) ) @ ( C @ c_Product__Type_OSigma ) ) ) @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( B @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ ( C @ c_COMBK ) ) @ ( C @ c_Product__Type_OSigma ) ) ) @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__subset__Sigma_0) ).
thf(861,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( B @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ ( C @ c_COMBK ) ) @ ( C @ c_Product__Type_OSigma ) ) ) @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( B @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ ( C @ c_COMBK ) ) @ ( C @ c_Product__Type_OSigma ) ) ) @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(249,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ c_Wellfounded_Owf ) )
| ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_Set_Oinsert ) ) @ c_Wellfounded_Owf ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__insert_2) ).
thf(1078,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ c_Wellfounded_Owf ) )
| ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_Set_Oinsert ) ) @ c_Wellfounded_Owf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(2,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_2) ).
thf(533,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(10,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_Relation_Osym ) )
| ( ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__conv__converse__eq_0) ).
thf(550,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_Relation_Osym ) )
| ( ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(89,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_Oantisym ) )
| ( B @ ( A @ c_Relation_Oantisym ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__converse_0) ).
thf(715,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_Oantisym ) )
| ( B @ ( A @ c_Relation_Oantisym ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(367,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( A @ c_in ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_2) ).
thf(1327,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( A @ c_in ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[367]) ).
thf(503,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
!= ( A @ ( D @ ( C @ ( B @ c_Set_Oimage ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__is__image_0) ).
thf(1640,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C
= ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
!= ( A @ ( D @ ( C @ ( B @ c_Set_Oimage ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).
thf(379,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( E @ ( D @ ( A @ ( C @ c_Relation_OImage ) ) ) @ ( B @ c_in ) ) )
| ( D @ ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__XImage__iff__1__1 ) ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__iff_0) ).
thf(1354,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( E @ ( D @ ( A @ ( C @ c_Relation_OImage ) ) ) @ ( B @ c_in ) ) )
| ( D @ ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__XImage__iff__1__1 ) ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(291,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( C @ ( C @ ( D @ c_Relation_Oconverse ) ) @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( C @ ( C @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ c_Relation_Oconverse ) ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__converseD_0) ).
thf(1164,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( C @ ( C @ ( D @ c_Relation_Oconverse ) ) @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( C @ ( C @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ c_Relation_Oconverse ) ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(124,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Relation_OId__on ) @ ( A @ c_in ) ) )
| ( A
= ( C @ ( C @ ( C @ ( A @ ( B @ c_ATP__Linkup_Osko__Relation__XId__onE__1__1 ) ) @ ( C @ ( A @ ( B @ c_ATP__Linkup_Osko__Relation__XId__onE__1__1 ) ) @ c_Pair ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Id__onE_1) ).
thf(797,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Relation_OId__on ) @ ( A @ c_in ) ) )
| ( A
= ( C @ ( C @ ( C @ ( A @ ( B @ c_ATP__Linkup_Osko__Relation__XId__onE__1__1 ) ) @ ( C @ ( A @ ( B @ c_ATP__Linkup_Osko__Relation__XId__onE__1__1 ) ) @ c_Pair ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(336,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( B @ c_in ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( A @ ( D @ c_Equiv__Relations_Oquotient ) ) @ ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_quotientI_0) ).
thf(1260,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( B @ c_in ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( A @ ( D @ c_Equiv__Relations_Oquotient ) ) @ ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[336]) ).
thf(80,axiom,
! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_Relation_Otrans ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__rtrancl_0) ).
thf(698,plain,
! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_Relation_Otrans ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(445,axiom,
! [A: $i] :
( ( ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Complete__Lattice_OSup__class_OSup ) )
= ( A @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sup__empty_0) ).
thf(1507,plain,
! [A: $i] :
( ( ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Complete__Lattice_OSup__class_OSup ) )
= ( A @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(318,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( D @ c_Pair ) ) ) @ c_in ) ) )
| ( B = D )
| ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
| ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( D @ ( B @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__below_2) ).
thf(1222,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( D @ c_Pair ) ) ) @ c_in ) ) )
| ( B = D )
| ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
| ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( D @ ( B @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(182,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( A @ c_in ) ) )
| ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( B @ ( A @ c_Arrow__Order__Mirabelle_Obelow ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_below__Lin_0) ).
thf(930,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( A @ c_in ) ) )
| ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( B @ ( A @ c_Arrow__Order__Mirabelle_Obelow ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(305,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( D @ ( B @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( B = D )
| ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
| ( A = D )
| ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( D @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__above_13) ).
thf(1196,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( D @ ( B @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( B = D )
| ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
| ( A = D )
| ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( D @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(215,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( A @ c_Relation_Orefl__on ) ) )
| ~ ( C @ ( E @ ( B @ c_Relation_Orefl__on ) ) )
| ( C @ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( E @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Relation_Orefl__on ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__Int_0) ).
thf(1001,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( A @ c_Relation_Orefl__on ) ) )
| ~ ( C @ ( E @ ( B @ c_Relation_Orefl__on ) ) )
| ( C @ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( E @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Relation_Orefl__on ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(272,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ c_Relation_Osym ) )
| ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_symD_0) ).
thf(1127,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ c_Relation_Osym ) )
| ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(476,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( B @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( D = B )
| ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
| ( A = B )
| ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__below_12) ).
thf(1576,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( B @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( D = B )
| ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
| ( A = B )
| ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).
thf(235,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( A = B )
| ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__eq__or__trancl_0) ).
thf(1046,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( A = B )
| ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(382,axiom,
! [B: $i,A: $i] :
~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( A @ ( B @ c_Arrow__Order__Mirabelle_Omkbot ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mkbot_1) ).
thf(1359,plain,
! [B: $i,A: $i] :
~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( A @ ( B @ c_Arrow__Order__Mirabelle_Omkbot ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(433,axiom,
! [B: $i,A: $i] :
( ~ ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_lessequals ) ) )
| ( A
= ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__empty_0) ).
thf(1482,plain,
! [B: $i,A: $i] :
( ~ ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_lessequals ) ) )
| ( A
= ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(57,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G @ ( E @ ( C @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Relation_Orel__comp ) ) ) ) @ c_Relation_Orel__comp ) ) ) ) )
= ( G @ ( D @ ( C @ ( G @ ( E @ ( D @ ( F @ ( B @ c_Relation_Orel__comp ) ) ) ) @ ( A @ c_Relation_Orel__comp ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_O__assoc_0) ).
thf(651,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( G @ ( E @ ( C @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Relation_Orel__comp ) ) ) ) @ c_Relation_Orel__comp ) ) ) ) )
= ( G @ ( D @ ( C @ ( G @ ( E @ ( D @ ( F @ ( B @ c_Relation_Orel__comp ) ) ) ) @ ( A @ c_Relation_Orel__comp ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(138,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( E @ ( B @ c_in ) ) )
| ~ ( C @ ( E @ ( D @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( A @ ( C @ ( C @ ( D @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( A @ ( E @ c_Equiv__Relations_Oequiv ) ) )
| ( ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) )
!= ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__class__eq__iff_3) ).
thf(829,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( E @ ( B @ c_in ) ) )
| ~ ( C @ ( E @ ( D @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( A @ ( C @ ( C @ ( D @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( A @ ( E @ c_Equiv__Relations_Oequiv ) ) )
| ( ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) )
!= ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(258,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( D @ ( A @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( D @ c_Pair ) ) ) @ c_in ) ) )
| ( A = D )
| ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
| ( D = B )
| ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__above_9) ).
thf(1095,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( D @ ( A @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( D @ c_Pair ) ) ) @ c_in ) ) )
| ( A = D )
| ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
| ( D = B )
| ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(508,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( A @ c_in ) ) )
| ( B @ ( B @ tc_prod ) @ ( B @ ( C @ c_Relation_OId__on ) @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Id__on__eqI_0) ).
thf(1650,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( A @ c_in ) ) )
| ( B @ ( B @ tc_prod ) @ ( B @ ( C @ c_Relation_OId__on ) @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).
thf(505,axiom,
! [A: $i] : ( A @ ( tc_bool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Relation_Oantisym ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__empty_0) ).
thf(1645,plain,
! [A: $i] : ( A @ ( tc_bool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Relation_Oantisym ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).
thf(450,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Wellfounded_Owf ) )
| ( ( B @ ( B @ ( B @ ( A @ ( A @ c_Relation_Orel__comp ) ) ) ) )
!= ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__no__loop_0) ).
thf(1518,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Wellfounded_Owf ) )
| ( ( B @ ( B @ ( B @ ( A @ ( A @ c_Relation_Orel__comp ) ) ) ) )
!= ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(339,axiom,
! [C: $i,B: $i,A: $i] :
~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( A @ ( C @ c_Arrow__Order__Mirabelle_Omktop ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mktop_0) ).
thf(1265,plain,
! [C: $i,B: $i,A: $i] :
~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( A @ ( C @ c_Arrow__Order__Mirabelle_Omktop ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(497,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__subset__rtrancl_0) ).
thf(1628,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[497]) ).
thf(239,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( A @ c_in ) ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__left_1) ).
thf(1055,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( A @ c_in ) ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(349,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( D @ ( A @ ( E @ c_Equiv__Relations_Ocongruent ) ) ) )
| ~ ( D @ ( D @ tc_prod ) @ ( E @ ( D @ ( D @ ( C @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ( ( B @ ( A @ hAPP ) )
= ( C @ ( A @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_congruent_Ocongruent_0) ).
thf(1287,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( D @ ( A @ ( E @ c_Equiv__Relations_Ocongruent ) ) ) )
| ~ ( D @ ( D @ tc_prod ) @ ( E @ ( D @ ( D @ ( C @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ( ( B @ ( A @ hAPP ) )
= ( C @ ( A @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(19,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infI2_0) ).
thf(570,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(353,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
| ~ ( C @ ( D @ ( A @ c_in ) ) )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subsetD_0) ).
thf(1298,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
| ~ ( C @ ( D @ ( A @ c_in ) ) )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[353]) ).
thf(91,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ c_Relation_Otrans ) )
| ( D @ ( D @ ( C @ ( B @ ( A @ c_Relation_Oinv__image ) ) ) @ c_Relation_Otrans ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__inv__image_0) ).
thf(719,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ c_Relation_Otrans ) )
| ( D @ ( D @ ( C @ ( B @ ( A @ c_Relation_Oinv__image ) ) ) @ c_Relation_Otrans ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(119,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ c_Finite__Set_Ofinite ) )
| ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( B @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ ( C @ c_COMBK ) ) @ ( C @ c_Product__Type_OSigma ) ) ) @ ( D @ c_lessequals ) ) )
| ~ ( tc_bool @ ( B @ tc_fun ) @ ( B @ ( D @ ( C @ c_Equiv__Relations_Oquotient ) ) @ ( A @ c_in ) ) )
| ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__equiv__class_0) ).
thf(785,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ c_Finite__Set_Ofinite ) )
| ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( B @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ ( C @ c_COMBK ) ) @ ( C @ c_Product__Type_OSigma ) ) ) @ ( D @ c_lessequals ) ) )
| ~ ( tc_bool @ ( B @ tc_fun ) @ ( B @ ( D @ ( C @ c_Equiv__Relations_Oquotient ) ) @ ( A @ c_in ) ) )
| ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(365,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( t_a @ ( t_a @ ( D @ c_Wellfounded_Oacc ) @ ( B @ c_in ) ) )
| ~ ( t_a @ ( t_a @ tc_prod ) @ ( D @ ( t_a @ ( t_a @ ( D @ ( A @ v_sko__Wellfounded__Xacc__Xinducts__1 ) @ ( C @ c_Pair ) ) ) @ c_in ) ) )
| ( t_a @ ( t_a @ ( D @ c_Wellfounded_Oacc ) @ ( C @ c_in ) ) )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_Oinducts_0) ).
thf(1323,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( t_a @ ( t_a @ ( D @ c_Wellfounded_Oacc ) @ ( B @ c_in ) ) )
| ~ ( t_a @ ( t_a @ tc_prod ) @ ( D @ ( t_a @ ( t_a @ ( D @ ( A @ v_sko__Wellfounded__Xacc__Xinducts__1 ) @ ( C @ c_Pair ) ) ) @ c_in ) ) )
| ( t_a @ ( t_a @ ( D @ c_Wellfounded_Oacc ) @ ( C @ c_in ) ) )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(421,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( G @ ( C @ tc_prod ) @ ( E @ ( G @ ( C @ ( H @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ ( G @ tc_prod ) @ ( F @ ( D @ ( G @ ( B @ ( H @ c_Pair ) ) ) @ c_in ) ) )
| ( D @ ( C @ tc_prod ) @ ( D @ ( G @ ( C @ ( F @ ( E @ c_Relation_Orel__comp ) ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__compI_0) ).
thf(1455,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( G @ ( C @ tc_prod ) @ ( E @ ( G @ ( C @ ( H @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( D @ ( G @ tc_prod ) @ ( F @ ( D @ ( G @ ( B @ ( H @ c_Pair ) ) ) @ c_in ) ) )
| ( D @ ( C @ tc_prod ) @ ( D @ ( G @ ( C @ ( F @ ( E @ c_Relation_Orel__comp ) ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(424,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__into__rtrancl_0) ).
thf(1462,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(191,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D = E )
| ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
| ( A = B )
| ( A = E )
| ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( E @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__above_8) ).
thf(949,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D = E )
| ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
| ( A = B )
| ( A = E )
| ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( E @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(177,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( E @ c_Equiv__Relations_Oequiv ) ) )
| ~ ( C @ ( E @ ( D @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( A @ ( C @ ( C @ ( D @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ( ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) )
!= ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__equiv__class_0) ).
thf(917,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( E @ c_Equiv__Relations_Oequiv ) ) )
| ~ ( C @ ( E @ ( D @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( A @ ( C @ ( C @ ( D @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ( ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) )
!= ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(82,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__trans_0) ).
thf(702,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(360,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( B @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ ( D @ c_COMBK ) ) @ ( C @ c_Product__Type_OSigma ) ) ) @ ( A @ c_lessequals ) ) )
| ( B @ ( D @ ( B @ ( A @ ( D @ ( C @ c_ATP__Linkup_Osko__Wellfounded__XwfI__1__1 ) ) ) @ c_in ) ) )
| ( B @ ( A @ c_Wellfounded_Owf ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wfI_3) ).
thf(1313,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( B @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ ( D @ c_COMBK ) ) @ ( C @ c_Product__Type_OSigma ) ) ) @ ( A @ c_lessequals ) ) )
| ( B @ ( D @ ( B @ ( A @ ( D @ ( C @ c_ATP__Linkup_Osko__Wellfounded__XwfI__1__1 ) ) ) @ c_in ) ) )
| ( B @ ( A @ c_Wellfounded_Owf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(345,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( F @ ( B @ ( A @ c_ATP__Linkup_Osko__Product__Type__XSigma__mono__1__1 ) ) ) ) @ ( F @ hAPP ) @ ( D @ ( C @ ( F @ ( B @ ( A @ c_ATP__Linkup_Osko__Product__Type__XSigma__mono__1__1 ) ) ) ) @ ( B @ hAPP ) @ c_lessequals ) ) )
| ( tc_bool @ ( D @ ( C @ tc_prod ) @ tc_fun ) @ ( D @ ( C @ ( F @ ( E @ c_Product__Type_OSigma ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Product__Type_OSigma ) ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sigma__mono_1) ).
thf(1279,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( F @ ( B @ ( A @ c_ATP__Linkup_Osko__Product__Type__XSigma__mono__1__1 ) ) ) ) @ ( F @ hAPP ) @ ( D @ ( C @ ( F @ ( B @ ( A @ c_ATP__Linkup_Osko__Product__Type__XSigma__mono__1__1 ) ) ) ) @ ( B @ hAPP ) @ c_lessequals ) ) )
| ( tc_bool @ ( D @ ( C @ tc_prod ) @ tc_fun ) @ ( D @ ( C @ ( F @ ( E @ c_Product__Type_OSigma ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Product__Type_OSigma ) ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(461,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( B @ tc_prod ) @ ( C @ ( B @ ( B @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( B @ ( C @ ( E @ c_Equiv__Relations_Oequiv ) ) )
| ~ ( B @ ( E @ ( A @ c_in ) ) )
| ~ ( B @ ( E @ ( D @ c_in ) ) )
| ( ( B @ ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ c_Equiv__Relations_Oquotient ) ) )
!= ( B @ ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ c_Equiv__Relations_Oquotient ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__equiv__class__iff2_0) ).
thf(1545,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( B @ tc_prod ) @ ( C @ ( B @ ( B @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( B @ ( C @ ( E @ c_Equiv__Relations_Oequiv ) ) )
| ~ ( B @ ( E @ ( A @ c_in ) ) )
| ~ ( B @ ( E @ ( D @ c_in ) ) )
| ( ( B @ ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ c_Equiv__Relations_Oquotient ) ) )
!= ( B @ ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ c_Equiv__Relations_Oquotient ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(170,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( D @ ( A @ c_Set_Oinsert ) ) @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__mono_0) ).
thf(902,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( D @ ( A @ c_Set_Oinsert ) ) @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(14,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= B )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__idem_0) ).
thf(559,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= B )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(149,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ ( B @ c_in ) ) )
| ( ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__right_1) ).
thf(853,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ ( B @ c_in ) ) )
| ( ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(254,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( B @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( D = B )
| ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
| ( A = D )
| ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__below_9) ).
thf(1087,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( B @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( D = B )
| ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
| ( A = D )
| ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(283,axiom,
! [A: $i] : ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Finite__Set_Ofinite ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite_OemptyI_0) ).
thf(1147,plain,
! [A: $i] : ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Finite__Set_Ofinite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(490,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_in ) ) )
| ~ ( C @ ( D @ ( A @ c_in ) ) )
| ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_Complete__Lattice_OSup__class_OSup ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnionI_0) ).
thf(1609,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_in ) ) )
| ~ ( C @ ( D @ ( A @ c_in ) ) )
| ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_Complete__Lattice_OSup__class_OSup ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).
thf(35,axiom,
! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_Relation_OId__on ) @ ( A @ c_Relation_Orefl__on ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__Id__on_0) ).
thf(606,plain,
! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_Relation_OId__on ) @ ( A @ c_Relation_Orefl__on ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(113,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ ( A @ c_Relation_Orel__comp ) ) ) ) )
= ( B @ ( B @ ( B @ ( A @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_Relation_Orel__comp ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_r__comp__rtrancl__eq_0) ).
thf(770,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ ( A @ c_Relation_Orel__comp ) ) ) ) )
= ( B @ ( B @ ( B @ ( A @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_Relation_Orel__comp ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(397,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( B @ tc_fun ) @ ( B @ ( C @ c_Relation_OField ) @ ( B @ ( A @ c_Relation_OField ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mono__Field_0) ).
thf(1398,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( B @ tc_fun ) @ ( B @ ( C @ c_Relation_OField ) @ ( B @ ( A @ c_Relation_OField ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(438,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__mono_0) ).
thf(1494,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).
thf(260,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_in ) ) )
| ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__absorb_0) ).
thf(1100,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_in ) ) )
| ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(363,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( B @ c_Relation_OId @ c_lessequals ) ) )
| ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( B @ ( B @ ( B @ ( A @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Relation_Orel__comp ) ) ) ) @ c_lessequals ) ) )
| ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__Int__subset_0) ).
thf(1319,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( B @ c_Relation_OId @ c_lessequals ) ) )
| ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( B @ ( B @ ( B @ ( A @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Relation_Orel__comp ) ) ) ) @ c_lessequals ) ) )
| ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[363]) ).
thf(156,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ ( A @ c_Wellfounded_Oacc ) @ ( B @ ( A @ c_ATP__Linkup_Osko__Wellfounded__Xwf__acc__iff__1__1 ) @ c_in ) ) )
| ( B @ ( A @ c_Wellfounded_Owf ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__acc__iff_1) ).
thf(870,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ ( A @ c_Wellfounded_Oacc ) @ ( B @ ( A @ c_ATP__Linkup_Osko__Wellfounded__Xwf__acc__iff__1__1 ) @ c_in ) ) )
| ( B @ ( A @ c_Wellfounded_Owf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(180,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D = E )
| ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
| ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( E @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( B = D )
| ( A = D )
| ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__below_3) ).
thf(924,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D = E )
| ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
| ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( E @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( B = D )
| ( A = D )
| ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(355,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ~ ( C @ ( A @ ( C @ ( A @ c_Relation_OField ) @ c_Relation_Orefl__on ) ) )
| ~ ( C @ ( A @ c_Relation_Oantisym ) )
| ~ ( C @ ( C @ ( A @ c_Relation_OField ) @ ( B @ c_in ) ) )
| ~ ( C @ ( C @ ( A @ c_Relation_OField ) @ ( D @ c_in ) ) )
| ( ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) )
!= ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Refl__antisym__eq__Image1__Image1__iff_0) ).
thf(1302,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ~ ( C @ ( A @ ( C @ ( A @ c_Relation_OField ) @ c_Relation_Orefl__on ) ) )
| ~ ( C @ ( A @ c_Relation_Oantisym ) )
| ~ ( C @ ( C @ ( A @ c_Relation_OField ) @ ( B @ c_in ) ) )
| ~ ( C @ ( C @ ( A @ c_Relation_OField ) @ ( D @ c_in ) ) )
| ( ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) )
!= ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(121,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( B @ c_in ) ) )
| ( ( E @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_Set_Oinsert ) ) )
= ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__image_0) ).
thf(789,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( B @ c_in ) ) )
| ( ( E @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_Set_Oinsert ) ) )
= ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(418,axiom,
! [B: $i,A: $i] : ( B @ ( B @ tc_prod ) @ ( B @ c_Relation_OId @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IdI_0) ).
thf(1450,plain,
! [B: $i,A: $i] : ( B @ ( B @ tc_prod ) @ ( B @ c_Relation_OId @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(404,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ c_Relation_Oantisym ) )
| ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisymD_0) ).
thf(1418,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ c_Relation_Oantisym ) )
| ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(55,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_Relation_Orefl__on ) ) )
| ( C @ ( C @ ( C @ ( B @ c_Relation_Oconverse ) ) @ ( A @ c_Relation_Orefl__on ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__converse_1) ).
thf(646,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_Relation_Orefl__on ) ) )
| ( C @ ( C @ ( C @ ( B @ c_Relation_Oconverse ) ) @ ( A @ c_Relation_Orefl__on ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(185,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_prod ) @ ( B @ ( C @ ( C @ ( A @ ( C @ ( A @ ( B @ c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1 ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_OaccI_0) ).
thf(937,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_prod ) @ ( B @ ( C @ ( C @ ( A @ ( C @ ( A @ ( B @ c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1 ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(199,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( D @ tc_prod ) @ ( D @ ( A @ c_Transitive__Closure_Otrancl ) @ ( D @ ( D @ ( C @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ( D @ ( D @ tc_prod ) @ ( A @ ( D @ ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1 ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tranclD2_1) ).
thf(966,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( D @ tc_prod ) @ ( D @ ( A @ c_Transitive__Closure_Otrancl ) @ ( D @ ( D @ ( C @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ( D @ ( D @ tc_prod ) @ ( A @ ( D @ ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1 ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(237,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( D @ tc_prod ) @ ( D @ ( A @ c_Transitive__Closure_Otrancl ) @ ( D @ ( D @ ( C @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ( D @ ( D @ tc_prod ) @ ( D @ ( A @ c_Transitive__Closure_Ortrancl ) @ ( D @ ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1 ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tranclD_1) ).
thf(1051,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( D @ tc_prod ) @ ( D @ ( A @ c_Transitive__Closure_Otrancl ) @ ( D @ ( D @ ( C @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ( D @ ( D @ tc_prod ) @ ( D @ ( A @ c_Transitive__Closure_Ortrancl ) @ ( D @ ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1 ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(264,axiom,
! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertCI_1) ).
thf(1109,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(499,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( B @ ( D @ ( E @ ( A @ ( C @ ( B @ c_FuncSet_Osko__FuncSet__XfuncsetI__1__1 ) ) ) ) @ c_in ) ) )
| ( D @ ( E @ tc_fun ) @ ( D @ ( E @ ( E @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ c_COMBK ) ) @ ( B @ c_FuncSet_OPi ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_funcsetI_0) ).
thf(1632,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( B @ ( D @ ( E @ ( A @ ( C @ ( B @ c_FuncSet_Osko__FuncSet__XfuncsetI__1__1 ) ) ) ) @ c_in ) ) )
| ( D @ ( E @ tc_fun ) @ ( D @ ( E @ ( E @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ c_COMBK ) ) @ ( B @ c_FuncSet_OPi ) ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).
thf(392,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Transitive__Closure_Otrancl__into__trancl_0) ).
thf(1383,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[392]) ).
thf(224,axiom,
tc_bool @ class_Orderings_Obot,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Obot) ).
thf(1020,plain,
tc_bool @ class_Orderings_Obot,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(299,axiom,
! [A: $i] : ( A @ ( tc_bool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Relation_Orefl__on ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__empty_0) ).
thf(1183,plain,
! [A: $i] : ( A @ ( tc_bool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Relation_Orefl__on ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[299]) ).
thf(347,axiom,
! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertI1_0) ).
thf(1283,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(33,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Transitive__Closure_Otrancl ) )
= ( B @ ( B @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_Relation_Oconverse ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__converse_0) ).
thf(602,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Transitive__Closure_Otrancl ) )
= ( B @ ( B @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_Relation_Oconverse ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(50,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_Equiv__Relations_Oequiv ) ) )
| ( C @ ( B @ ( A @ c_Relation_Orefl__on ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv_Orefl__on_0) ).
thf(634,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_Equiv__Relations_Oequiv ) ) )
| ( C @ ( B @ ( A @ c_Relation_Orefl__on ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(453,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_in ) ) )
| ( A @ ( C @ ( A @ ( B @ c_Complete__Lattice_OInf__class_OInf ) @ c_lessequals ) ) )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Inf__lower_0) ).
thf(1526,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_in ) ) )
| ( A @ ( C @ ( A @ ( B @ c_Complete__Lattice_OInf__class_OInf ) @ c_lessequals ) ) )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(61,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Transitive__Closure_Otrancl ) )
= ( B @ ( B @ ( B @ ( A @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_Relation_Orel__comp ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__unfold__right_0) ).
thf(660,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Transitive__Closure_Otrancl ) )
= ( B @ ( B @ ( B @ ( A @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_Relation_Orel__comp ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(411,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( D @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( B @ ( C @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_Ocases_0) ).
thf(1433,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( D @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( B @ ( C @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[411]) ).
thf(307,axiom,
! [B: $i,A: $i] : ( B @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__iff_1) ).
thf(1201,plain,
! [B: $i,A: $i] : ( B @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[307]) ).
thf(486,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( E @ ( D @ c_Equiv__Relations_Oequiv ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( E @ ( D @ c_Equiv__Relations_Oquotient ) ) @ ( A @ c_in ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( E @ ( D @ c_Equiv__Relations_Oquotient ) ) @ ( B @ c_in ) ) )
| ( A = B )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_quotient__disj_0) ).
thf(1600,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( E @ ( D @ c_Equiv__Relations_Oequiv ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( E @ ( D @ c_Equiv__Relations_Oquotient ) ) @ ( A @ c_in ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( E @ ( D @ c_Equiv__Relations_Oquotient ) ) @ ( B @ c_in ) ) )
| ( A = B )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).
thf(451,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insertI2_0) ).
thf(1521,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).
thf(529,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( A @ ( C @ c_lessequals ) ) )
| ( tc_bool @ ( B @ tc_fun ) @ ( B @ ( C @ c_Wellfounded_Oacc ) @ ( B @ ( A @ c_Wellfounded_Oacc ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__subset_0) ).
thf(1696,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( A @ ( C @ c_lessequals ) ) )
| ( tc_bool @ ( B @ tc_fun ) @ ( B @ ( C @ c_Wellfounded_Oacc ) @ ( B @ ( A @ c_Wellfounded_Oacc ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[529]) ).
thf(470,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( B @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ ( D @ c_COMBK ) ) @ ( C @ c_Product__Type_OSigma ) ) ) @ ( A @ c_lessequals ) ) )
| ~ ( B @ ( B @ ( A @ ( D @ ( C @ c_ATP__Linkup_Osko__Wellfounded__XwfI__1__1 ) ) ) @ ( A @ ( D @ ( C @ c_ATP__Linkup_Osko__Wellfounded__XwfI__1__2 ) ) ) ) )
| ( B @ ( A @ c_Wellfounded_Owf ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wfI_4) ).
thf(1564,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( B @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ ( D @ c_COMBK ) ) @ ( C @ c_Product__Type_OSigma ) ) ) @ ( A @ c_lessequals ) ) )
| ~ ( B @ ( B @ ( A @ ( D @ ( C @ c_ATP__Linkup_Osko__Wellfounded__XwfI__1__1 ) ) ) @ ( A @ ( D @ ( C @ c_ATP__Linkup_Osko__Wellfounded__XwfI__1__2 ) ) ) ) )
| ( B @ ( A @ c_Wellfounded_Owf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(375,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( B = D )
| ( ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
!= ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ c_Set_Oinsert ) ) @ ( D @ c_Set_Oinsert ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_3) ).
thf(1345,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( B = D )
| ( ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
!= ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ c_Set_Oinsert ) ) @ ( D @ c_Set_Oinsert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(210,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( B = D )
| ( ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
!= ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ c_Set_Oinsert ) ) @ ( D @ c_Set_Oinsert ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_1) ).
thf(988,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( B = D )
| ( ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
!= ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ c_Set_Oinsert ) ) @ ( D @ c_Set_Oinsert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(327,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ c_Wellfounded_Owf ) )
| ( C @ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Wellfounded_Owf ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__Int1_0) ).
thf(1242,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ c_Wellfounded_Owf ) )
| ( C @ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Wellfounded_Owf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(147,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( C @ ( B @ ( D @ c_Set_Oimage ) ) ) @ ( E @ ( C @ ( A @ ( D @ c_Set_Oimage ) ) ) @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__image__iff_2) ).
thf(849,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( C @ ( B @ ( D @ c_Set_Oimage ) ) ) @ ( E @ ( C @ ( A @ ( D @ c_Set_Oimage ) ) ) @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(178,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( B @ c_in ) ) )
| ( E @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_imageI_0) ).
thf(920,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( B @ c_in ) ) )
| ( E @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(188,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ c_Nitpick_Orefl_H ) )
| ( B @ ( B @ tc_prod ) @ ( C @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nitpick_Orefl_H__def_0) ).
thf(942,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ c_Nitpick_Orefl_H ) )
| ( B @ ( B @ tc_prod ) @ ( C @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(69,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ c_Finite__Set_Ofinite ) )
| ~ ( A @ class_Finite__Set_Ofinite_Ofinite ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite_0) ).
thf(678,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ c_Finite__Set_Ofinite ) )
| ~ ( A @ class_Finite__Set_Ofinite_Ofinite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(526,axiom,
! [A: $i] : ( A @ ( tc_bool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Wellfounded_Owf ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__empty_0) ).
thf(1691,plain,
! [A: $i] : ( A @ ( tc_bool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Wellfounded_Owf ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).
thf(306,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ c_Relation_Otrans ) )
| ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__def_0) ).
thf(1199,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ c_Relation_Otrans ) )
| ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[306]) ).
thf(372,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( B = D )
| ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Omktop ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mktop_3) ).
thf(1338,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( B = D )
| ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Omktop ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[372]) ).
thf(359,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_COMBK ) ) @ ( A @ c_Product__Type_OSigma ) ) ) )
= ( tc_bool @ ( B @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sigma__empty2_0) ).
thf(1311,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_COMBK ) ) @ ( A @ c_Product__Type_OSigma ) ) ) )
= ( tc_bool @ ( B @ ( C @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(343,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D
= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( ( B @ ( C @ ( D @ ( C @ ( B @ ( A @ c_COMBK ) ) @ c_Set_Oimage ) ) ) )
= ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__constant__conv_1) ).
thf(1274,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D
= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( ( B @ ( C @ ( D @ ( C @ ( B @ ( A @ c_COMBK ) ) @ c_Set_Oimage ) ) ) )
= ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[343]) ).
thf(174,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( B @ ( A @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Transitive__Closure_Otrancl ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_r__into__trancl_H_0) ).
thf(910,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( B @ ( A @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Transitive__Closure_Otrancl ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(195,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_r__r__into__trancl_0) ).
thf(957,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(103,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_Relation_Osym ) )
| ( B @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_Relation_Osym ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__rtrancl_0) ).
thf(746,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_Relation_Osym ) )
| ( B @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_Relation_Osym ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(374,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( t_a @ ( t_a @ ( C @ c_Wellfounded_Oacc ) @ ( B @ c_in ) ) )
| ~ ( C @ ( A @ v_sko__Wellfounded__Xacc__Xinducts__1 ) @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_Oinducts_2) ).
thf(1343,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( t_a @ ( t_a @ ( C @ c_Wellfounded_Oacc ) @ ( B @ c_in ) ) )
| ~ ( C @ ( A @ v_sko__Wellfounded__Xacc__Xinducts__1 ) @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(225,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__left__commute_0) ).
thf(1021,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(192,axiom,
! [B: $i,A: $i] : ( B @ ( B @ tc_prod ) @ ( B @ c_Relation_OId @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pair__in__Id__conv_1) ).
thf(952,plain,
! [B: $i,A: $i] : ( B @ ( B @ tc_prod ) @ ( B @ c_Relation_OId @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(477,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ c_Relation_Otrans ) )
| ~ ( C @ ( B @ c_Relation_Otrans ) )
| ( C @ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Relation_Otrans ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__Int_0) ).
thf(1580,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ c_Relation_Otrans ) )
| ~ ( C @ ( B @ c_Relation_Otrans ) )
| ( C @ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Relation_Otrans ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[477]) ).
thf(334,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( E @ ( B @ c_Relation_Orefl__on ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( E @ ( C @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__onD1_0) ).
thf(1255,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( E @ ( B @ c_Relation_Orefl__on ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( E @ ( C @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(270,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( B @ c_Set_Oinsert ) ) @ c_Complete__Lattice_OInf__class_OInf ) )
= ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Inf__binary_0) ).
thf(1123,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( B @ c_Set_Oinsert ) ) @ c_Complete__Lattice_OInf__class_OInf ) )
= ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(133,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( D @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__downwards_0) ).
thf(820,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( D @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(131,axiom,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ ( F @ ( H @ ( A @ ( G @ ( I @ c_Equiv__Relations_Ocongruent2 ) ) ) ) ) )
| ~ ( H @ ( H @ tc_prod ) @ ( I @ ( H @ ( H @ ( D @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( F @ ( F @ tc_prod ) @ ( G @ ( F @ ( F @ ( E @ ( C @ c_Pair ) ) ) @ c_in ) ) )
| ( ( C @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( E @ ( D @ ( A @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_congruent2_Ocongruent2_0) ).
thf(815,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( J @ ( F @ ( H @ ( A @ ( G @ ( I @ c_Equiv__Relations_Ocongruent2 ) ) ) ) ) )
| ~ ( H @ ( H @ tc_prod ) @ ( I @ ( H @ ( H @ ( D @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( F @ ( F @ tc_prod ) @ ( G @ ( F @ ( F @ ( E @ ( C @ c_Pair ) ) ) @ c_in ) ) )
| ( ( C @ ( B @ ( A @ hAPP ) @ hAPP ) )
= ( E @ ( D @ ( A @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(325,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
= ( A @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oimage ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__is__image_1) ).
thf(1238,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
= ( A @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oimage ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(295,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_Set_Oinsert ) ) @ c_Wellfounded_Owf ) )
| ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__insert_1) ).
thf(1174,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_Set_Oinsert ) ) @ c_Wellfounded_Owf ) )
| ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(519,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ c_Relation_Orefl__on ) ) )
| ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_COMBK ) ) @ ( B @ c_Product__Type_OSigma ) ) ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__def_0) ).
thf(1676,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ c_Relation_Orefl__on ) ) )
| ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_COMBK ) ) @ ( B @ c_Product__Type_OSigma ) ) ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).
thf(77,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( C @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_ORange ) ) )
= ( C @ ( B @ ( A @ c_Relation_ODomain ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__converse_0) ).
thf(693,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( C @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_ORange ) ) )
= ( C @ ( B @ ( A @ c_Relation_ODomain ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(48,axiom,
! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_Relation_Otrans ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__trancl_0) ).
thf(630,plain,
! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_Relation_Otrans ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(17,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Relation_ORange ) ) )
= ( B @ ( C @ ( C @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_ODomain ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__def_0) ).
thf(566,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Relation_ORange ) ) )
= ( B @ ( C @ ( C @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_ODomain ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(230,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( C @ c_in ) ) )
| ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ ( A @ c_Complete__Lattice_OInf__class_OInf ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Inter__lower_0) ).
thf(1032,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( C @ c_in ) ) )
| ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ ( A @ c_Complete__Lattice_OInf__class_OInf ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(385,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ ( B @ c_in ) ) )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_2) ).
thf(1365,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ ( B @ c_in ) ) )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(63,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( F @ ( E @ ( D @ ( C @ ( A @ c_Recdef_Ocut ) ) ) ) )
= ( F @ ( E @ ( D @ ( C @ ( B @ c_Recdef_Ocut ) ) ) ) ) )
| ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_List_Osko__Recdef__Xcuts__eq__1__1 ) ) ) ) ) @ ( A @ hAPP ) )
!= ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_List_Osko__Recdef__Xcuts__eq__1__1 ) ) ) ) ) @ ( B @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cuts__eq_2) ).
thf(665,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( F @ ( E @ ( D @ ( C @ ( A @ c_Recdef_Ocut ) ) ) ) )
= ( F @ ( E @ ( D @ ( C @ ( B @ c_Recdef_Ocut ) ) ) ) ) )
| ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_List_Osko__Recdef__Xcuts__eq__1__1 ) ) ) ) ) @ ( A @ hAPP ) )
!= ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_List_Osko__Recdef__Xcuts__eq__1__1 ) ) ) ) ) @ ( B @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(24,axiom,
! [A: $i] : ( A @ ( A @ c_Relation_OId @ c_Relation_Oantisym ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__Id_0) ).
thf(583,plain,
! [A: $i] : ( A @ ( A @ c_Relation_OId @ c_Relation_Oantisym ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(228,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ c_Wellfounded_Owf ) )
| ~ ( tc_bool @ ( B @ tc_fun ) @ ( B @ ( B @ ( A @ ( C @ c_Relation_OImage ) ) ) @ ( A @ c_lessequals ) ) )
| ( A
= ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wfE__pf_0) ).
thf(1027,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ c_Wellfounded_Owf ) )
| ~ ( tc_bool @ ( B @ tc_fun ) @ ( B @ ( B @ ( A @ ( C @ c_Relation_OImage ) ) ) @ ( A @ c_lessequals ) ) )
| ( A
= ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(108,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I4_J_0) ).
thf(757,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(346,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl_Ortrancl__into__rtrancl_0) ).
thf(1281,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(500,axiom,
! [C: $i,B: $i,A: $i] : ( B @ ( B @ tc_prod ) @ ( B @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl_Ortrancl__refl_0) ).
thf(1634,plain,
! [C: $i,B: $i,A: $i] : ( B @ ( B @ tc_prod ) @ ( B @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).
thf(86,axiom,
! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_Relation_OId__on ) @ c_Relation_Oantisym ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__Id__on_0) ).
thf(710,plain,
! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_Relation_OId__on ) @ c_Relation_Oantisym ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(144,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Lattices_Obounded__lattice )
| ( B @ ( A @ tc_fun ) @ class_Lattices_Obounded__lattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Obounded__lattice) ).
thf(842,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Lattices_Obounded__lattice )
| ( B @ ( A @ tc_fun ) @ class_Lattices_Obounded__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(220,axiom,
! [C: $i,B: $i,A: $i] :
~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( B @ ( C @ c_Arrow__Order__Mirabelle_Omkbot ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mkbot_0) ).
thf(1012,plain,
! [C: $i,B: $i,A: $i] :
~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( B @ ( C @ c_Arrow__Order__Mirabelle_Omkbot ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(524,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( D @ c_in ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( B @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert_0) ).
thf(1687,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( D @ c_in ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( B @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[524]) ).
thf(422,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( E @ c_Equiv__Relations_Oequiv ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( A @ ( C @ ( C @ ( D @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ( ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) )
= ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__class__eq__iff_0) ).
thf(1457,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( E @ c_Equiv__Relations_Oequiv ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( A @ ( C @ ( C @ ( D @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ( ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) )
= ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(71,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_Transitive__Closure_Ortrancl ) )
= ( B @ ( A @ c_Transitive__Closure_Ortrancl ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__rtrancl__absorb_0) ).
thf(682,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_Transitive__Closure_Ortrancl ) )
= ( B @ ( A @ c_Transitive__Closure_Ortrancl ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(400,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__eq__or__trancl_2) ).
thf(1407,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = B )
| ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(475,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_in ) ) )
| ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
!= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comm__monoid__add_Ononempty__iff_2) ).
thf(1573,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_in ) ) )
| ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
!= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).
thf(203,axiom,
! [B: $i,A: $i] :
( ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( A @ c_in ) ) )
| ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( B @ ( A @ c_Arrow__Order__Mirabelle_Omkbot ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mkbot__Lin_0) ).
thf(974,plain,
! [B: $i,A: $i] :
( ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( A @ c_in ) ) )
| ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( B @ ( A @ c_Arrow__Order__Mirabelle_Omkbot ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(377,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ ( C @ tc_prod ) @ tc_fun ) @ ( D @ ( C @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( E @ c_COMBK ) ) @ ( F @ c_Product__Type_OSigma ) ) ) @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( D @ tc_fun ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Relation_OImage ) ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__subset_0) ).
thf(1350,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ ( C @ tc_prod ) @ tc_fun ) @ ( D @ ( C @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( E @ c_COMBK ) ) @ ( F @ c_Product__Type_OSigma ) ) ) @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( D @ tc_fun ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Relation_OImage ) ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[377]) ).
thf(269,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( A @ ( E @ c_Pair ) ) ) @ c_in ) ) )
| ( D @ ( D @ ( C @ ( B @ c_Relation_ORange ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__iff_1) ).
thf(1121,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( A @ ( E @ c_Pair ) ) ) @ c_in ) ) )
| ( D @ ( D @ ( C @ ( B @ c_Relation_ORange ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(242,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( A @ c_lessequals ) ) )
| ( C @ ( A @ ( D @ ( C @ ( F @ ( B @ ( A @ c_ATP__Linkup_Osko__Product__Type__XSigma__mono__1__1 ) ) ) ) @ c_in ) ) )
| ( tc_bool @ ( D @ ( C @ tc_prod ) @ tc_fun ) @ ( D @ ( C @ ( F @ ( E @ c_Product__Type_OSigma ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Product__Type_OSigma ) ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sigma__mono_0) ).
thf(1064,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( A @ c_lessequals ) ) )
| ( C @ ( A @ ( D @ ( C @ ( F @ ( B @ ( A @ c_ATP__Linkup_Osko__Product__Type__XSigma__mono__1__1 ) ) ) ) @ c_in ) ) )
| ( tc_bool @ ( D @ ( C @ tc_prod ) @ tc_fun ) @ ( D @ ( C @ ( F @ ( E @ c_Product__Type_OSigma ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Product__Type_OSigma ) ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(320,axiom,
! [A: $i] :
( ( A @ ( tc_bool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Transitive__Closure_Ortrancl ) )
= ( A @ c_Relation_OId ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__empty_0) ).
thf(1227,plain,
! [A: $i] :
( ( A @ ( tc_bool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Transitive__Closure_Ortrancl ) )
= ( A @ c_Relation_OId ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(407,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_Relation_Otrans ) )
| ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( A @ ( B @ ( B @ ( B @ ( A @ ( A @ c_Relation_Orel__comp ) ) ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__O__subset_0) ).
thf(1425,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_Relation_Otrans ) )
| ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( A @ ( B @ ( B @ ( B @ ( A @ ( A @ c_Relation_Orel__comp ) ) ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(277,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ tc_prod ) @ ( E @ ( C @ ( D @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ( D @ ( C @ tc_prod ) @ ( C @ ( D @ ( E @ c_Relation_Oconverse ) ) @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converseI_0) ).
thf(1138,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ tc_prod ) @ ( E @ ( C @ ( D @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ( D @ ( C @ tc_prod ) @ ( C @ ( D @ ( E @ c_Relation_Oconverse ) ) @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(29,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infI1_0) ).
thf(593,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(268,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
= ( tc_bool @ ( C @ ( B @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( ( C @ ( B @ ( A @ c_Relation_ODomain ) ) )
!= ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__empty__iff_0) ).
thf(1118,plain,
! [C: $i,B: $i,A: $i] :
( ( A
= ( tc_bool @ ( C @ ( B @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( ( C @ ( B @ ( A @ c_Relation_ODomain ) ) )
!= ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(101,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_Relation_Otrans ) )
| ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_Otrans ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__converse_1) ).
thf(742,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_Relation_Otrans ) )
| ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_Otrans ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(22,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_OField ) )
= ( B @ ( A @ c_Relation_OField ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Field__converse_0) ).
thf(578,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_OField ) )
= ( B @ ( A @ c_Relation_OField ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(79,axiom,
! [C: $i,B: $i,A: $i] : ( A @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_1) ).
thf(697,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(323,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ c_Equiv__Relations_Oequiv ) ) )
| ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_COMBK ) ) @ ( B @ c_Product__Type_OSigma ) ) ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__type_0) ).
thf(1234,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ c_Equiv__Relations_Oequiv ) ) )
| ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_COMBK ) ) @ ( B @ c_Product__Type_OSigma ) ) ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(158,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ ( C @ ( B @ c_Relation_ODomain ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Not__Domain__rtrancl_1) ).
thf(874,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ ( C @ ( B @ c_Relation_ODomain ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(281,axiom,
! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__iff_1) ).
thf(1143,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(206,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( E @ ( D @ ( A @ ( C @ c_Relation_OImage ) ) ) @ ( B @ c_in ) ) )
| ( E @ ( D @ tc_prod ) @ ( C @ ( E @ ( D @ ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__XImageE__1__1 ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ImageE_0) ).
thf(980,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( E @ ( D @ ( A @ ( C @ c_Relation_OImage ) ) ) @ ( B @ c_in ) ) )
| ( E @ ( D @ tc_prod ) @ ( C @ ( E @ ( D @ ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__XImageE__1__1 ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(440,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( D @ ( B @ c_Relation_ORange ) ) @ ( A @ c_in ) ) )
| ( C @ ( D @ tc_prod ) @ ( B @ ( C @ ( D @ ( A @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__XRangeE__1__1 ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_RangeE_0) ).
thf(1498,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( D @ ( B @ c_Relation_ORange ) ) @ ( A @ c_in ) ) )
| ( C @ ( D @ tc_prod ) @ ( B @ ( C @ ( D @ ( A @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__XRangeE__1__1 ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).
thf(459,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ c_Wellfounded_Owf ) )
| ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
| ( B @ ( A @ c_Wellfounded_Owf ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__subset_0) ).
thf(1540,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ c_Wellfounded_Owf ) )
| ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
| ( B @ ( A @ c_Wellfounded_Owf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(217,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( F @ c_Equiv__Relations_Oequiv ) ) )
| ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( D @ c_Relation_OImage ) ) ) @ ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( D @ c_Relation_OImage ) ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( E @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__class__nondisjoint_0) ).
thf(1006,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( F @ c_Equiv__Relations_Oequiv ) ) )
| ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( D @ c_Relation_OImage ) ) ) @ ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( D @ c_Relation_OImage ) ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( E @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(472,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( D @ ( C @ c_Wellfounded_Oacc ) @ ( B @ c_in ) ) )
| ~ ( D @ ( C @ ( A @ c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 ) ) @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__induct__rule_2) ).
thf(1567,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( D @ ( C @ c_Wellfounded_Oacc ) @ ( B @ c_in ) ) )
| ~ ( D @ ( C @ ( A @ c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 ) ) @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).
thf(522,axiom,
! [B: $i,A: $i] :
~ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_emptyE_0) ).
thf(1683,plain,
! [B: $i,A: $i] :
~ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).
thf(251,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( A @ c_in ) ) )
| ~ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
| ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Transitive__Closure_Otrancl ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__mono_0) ).
thf(1082,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( A @ c_in ) ) )
| ~ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
| ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Transitive__Closure_Otrancl ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(383,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Complete__Lattice__XInterI__1__1 ) ) @ c_in ) ) )
| ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_Complete__Lattice_OInf__class_OInf ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_InterI_0) ).
thf(1361,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Complete__Lattice__XInterI__1__1 ) ) @ c_in ) ) )
| ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_Complete__Lattice_OInf__class_OInf ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(183,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( A @ c_Wellfounded_Oacc ) @ ( B @ c_in ) ) )
| ~ ( C @ ( C @ ( A @ c_Wellfounded_Oacc ) @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1 ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__acc__down_1) ).
thf(933,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( A @ c_Wellfounded_Oacc ) @ ( B @ c_in ) ) )
| ~ ( C @ ( C @ ( A @ c_Wellfounded_Oacc ) @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1 ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( B @ ( B @ ( A @ c_Relation_ODomain ) ) @ c_Equiv__Relations_Oequiv ) ) )
| ( ( B @ ( B @ ( B @ ( A @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_Orel__comp ) ) ) ) )
!= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comp__equivI_0) ).
thf(537,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( B @ ( B @ ( A @ c_Relation_ODomain ) ) @ c_Equiv__Relations_Oequiv ) ) )
| ( ( B @ ( B @ ( B @ ( A @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_Orel__comp ) ) ) ) )
!= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(65,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( B @ ( A @ ( C @ c_Set_Oinsert ) ) @ c_Finite__Set_Ofinite ) )
| ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__insert_0) ).
thf(669,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( B @ ( A @ ( C @ c_Set_Oinsert ) ) @ c_Finite__Set_Ofinite ) )
| ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(479,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( C @ c_in ) ) )
| ~ ( B @ ( C @ c_Finite__Set_Ofinite ) )
| ( B @ ( tc_bool @ ( B @ tc_fun ) @ ( A @ c_Complete__Lattice_OInf__class_OInf ) @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Inter_0) ).
thf(1584,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( C @ c_in ) ) )
| ~ ( B @ ( C @ c_Finite__Set_Ofinite ) )
| ( B @ ( tc_bool @ ( B @ tc_fun ) @ ( A @ c_Complete__Lattice_OInf__class_OInf ) @ c_Finite__Set_Ofinite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).
thf(416,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( D @ ( E @ ( A @ ( C @ ( B @ c_FuncSet_Osko__FuncSet__XfuncsetI__1__1 ) ) ) ) @ ( A @ hAPP ) @ c_in ) ) )
| ( D @ ( E @ tc_fun ) @ ( D @ ( E @ ( E @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ c_COMBK ) ) @ ( B @ c_FuncSet_OPi ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_funcsetI_1) ).
thf(1446,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( D @ ( E @ ( A @ ( C @ ( B @ c_FuncSet_Osko__FuncSet__XfuncsetI__1__1 ) ) ) ) @ ( A @ hAPP ) @ c_in ) ) )
| ( D @ ( E @ tc_fun ) @ ( D @ ( E @ ( E @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ c_COMBK ) ) @ ( B @ c_FuncSet_OPi ) ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(8,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Wellfounded_Owf ) )
| ( B @ ( B @ ( B @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_Relation_Oconverse ) ) @ c_Wellfounded_Owf ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__converse__trancl_0) ).
thf(547,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Wellfounded_Owf ) )
| ( B @ ( B @ ( B @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_Relation_Oconverse ) ) @ c_Wellfounded_Owf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(84,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
= ( C @ ( B @ ( A @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__absorb2_0) ).
thf(706,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
= ( C @ ( B @ ( A @ c_Set_Oinsert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(163,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Relation_OId__on ) @ ( C @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Id__on__iff_1) ).
thf(884,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Relation_OId__on ) @ ( C @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(368,axiom,
! [A: $i] :
( ( A @ ( tc_bool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Relation_OField ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Field__empty_0) ).
thf(1329,plain,
! [A: $i] :
( ( A @ ( tc_bool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Relation_OField ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(73,axiom,
( ( t_b @ ( t_a @ ( v_r @ c_Relation_ORange ) ) )
= ( t_a @ ( t_b @ ( t_b @ ( t_a @ ( v_r @ c_Relation_Oconverse ) ) @ c_Relation_ODomain ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__def__raw_0) ).
thf(686,plain,
( ( t_b @ ( t_a @ ( v_r @ c_Relation_ORange ) ) )
= ( t_a @ ( t_b @ ( t_b @ ( t_a @ ( v_r @ c_Relation_Oconverse ) ) @ c_Relation_ODomain ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(247,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( A @ ( E @ c_Pair ) ) ) @ c_in ) ) )
| ( D @ ( D @ ( C @ ( B @ c_Relation_ORange ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_RangeI_0) ).
thf(1075,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( A @ ( E @ c_Pair ) ) ) @ c_in ) ) )
| ( D @ ( D @ ( C @ ( B @ c_Relation_ORange ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(222,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Orderings_Obot )
| ( B @ ( A @ tc_fun ) @ class_Orderings_Obot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Obot) ).
thf(1016,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Orderings_Obot )
| ( B @ ( A @ tc_fun ) @ class_Orderings_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(311,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ ( B @ c_in ) ) )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert_1) ).
thf(1207,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ ( B @ c_in ) ) )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(28,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
!= B )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__inf_1) ).
thf(590,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
!= B )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(233,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__assoc_0) ).
thf(1039,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(201,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
| ~ ( B @ ( C @ c_Relation_Oantisym ) )
| ( B @ ( A @ c_Relation_Oantisym ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__subset_0) ).
thf(970,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
| ~ ( B @ ( C @ c_Relation_Oantisym ) )
| ( B @ ( A @ c_Relation_Oantisym ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(266,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( E @ tc_prod ) @ ( F @ ( G @ ( E @ ( D @ ( C @ c_Relation_Orel__comp ) ) ) ) @ ( F @ ( E @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( F @ ( G @ tc_prod ) @ ( D @ ( F @ ( G @ ( B @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1 ) ) ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__compEpair_1) ).
thf(1114,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( E @ tc_prod ) @ ( F @ ( G @ ( E @ ( D @ ( C @ c_Relation_Orel__comp ) ) ) ) @ ( F @ ( E @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( F @ ( G @ tc_prod ) @ ( D @ ( F @ ( G @ ( B @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1 ) ) ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(338,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( D @ ( C @ c_Wellfounded_Oacc ) @ ( B @ c_in ) ) )
| ( D @ ( D @ ( C @ c_Wellfounded_Oacc ) @ ( D @ ( C @ ( A @ c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 ) ) @ c_in ) ) )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__induct_0) ).
thf(1263,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( D @ ( C @ c_Wellfounded_Oacc ) @ ( B @ c_in ) ) )
| ( D @ ( D @ ( C @ c_Wellfounded_Oacc ) @ ( D @ ( C @ ( A @ c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 ) ) @ c_in ) ) )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(455,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D = E )
| ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
| ( A = B )
| ( B = D )
| ( A = D )
| ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( E @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__below_4) ).
thf(1530,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D = E )
| ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
| ( A = B )
| ( B = D )
| ( A = D )
| ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( E @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(322,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_lessequals ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equalityI_0) ).
thf(1231,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_lessequals ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[322]) ).
thf(274,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( A @ c_Wellfounded_Oacc ) @ ( B @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( A @ ( C @ ( C @ ( B @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1 ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__acc__down_0) ).
thf(1131,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( A @ c_Wellfounded_Oacc ) @ ( B @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( A @ ( C @ ( C @ ( B @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Wellfounded__Xnot__acc__down__1__1 ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(303,axiom,
! [B: $i,A: $i] :
~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( A @ ( B @ c_Arrow__Order__Mirabelle_Omktop ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mktop_1) ).
thf(1192,plain,
! [B: $i,A: $i] :
~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( A @ ( B @ c_Arrow__Order__Mirabelle_Omktop ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(208,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ ( B @ tc_prod ) @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( B @ ( D @ c_Relation_ODomain ) ) @ ( C @ ( B @ ( A @ c_Relation_ODomain ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__mono_0) ).
thf(984,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ ( B @ tc_prod ) @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( B @ ( D @ c_Relation_ODomain ) ) @ ( C @ ( B @ ( A @ c_Relation_ODomain ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(92,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_Wellfounded_Owf ) )
| ( B @ ( B @ ( B @ ( B @ ( A @ ( A @ c_Relation_Orel__comp ) ) ) ) @ c_Wellfounded_Owf ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__comp__self_0) ).
thf(721,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_Wellfounded_Owf ) )
| ( B @ ( B @ ( B @ ( B @ ( A @ ( A @ c_Relation_Orel__comp ) ) ) ) @ c_Wellfounded_Owf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(409,axiom,
! [B: $i,A: $i] :
~ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__iff_0) ).
thf(1429,plain,
! [B: $i,A: $i] :
~ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[409]) ).
thf(117,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( E @ ( C @ ( B @ ( D @ c_Set_Oimage ) ) ) @ ( A @ ( D @ hAPP ) @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__iff_2) ).
thf(779,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( E @ ( C @ ( B @ ( D @ c_Set_Oimage ) ) ) @ ( A @ ( D @ hAPP ) @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(395,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( C @ ( B @ ( A @ c_in ) ) )
| ( C @ ( D @ ( A @ c_in ) ) )
| ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
!= ( C @ ( D @ ( A @ c_Set_Oinsert ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__ident_0) ).
thf(1393,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( C @ ( B @ ( A @ c_in ) ) )
| ( C @ ( D @ ( A @ c_in ) ) )
| ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
!= ( C @ ( D @ ( A @ c_Set_Oinsert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(44,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I6_J_0) ).
thf(622,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(141,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( D @ ( C @ ( B @ c_Relation_ODomain ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__iff_1) ).
thf(837,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( D @ ( C @ ( B @ c_Relation_ODomain ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(285,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ ( A @ c_Wellfounded_Oacc ) @ ( B @ ( A @ c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1 ) @ c_in ) ) )
| ( B @ ( A @ c_Wellfounded_Owf ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__wfI_0) ).
thf(1150,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ ( A @ c_Wellfounded_Oacc ) @ ( B @ ( A @ c_ATP__Linkup_Osko__Wellfounded__Xacc__wfI__1__1 ) @ c_in ) ) )
| ( B @ ( A @ c_Wellfounded_Owf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(431,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__subset__iff_0) ).
thf(1478,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(419,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__into__trancl2_0) ).
thf(1451,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(99,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ c_Wellfounded_Owf ) )
| ( D @ ( D @ ( C @ ( B @ ( A @ c_Relation_Oinv__image ) ) ) @ c_Wellfounded_Owf ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__inv__image_0) ).
thf(738,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ c_Wellfounded_Owf ) )
| ( D @ ( D @ ( C @ ( B @ ( A @ c_Relation_Oinv__image ) ) ) @ c_Wellfounded_Owf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(485,axiom,
tc_bool @ class_Finite__Set_Ofinite_Ofinite,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Finite__Set_Ofinite_Ofinite) ).
thf(1599,plain,
tc_bool @ class_Finite__Set_Ofinite_Ofinite,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).
thf(329,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( tc_bool @ ( D @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Relation_Oconverse ) ) )
= ( tc_bool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ ( C @ ( B @ c_Relation_Oconverse ) ) @ ( D @ ( C @ ( A @ c_Relation_Oconverse ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__Int_0) ).
thf(1246,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( tc_bool @ ( D @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Relation_Oconverse ) ) )
= ( tc_bool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( D @ ( C @ ( B @ c_Relation_Oconverse ) ) @ ( D @ ( C @ ( A @ c_Relation_Oconverse ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[329]) ).
thf(370,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( C @ ( B @ c_Relation_ODomain ) ) @ ( A @ c_in ) ) )
| ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1 ) ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__iff_0) ).
thf(1333,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( C @ ( B @ c_Relation_ODomain ) ) @ ( A @ c_in ) ) )
| ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__XDomain__iff__1__1 ) ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(127,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D = E )
| ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
| ( A = B )
| ( B = D )
| ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( E @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__below_8) ).
thf(805,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D = E )
| ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
| ( A = B )
| ( B = D )
| ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( E @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(469,axiom,
! [B: $i,A: $i] : ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__refl_0) ).
thf(1563,plain,
! [B: $i,A: $i] : ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).
thf(301,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( E @ ( D @ c_Wellfounded_Oacc ) @ ( B @ c_in ) ) )
| ~ ( E @ ( E @ tc_prod ) @ ( D @ ( E @ ( E @ ( E @ ( D @ ( A @ c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 ) ) @ ( C @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__induct_1) ).
thf(1187,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( E @ ( D @ c_Wellfounded_Oacc ) @ ( B @ c_in ) ) )
| ~ ( E @ ( E @ tc_prod ) @ ( D @ ( E @ ( E @ ( E @ ( D @ ( A @ c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 ) ) @ ( C @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(449,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( B @ c_in ) ) )
| ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( D @ ( C @ ( B @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__above_0) ).
thf(1515,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( B @ c_in ) ) )
| ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( D @ ( C @ ( B @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[449]) ).
thf(493,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_Relation_Orefl__on ) ) )
| ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( B @ ( B @ ( A @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_Orel__comp ) ) ) ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__comp__subset_0) ).
thf(1616,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_Relation_Orefl__on ) ) )
| ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( B @ ( B @ ( A @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_Orel__comp ) ) ) ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).
thf(193,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( D @ c_Relation_Orefl__on ) ) )
| ~ ( B @ ( D @ ( A @ c_in ) ) )
| ( B @ ( B @ tc_prod ) @ ( C @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__onD_0) ).
thf(953,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( D @ c_Relation_Orefl__on ) ) )
| ~ ( B @ ( D @ ( A @ c_in ) ) )
| ( B @ ( B @ tc_prod ) @ ( C @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(26,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ ( A @ c_Relation_OId__on ) @ c_Relation_ODomain ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__Id__on_0) ).
thf(586,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ ( A @ c_Relation_OId__on ) @ c_Relation_ODomain ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(308,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ c_Relation_Otrans ) )
| ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_transD_0) ).
thf(1202,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ c_Relation_Otrans ) )
| ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[308]) ).
thf(122,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( B @ c_in ) ) )
| ( ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Set_Oinsert ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__right_0) ).
thf(792,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( B @ c_in ) ) )
| ( ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Set_Oinsert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(62,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= B )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__inf_0) ).
thf(662,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= B )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(165,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( D @ c_in ) ) )
| ( ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ ( A @ c_Complete__Lattice_OSup__class_OSup ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
!= ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Union__disjoint_0) ).
thf(888,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( D @ c_in ) ) )
| ( ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ ( A @ c_Complete__Lattice_OSup__class_OSup ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
!= ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(172,axiom,
! [B: $i,A: $i] :
~ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ex__in__conv_0) ).
thf(906,plain,
! [B: $i,A: $i] :
~ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(42,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_COMBK ) ) @ hAPP ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBK__def_0) ).
thf(618,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( B @ ( A @ c_COMBK ) ) @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(521,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( A @ c_in ) ) )
| ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( B @ ( A @ c_Arrow__Order__Mirabelle_Oabove ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_above__Lin_0) ).
thf(1680,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( A @ c_in ) ) )
| ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ ( B @ ( A @ c_Arrow__Order__Mirabelle_Oabove ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).
thf(135,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( D @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( E @ c_Relation_OImage ) ) ) @ ( B @ c_in ) ) )
| ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__singleton__iff_0) ).
thf(824,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( D @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( E @ c_Relation_OImage ) ) ) @ ( B @ c_in ) ) )
| ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(462,axiom,
! [B: $i,A: $i] :
( ~ ( A @ class_Finite__Set_Ofinite_Ofinite )
| ~ ( B @ class_Finite__Set_Ofinite_Ofinite )
| ( B @ ( A @ tc_fun ) @ class_Finite__Set_Ofinite_Ofinite ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Finite__Set_Ofinite_Ofinite) ).
thf(1548,plain,
! [B: $i,A: $i] :
( ~ ( A @ class_Finite__Set_Ofinite_Ofinite )
| ~ ( B @ class_Finite__Set_Ofinite_Ofinite )
| ( B @ ( A @ tc_fun ) @ class_Finite__Set_Ofinite_Ofinite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).
thf(150,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( D @ ( C @ ( B @ c_Relation_ODomain ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DomainI_0) ).
thf(856,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( D @ ( C @ ( B @ c_Relation_ODomain ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(483,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ tc_fun ) @ ( D @ ( C @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( E @ c_COMBK ) ) @ ( B @ c_FuncSet_OPi ) ) ) @ ( A @ c_in ) ) )
| ( tc_bool @ ( D @ tc_fun ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_funcset__image_0) ).
thf(1595,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ tc_fun ) @ ( D @ ( C @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( E @ c_COMBK ) ) @ ( B @ c_FuncSet_OPi ) ) ) @ ( A @ c_in ) ) )
| ( tc_bool @ ( D @ tc_fun ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).
thf(75,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_Relation_Orel__comp ) ) ) ) )
= ( B @ ( A @ c_Transitive__Closure_Ortrancl ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__idemp__self__comp_0) ).
thf(689,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_Relation_Orel__comp ) ) ) ) )
= ( B @ ( A @ c_Transitive__Closure_Ortrancl ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(97,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__inf__iff_1) ).
thf(733,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(276,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( B = D )
| ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
| ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( D @ ( B @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__below_1) ).
thf(1135,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( B = D )
| ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
| ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( D @ ( B @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(507,axiom,
! [B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__empty__left_0) ).
thf(1648,plain,
! [B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[507]) ).
thf(105,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_Relation_Osym ) )
| ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_Osym ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__converse_1) ).
thf(750,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_Relation_Osym ) )
| ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_Osym ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(446,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( F @ c_in ) ) )
| ~ ( tc_bool @ ( E @ ( C @ tc_prod ) @ tc_fun ) @ ( E @ ( C @ ( C @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ c_COMBK ) ) @ ( B @ c_Product__Type_OSigma ) ) ) @ ( E @ ( C @ ( C @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ c_COMBK ) ) @ ( A @ c_Product__Type_OSigma ) ) ) @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Times__subset__cancel2_0) ).
thf(1510,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( F @ c_in ) ) )
| ~ ( tc_bool @ ( E @ ( C @ tc_prod ) @ tc_fun ) @ ( E @ ( C @ ( C @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ c_COMBK ) ) @ ( B @ c_Product__Type_OSigma ) ) ) @ ( E @ ( C @ ( C @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ c_COMBK ) ) @ ( A @ c_Product__Type_OSigma ) ) ) @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(530,axiom,
! [A: $i] :
( ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( A @ c_in ) ) )
| ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ c_Relation_Oconverse ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__in__Lin_1) ).
thf(1698,plain,
! [A: $i] :
( ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( A @ c_in ) ) )
| ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ c_Relation_Oconverse ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).
thf(261,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ c_Wellfounded_Owf ) )
| ( C @ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Wellfounded_Owf ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__Int2_0) ).
thf(1103,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ c_Wellfounded_Owf ) )
| ( C @ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Wellfounded_Owf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(394,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( B @ ( A @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( A = B )
| ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
| ( A = B )
| ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__below_11) ).
thf(1389,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( B @ ( A @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( A = B )
| ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
| ( A = B )
| ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(114,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) )
!= ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__inject_0) ).
thf(772,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) )
!= ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(509,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( E @ ( D @ ( A @ ( C @ c_Relation_OImage ) ) ) @ ( B @ c_in ) ) )
| ( D @ ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__XImageE__1__1 ) ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ImageE_1) ).
thf(1652,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( E @ ( D @ ( A @ ( C @ c_Relation_OImage ) ) ) @ ( B @ c_in ) ) )
| ( D @ ( A @ ( E @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__XImageE__1__1 ) ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).
thf(399,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( A @ ( B @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ( B = A )
| ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
| ( B = A )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__below_5) ).
thf(1403,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( A @ ( B @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ( B = A )
| ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
| ( B = A )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[399]) ).
thf(25,axiom,
! [A: $i] :
( ( A @ ( A @ ( A @ c_Relation_OId @ c_Relation_Oconverse ) ) )
= ( A @ c_Relation_OId ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__Id_0) ).
thf(584,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ c_Relation_OId @ c_Relation_Oconverse ) ) )
= ( A @ c_Relation_OId ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(287,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__greatest_0) ).
thf(1154,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(15,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_Relation_Ototal__on ) ) )
| ( C @ ( C @ ( C @ ( B @ c_Relation_Oconverse ) ) @ ( A @ c_Relation_Ototal__on ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_total__on__converse_1) ).
thf(562,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_Relation_Ototal__on ) ) )
| ( C @ ( C @ ( C @ ( B @ c_Relation_Oconverse ) ) @ ( A @ c_Relation_Ototal__on ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(171,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( D @ ( C @ c_Wellfounded_Oacc ) @ ( B @ c_in ) ) )
| ( D @ ( D @ ( C @ c_Wellfounded_Oacc ) @ ( D @ ( C @ ( A @ c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 ) ) @ c_in ) ) )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__induct__rule_0) ).
thf(904,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( D @ ( C @ c_Wellfounded_Oacc ) @ ( B @ c_in ) ) )
| ( D @ ( D @ ( C @ c_Wellfounded_Oacc ) @ ( D @ ( C @ ( A @ c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 ) ) @ c_in ) ) )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(136,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( E @ ( A @ c_in ) ) )
| ~ ( D @ ( A @ ( F @ hAPP ) @ ( B @ c_in ) ) )
| ( D @ ( C @ tc_prod ) @ ( D @ ( C @ ( F @ ( E @ c_Product__Type_OSigma ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SigmaI_0) ).
thf(826,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( E @ ( A @ c_in ) ) )
| ~ ( D @ ( A @ ( F @ hAPP ) @ ( B @ c_in ) ) )
| ( D @ ( C @ tc_prod ) @ ( D @ ( C @ ( F @ ( E @ c_Product__Type_OSigma ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(87,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( C @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_Oconverse ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__converse_0) ).
thf(711,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( C @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_Oconverse ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(7,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( C @ ( B @ c_Relation_OId @ ( A @ c_Relation_Orel__comp ) ) ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_R__O__Id_0) ).
thf(545,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( C @ ( B @ c_Relation_OId @ ( A @ c_Relation_Orel__comp ) ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(435,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__rtrancl__into__rtrancl_0) ).
thf(1488,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(53,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infE_1) ).
thf(641,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( C @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(443,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
| ~ ( C @ ( D @ ( A @ c_in ) ) )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__iff_0) ).
thf(1503,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
| ~ ( C @ ( D @ ( A @ c_in ) ) )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(516,axiom,
! [C: $i,B: $i,A: $i] : ( B @ ( B @ tc_prod ) @ ( B @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__eq__or__trancl_1) ).
thf(1669,plain,
! [C: $i,B: $i,A: $i] : ( B @ ( B @ tc_prod ) @ ( B @ ( C @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[516]) ).
thf(20,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Set_Oinsert ) ) @ c_Complete__Lattice_OInf__class_OInf ) )
= ( A @ ( A @ ( C @ c_Complete__Lattice_OInf__class_OInf ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Inf__insert_0) ).
thf(572,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Set_Oinsert ) ) @ c_Complete__Lattice_OInf__class_OInf ) )
= ( A @ ( A @ ( C @ c_Complete__Lattice_OInf__class_OInf ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(342,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__absorb2_0) ).
thf(1271,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(88,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__linear_0) ).
thf(713,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(501,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_OInf__class_OInf ) @ ( A @ c_in ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_in ) ) )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_InterD_0) ).
thf(1635,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ c_Complete__Lattice_OInf__class_OInf ) @ ( A @ c_in ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_in ) ) )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).
thf(256,axiom,
tc_bool @ class_Lattices_Olattice,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olattice) ).
thf(1092,plain,
tc_bool @ class_Lattices_Olattice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(255,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( C @ ( B @ c_Relation_ODomain ) ) @ ( A @ c_in ) ) )
| ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__XDomainE__1__1 ) ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DomainE_0) ).
thf(1090,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( C @ ( B @ c_Relation_ODomain ) ) @ ( A @ c_in ) ) )
| ( D @ ( C @ tc_prod ) @ ( B @ ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__XDomainE__1__1 ) ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(83,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( C @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Relation_Orel__comp ) ) ) ) @ c_Relation_Oconverse ) ) )
= ( C @ ( D @ ( E @ ( D @ ( C @ ( A @ c_Relation_Oconverse ) ) @ ( E @ ( D @ ( B @ c_Relation_Oconverse ) ) @ c_Relation_Orel__comp ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__rel__comp_0) ).
thf(704,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( C @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Relation_Orel__comp ) ) ) ) @ c_Relation_Oconverse ) ) )
= ( C @ ( D @ ( E @ ( D @ ( C @ ( A @ c_Relation_Oconverse ) ) @ ( E @ ( D @ ( B @ c_Relation_Oconverse ) ) @ c_Relation_Orel__comp ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(380,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( E @ ( D @ c_Wellfounded_Oacc ) @ ( B @ c_in ) ) )
| ~ ( E @ ( E @ tc_prod ) @ ( D @ ( E @ ( E @ ( E @ ( D @ ( A @ c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 ) ) @ ( C @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__induct__rule_1) ).
thf(1356,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( E @ ( D @ c_Wellfounded_Oacc ) @ ( B @ c_in ) ) )
| ~ ( E @ ( E @ tc_prod ) @ ( D @ ( E @ ( E @ ( E @ ( D @ ( A @ c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__rule__1__1 ) ) @ ( C @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[380]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_Orderings_Obot__class_Obot @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Lattices_Obounded__lattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__bot__right_0) ).
thf(540,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_Orderings_Obot__class_Obot @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Lattices_Obounded__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(38,axiom,
! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_Relation_OId__on ) @ c_Relation_Osym ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__Id__on_0) ).
thf(611,plain,
! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_Relation_OId__on ) @ c_Relation_Osym ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(120,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( F @ tc_prod ) @ ( F @ ( D @ ( A @ ( E @ c_Relation_Oinv__image ) ) ) @ ( F @ ( F @ ( C @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ( D @ ( D @ tc_prod ) @ ( E @ ( D @ ( D @ ( C @ ( A @ hAPP ) @ ( B @ ( A @ hAPP ) @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__inv__image_0) ).
thf(787,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( F @ tc_prod ) @ ( F @ ( D @ ( A @ ( E @ c_Relation_Oinv__image ) ) ) @ ( F @ ( F @ ( C @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ( D @ ( D @ tc_prod ) @ ( E @ ( D @ ( D @ ( C @ ( A @ hAPP ) @ ( B @ ( A @ hAPP ) @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(240,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( C @ ( D @ c_Relation_ODomain ) ) @ ( A @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Not__Domain__rtrancl_0) ).
thf(1058,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( C @ ( D @ c_Relation_ODomain ) ) @ ( A @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(263,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ c_Wellfounded_Owf ) )
| ~ ( C @ ( A @ ( D @ c_in ) ) )
| ( C @ ( A @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__eq__minimal_0) ).
thf(1107,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ c_Wellfounded_Owf ) )
| ~ ( C @ ( A @ ( D @ c_in ) ) )
| ( C @ ( A @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(425,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D = E )
| ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
| ( A = B )
| ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( D @ c_Pair ) ) ) @ c_in ) ) )
| ( B = E )
| ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( E @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__above_10) ).
thf(1464,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D = E )
| ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
| ( A = B )
| ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( D @ c_Pair ) ) ) @ c_in ) ) )
| ( B = E )
| ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( E @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(190,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ ( C @ tc_prod ) @ tc_fun ) @ ( E @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( F @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( F @ ( E @ c_Relation_OImage ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Relation_OImage ) ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__mono_0) ).
thf(947,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ ( C @ tc_prod ) @ tc_fun ) @ ( E @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( F @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( F @ ( E @ c_Relation_OImage ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Relation_OImage ) ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(304,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( t_a @ ( t_a @ ( D @ c_Wellfounded_Oacc ) @ ( B @ c_in ) ) )
| ~ ( t_a @ ( t_a @ tc_prod ) @ ( D @ ( t_a @ ( t_a @ ( D @ ( A @ v_sko__Wellfounded__Xacc__Xinduct__1 ) @ ( C @ c_Pair ) ) ) @ c_in ) ) )
| ( t_a @ ( t_a @ ( D @ c_Wellfounded_Oacc ) @ ( C @ c_in ) ) )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_Oinduct_0) ).
thf(1194,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( t_a @ ( t_a @ ( D @ c_Wellfounded_Oacc ) @ ( B @ c_in ) ) )
| ~ ( t_a @ ( t_a @ tc_prod ) @ ( D @ ( t_a @ ( t_a @ ( D @ ( A @ v_sko__Wellfounded__Xacc__Xinduct__1 ) @ ( C @ c_Pair ) ) ) @ c_in ) ) )
| ( t_a @ ( t_a @ ( D @ c_Wellfounded_Oacc ) @ ( C @ c_in ) ) )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(312,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__subset__iff_1) ).
thf(1209,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(213,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( F @ ( G @ c_Equiv__Relations_Oequiv ) ) )
| ~ ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( F @ ( G @ c_Equiv__Relations_Oquotient ) ) @ ( A @ c_in ) ) )
| ~ ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( F @ ( G @ c_Equiv__Relations_Oquotient ) ) @ ( B @ c_in ) ) )
| ~ ( E @ ( A @ ( C @ c_in ) ) )
| ~ ( E @ ( B @ ( D @ c_in ) ) )
| ~ ( E @ ( E @ tc_prod ) @ ( F @ ( E @ ( E @ ( D @ ( C @ c_Pair ) ) ) @ c_in ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_quotient__eqI_0) ).
thf(996,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( F @ ( G @ c_Equiv__Relations_Oequiv ) ) )
| ~ ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( F @ ( G @ c_Equiv__Relations_Oquotient ) ) @ ( A @ c_in ) ) )
| ~ ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( F @ ( G @ c_Equiv__Relations_Oquotient ) ) @ ( B @ c_in ) ) )
| ~ ( E @ ( A @ ( C @ c_in ) ) )
| ~ ( E @ ( B @ ( D @ c_in ) ) )
| ~ ( E @ ( E @ tc_prod ) @ ( F @ ( E @ ( E @ ( D @ ( C @ c_Pair ) ) ) @ c_in ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(460,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( A = E )
| ( ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
!= ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ c_Set_Oinsert ) ) @ ( D @ c_Set_Oinsert ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_2) ).
thf(1542,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( B = E )
| ( A = E )
| ( ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
!= ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( E @ c_Set_Oinsert ) ) @ ( D @ c_Set_Oinsert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[460]) ).
thf(282,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( A = B )
| ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Omktop ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mktop_5) ).
thf(1144,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( A = B )
| ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Omktop ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(161,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ ( A @ c_COMBK ) ) @ c_Set_Oimage ) ) ) )
= ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__constant__conv_0) ).
thf(880,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ ( B @ ( A @ c_COMBK ) ) @ c_Set_Oimage ) ) ) )
= ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(41,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_Transitive__Closure_Otrancl ) )
= ( B @ ( A @ c_Transitive__Closure_Ortrancl ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__trancl__absorb_0) ).
thf(616,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_Transitive__Closure_Otrancl ) )
= ( B @ ( A @ c_Transitive__Closure_Ortrancl ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(357,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_lessequals ) ) )
| ~ ( B @ ( C @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_predicate1D_0) ).
thf(1307,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_lessequals ) ) )
| ~ ( B @ ( C @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(153,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__into__trancl1_0) ).
thf(863,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(111,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( A @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I3_J_0) ).
thf(764,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( A @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(34,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Transitive__Closure_Ortrancl ) )
= ( B @ ( B @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_Relation_Oconverse ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__converse_0) ).
thf(604,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Transitive__Closure_Ortrancl ) )
= ( B @ ( B @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ c_Relation_Oconverse ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(437,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( C @ ( A @ ( B @ c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1 ) ) @ c_in ) ) )
| ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_OaccI_1) ).
thf(1492,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( C @ ( A @ ( B @ c_ATP__Linkup_Osko__Wellfounded__Xacc__Xintros__1__1 ) ) @ c_in ) ) )
| ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[437]) ).
thf(487,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( D @ tc_prod ) @ ( B @ ( D @ ( D @ ( C @ ( F @ c_Pair ) ) ) @ c_in ) ) )
| ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Recdef_Ocut ) ) ) ) @ hAPP ) )
= ( F @ ( A @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cut__apply_0) ).
thf(1603,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( D @ tc_prod ) @ ( B @ ( D @ ( D @ ( C @ ( F @ c_Pair ) ) ) @ c_in ) ) )
| ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Recdef_Ocut ) ) ) ) @ hAPP ) )
= ( F @ ( A @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).
thf(474,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ c_in ) ) )
| ( D @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__iff_2) ).
thf(1571,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ c_in ) ) )
| ( D @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(389,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( E @ tc_prod ) @ ( D @ ( E @ ( B @ ( F @ c_Product__Type_OSigma ) ) ) @ ( D @ ( E @ ( A @ ( C @ c_Pair ) ) ) @ c_in ) ) )
| ( D @ ( C @ ( B @ hAPP ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SigmaD2_0) ).
thf(1376,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( E @ tc_prod ) @ ( D @ ( E @ ( B @ ( F @ c_Product__Type_OSigma ) ) ) @ ( D @ ( E @ ( A @ ( C @ c_Pair ) ) ) @ c_in ) ) )
| ( D @ ( C @ ( B @ hAPP ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(414,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( C @ c_Pair ) ) ) @ c_in ) ) )
| ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( A @ ( B @ ( D @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( C @ c_Pair ) ) ) @ c_in ) ) )
| ( B = A )
| ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( D @ c_in ) ) )
| ( C = A )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__below_6) ).
thf(1439,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( C @ c_Pair ) ) ) @ c_in ) ) )
| ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( A @ ( B @ ( D @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( C @ c_Pair ) ) ) @ c_in ) ) )
| ( B = A )
| ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( D @ c_in ) ) )
| ( C = A )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(515,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( A @ c_Relation_OId__on ) @ ( B @ c_in ) ) )
| ( C @ ( A @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__XId__onE__1__1 ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Id__onE_0) ).
thf(1667,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( A @ c_Relation_OId__on ) @ ( B @ c_in ) ) )
| ( C @ ( A @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__XId__onE__1__1 ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).
thf(129,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1E_1) ).
thf(811,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(250,axiom,
! [B: $i,A: $i] :
~ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot1E_0) ).
thf(1080,plain,
! [B: $i,A: $i] :
~ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(49,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_2) ).
thf(631,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(151,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_prod ) @ ( F @ ( C @ ( C @ ( A @ ( D @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( F @ ( E @ c_Equiv__Relations_Oequiv ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( F @ ( E @ c_Equiv__Relations_Oquotient ) ) @ ( B @ c_in ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( F @ ( E @ c_Equiv__Relations_Oquotient ) ) @ ( B @ c_in ) ) )
| ~ ( C @ ( B @ ( D @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_quotient__eq__iff_0) ).
thf(858,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_prod ) @ ( F @ ( C @ ( C @ ( A @ ( D @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( F @ ( E @ c_Equiv__Relations_Oequiv ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( F @ ( E @ c_Equiv__Relations_Oquotient ) ) @ ( B @ c_in ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( F @ ( E @ c_Equiv__Relations_Oquotient ) ) @ ( B @ c_in ) ) )
| ~ ( C @ ( B @ ( D @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(3,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infI_0) ).
thf(535,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(37,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_Relation_ORange ) ) )
= ( B @ ( B @ ( A @ c_Relation_ORange ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__range_0) ).
thf(609,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_Relation_ORange ) ) )
= ( B @ ( B @ ( A @ c_Relation_ORange ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(498,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( C @ tc_prod ) @ ( E @ ( C @ ( F @ ( B @ c_Product__Type_OSigma ) ) ) @ ( E @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SigmaD1_0) ).
thf(1630,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( C @ tc_prod ) @ ( E @ ( C @ ( F @ ( B @ c_Product__Type_OSigma ) ) ) @ ( E @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).
thf(366,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( E @ c_Equiv__Relations_Oequiv ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( A @ ( C @ ( C @ ( D @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) @ ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__class__subset_0) ).
thf(1325,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( E @ c_Equiv__Relations_Oequiv ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( A @ ( C @ ( C @ ( D @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) @ ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(198,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( tc_bool @ ( B @ ( A @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Relation_ORange ) ) )
= ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__empty_0) ).
thf(964,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( tc_bool @ ( B @ ( A @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Relation_ORange ) ) )
= ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(391,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ c_Relation_Osym ) )
| ~ ( C @ ( B @ c_Relation_Osym ) )
| ( C @ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Relation_Osym ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__Int_0) ).
thf(1381,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ c_Relation_Osym ) )
| ~ ( C @ ( B @ c_Relation_Osym ) )
| ( C @ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Relation_Osym ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[391]) ).
thf(241,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = E )
| ~ ( C @ ( B @ ( F @ c_in ) ) )
| ( ( C @ ( D @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_COMBK ) ) @ ( A @ c_Product__Type_OSigma ) ) ) )
!= ( C @ ( D @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_COMBK ) ) @ ( E @ c_Product__Type_OSigma ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Times__eq__cancel2_0) ).
thf(1061,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A = E )
| ~ ( C @ ( B @ ( F @ c_in ) ) )
| ( ( C @ ( D @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_COMBK ) ) @ ( A @ c_Product__Type_OSigma ) ) ) )
!= ( C @ ( D @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_COMBK ) ) @ ( E @ c_Product__Type_OSigma ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(290,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( E @ ( A @ c_Set_Oimage ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__mono_0) ).
thf(1162,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( E @ ( A @ c_Set_Oimage ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(94,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ ( A @ c_Relation_OId__on ) @ c_Relation_ORange ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__Id__on_0) ).
thf(726,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ ( A @ c_Relation_OId__on ) @ c_Relation_ORange ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(46,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
| ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__insert_1) ).
thf(626,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
| ( C @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Finite__Set_Ofinite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(176,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__trans_0) ).
thf(915,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(466,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( E @ tc_prod ) @ ( F @ ( G @ ( E @ ( D @ ( C @ c_Relation_Orel__comp ) ) ) ) @ ( F @ ( E @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( G @ ( E @ tc_prod ) @ ( C @ ( G @ ( E @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1 ) ) ) ) ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__compEpair_0) ).
thf(1556,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( E @ tc_prod ) @ ( F @ ( G @ ( E @ ( D @ ( C @ c_Relation_Orel__comp ) ) ) ) @ ( F @ ( E @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( G @ ( E @ tc_prod ) @ ( C @ ( G @ ( E @ ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__Xrel__compEpair__1__1 ) ) ) ) ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[466]) ).
thf(423,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( C @ ( C @ ( C @ ( D @ c_Relation_Oconverse ) ) @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__converseI_0) ).
thf(1460,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( C @ ( C @ ( C @ ( D @ c_Relation_Oconverse ) ) @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(351,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( E @ ( A @ c_in ) ) )
| ~ ( D @ ( A @ ( F @ hAPP ) @ ( B @ c_in ) ) )
| ( D @ ( C @ tc_prod ) @ ( D @ ( C @ ( F @ ( E @ c_Product__Type_OSigma ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__Sigma__iff_2) ).
thf(1293,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( E @ ( A @ c_in ) ) )
| ~ ( D @ ( A @ ( F @ hAPP ) @ ( B @ c_in ) ) )
| ( D @ ( C @ tc_prod ) @ ( D @ ( C @ ( F @ ( E @ c_Product__Type_OSigma ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(64,axiom,
! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_Relation_OId__on ) @ c_Relation_Otrans ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__Id__on_0) ).
thf(668,plain,
! [B: $i,A: $i] : ( B @ ( B @ ( A @ c_Relation_OId__on ) @ c_Relation_Otrans ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(396,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_in ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_Complete__Lattice_OSup__class_OSup ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Union__upper_0) ).
thf(1396,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_in ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_Complete__Lattice_OSup__class_OSup ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(429,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_prod ) @ ( A @ ( C @ ( C @ ( D @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( A @ ( E @ c_Equiv__Relations_Oequiv ) ) )
| ~ ( C @ ( E @ ( B @ c_in ) ) )
| ~ ( C @ ( E @ ( D @ c_in ) ) )
| ( ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) )
!= ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__equiv__class__iff_0) ).
thf(1474,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( C @ tc_prod ) @ ( A @ ( C @ ( C @ ( D @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( A @ ( E @ c_Equiv__Relations_Oequiv ) ) )
| ~ ( C @ ( E @ ( B @ c_in ) ) )
| ~ ( C @ ( E @ ( D @ c_in ) ) )
| ( ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) )
!= ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(196,axiom,
! [B: $i,A: $i] :
( ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__empty__right_0) ).
thf(959,plain,
! [B: $i,A: $i] :
( ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(314,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( A = B )
| ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Omkbot ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mkbot_5) ).
thf(1213,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( A = B )
| ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Omkbot ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(504,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( F @ c_in ) ) )
| ~ ( E @ ( D @ tc_prod ) @ ( B @ ( E @ ( D @ ( A @ ( F @ c_Pair ) ) ) @ c_in ) ) )
| ( E @ ( E @ ( D @ ( C @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__iff_2) ).
thf(1643,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( F @ c_in ) ) )
| ~ ( E @ ( D @ tc_prod ) @ ( B @ ( E @ ( D @ ( A @ ( F @ c_Pair ) ) ) @ c_in ) ) )
| ( E @ ( E @ ( D @ ( C @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[504]) ).
thf(296,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
| ( B = A )
| ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_notin__Lin__iff_0) ).
thf(1176,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
| ( B = A )
| ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(209,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_Set_Oinsert ) ) @ c_Relation_ODomain ) ) )
= ( C @ ( D @ ( C @ ( E @ c_Relation_ODomain ) ) @ ( A @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__insert_0) ).
thf(986,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_Set_Oinsert ) ) @ c_Relation_ODomain ) ) )
= ( C @ ( D @ ( C @ ( E @ c_Relation_ODomain ) ) @ ( A @ c_Set_Oinsert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(412,axiom,
! [B: $i,A: $i] : ( tc_bool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ ( B @ ( tc_bool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__by__empty_0) ).
thf(1435,plain,
! [B: $i,A: $i] : ( tc_bool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ ( B @ ( tc_bool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(430,axiom,
tc_bool @ class_HOL_Oord,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__HOL_Oord) ).
thf(1477,plain,
tc_bool @ class_HOL_Oord,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[430]) ).
thf(331,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ c_Wellfounded_Owf ) )
| ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__wfD_0) ).
thf(1250,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ c_Wellfounded_Owf ) )
| ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(439,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( t_a @ ( t_a @ ( C @ c_Wellfounded_Oacc ) @ ( B @ c_in ) ) )
| ~ ( C @ ( A @ v_sko__Wellfounded__Xacc__Xinduct__1 ) @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_Oinduct_2) ).
thf(1496,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( t_a @ ( t_a @ ( C @ c_Wellfounded_Oacc ) @ ( B @ c_in ) ) )
| ~ ( C @ ( A @ v_sko__Wellfounded__Xacc__Xinduct__1 ) @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(148,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( D @ c_Equiv__Relations_Oequiv ) ) )
| ~ ( C @ ( D @ ( A @ c_in ) ) )
| ( C @ ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__class__self_0) ).
thf(851,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( D @ c_Equiv__Relations_Oequiv ) ) )
| ~ ( C @ ( D @ ( A @ c_in ) ) )
| ( C @ ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(58,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I2_J_0) ).
thf(653,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(60,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_Wellfounded_Owf ) )
| ( B @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_Wellfounded_Owf ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__trancl_0) ).
thf(658,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_Wellfounded_Owf ) )
| ( B @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_Wellfounded_Owf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(175,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( B @ ( C @ c_Equiv__Relations_Oquotient ) ) @ ( A @ c_in ) ) )
| ( A
= ( D @ ( D @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ ( B @ ( A @ ( C @ c_List_Osko__Equiv__Relations__XquotientE__1__1 ) ) ) @ c_Set_Oinsert ) ) @ ( B @ c_Relation_OImage ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_quotientE_0) ).
thf(912,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( B @ ( C @ c_Equiv__Relations_Oquotient ) ) @ ( A @ c_in ) ) )
| ( A
= ( D @ ( D @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ ( B @ ( A @ ( C @ c_List_Osko__Equiv__Relations__XquotientE__1__1 ) ) ) @ c_Set_Oinsert ) ) @ ( B @ c_Relation_OImage ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(294,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( B @ ( C @ c_Arrow__Order__Mirabelle_Omktop ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( A = B )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mktop_4) ).
thf(1171,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( B @ ( C @ c_Arrow__Order__Mirabelle_Omktop ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(51,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= C )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__absorb2_0) ).
thf(636,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= C )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(78,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_Equiv__Relations_Oequiv ) ) )
| ( B @ ( A @ c_Relation_Osym ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv_Osym_0) ).
thf(695,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_Equiv__Relations_Oequiv ) ) )
| ( B @ ( A @ c_Relation_Osym ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(243,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( F @ tc_prod ) @ ( D @ ( F @ ( F @ ( B @ ( E @ hAPP ) @ ( A @ ( E @ hAPP ) @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( C @ ( F @ ( E @ ( D @ c_Relation_Oinv__image ) ) ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__inv__image_1) ).
thf(1066,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( F @ tc_prod ) @ ( D @ ( F @ ( F @ ( B @ ( E @ hAPP ) @ ( A @ ( E @ hAPP ) @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( C @ ( F @ ( E @ ( D @ c_Relation_Oinv__image ) ) ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(454,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( E @ ( B @ c_Equiv__Relations_Oequiv ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( E @ ( C @ ( C @ ( A @ ( D @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__class__eq__iff_2) ).
thf(1528,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( E @ ( B @ c_Equiv__Relations_Oequiv ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( E @ ( C @ ( C @ ( A @ ( D @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).
thf(155,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_in ) ) )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ball__empty_0) ).
thf(868,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_in ) ) )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(528,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( E @ ( B @ c_Relation_Orefl__on ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( E @ ( C @ ( C @ ( A @ ( D @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__onD2_0) ).
thf(1694,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( E @ ( B @ c_Relation_Orefl__on ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( E @ ( C @ ( C @ ( A @ ( D @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).
thf(179,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ c_Wellfounded_Owf ) )
| ~ ( C @ ( A @ ( D @ c_in ) ) )
| ( C @ ( A @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wfE__min_0) ).
thf(922,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ c_Wellfounded_Owf ) )
| ~ ( C @ ( A @ ( D @ c_in ) ) )
| ( C @ ( A @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Wellfounded__XwfE__min__1__1 ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(402,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( D = B )
| ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
| ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( B @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__above_2) ).
thf(1413,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A = D )
| ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( D = B )
| ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
| ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( B @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(231,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( E @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_COMBK ) ) @ ( B @ c_Product__Type_OSigma ) ) ) @ ( E @ c_lessequals ) ) )
| ( A = D )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__subset__Sigma__aux_0) ).
thf(1034,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( E @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_COMBK ) ) @ ( B @ c_Product__Type_OSigma ) ) ) @ ( E @ c_lessequals ) ) )
| ( A = D )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(68,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ ( A @ ( C @ c_Set_Oinsert ) ) @ hAPP ) @ hBOOL )
| ( C = B )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__code_0) ).
thf(675,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( D @ ( A @ ( C @ c_Set_Oinsert ) ) @ hAPP ) @ hBOOL )
| ( C = B )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(513,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singletonE_0) ).
thf(1662,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).
thf(292,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1E_0) ).
thf(1166,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(426,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( t_a @ ( t_a @ ( D @ c_Wellfounded_Oacc ) @ ( B @ c_in ) ) )
| ~ ( t_a @ ( t_a @ tc_prod ) @ ( D @ ( t_a @ ( t_a @ ( D @ ( A @ v_sko__Wellfounded__Xacc__Xinduct__1 ) @ ( C @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_Oinduct_1) ).
thf(1467,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( t_a @ ( t_a @ ( D @ c_Wellfounded_Oacc ) @ ( B @ c_in ) ) )
| ~ ( t_a @ ( t_a @ tc_prod ) @ ( D @ ( t_a @ ( t_a @ ( D @ ( A @ v_sko__Wellfounded__Xacc__Xinduct__1 ) @ ( C @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(181,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D = E )
| ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
| ( A = B )
| ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( E @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__below_14) ).
thf(927,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D = E )
| ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
| ( A = B )
| ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( E @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(344,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( C @ ( A @ ( D @ c_Set_Oinsert ) ) @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_1) ).
thf(1277,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( C @ ( A @ ( D @ c_Set_Oinsert ) ) @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(56,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__antisym_0) ).
thf(648,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(186,axiom,
tc_bool @ class_Lattices_Obounded__lattice,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Obounded__lattice) ).
thf(939,plain,
tc_bool @ class_Lattices_Obounded__lattice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(428,axiom,
! [A: $i] :
( ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Relation_OId__on ) )
= ( tc_bool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Id__on__empty_0) ).
thf(1472,plain,
! [A: $i] :
( ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Relation_OId__on ) )
= ( tc_bool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(223,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( B @ ( A @ c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1 ) @ ( B @ ( A @ c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1 ) @ c_Pair ) ) ) @ c_in ) ) )
| ( B @ ( A @ c_Nitpick_Orefl_H ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Nitpick_Orefl_H__def_1) ).
thf(1018,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ tc_prod ) @ ( A @ ( B @ ( B @ ( B @ ( A @ c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1 ) @ ( B @ ( A @ c_Nitpick_Osko__Nitpick__Xrefl_H__def__1__1 ) @ c_Pair ) ) ) @ c_in ) ) )
| ( B @ ( A @ c_Nitpick_Orefl_H ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(107,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_Equiv__Relations_Oequiv ) ) )
| ( ( B @ ( B @ ( B @ ( A @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_Orel__comp ) ) ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__comp__eq_0) ).
thf(754,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_Equiv__Relations_Oequiv ) ) )
| ( ( B @ ( B @ ( B @ ( A @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_Orel__comp ) ) ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(11,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ c_Orderings_Obot__class_Obot @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Obot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot__least_0) ).
thf(553,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( A @ c_Orderings_Obot__class_Obot @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(236,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ c_COMBK ) ) @ ( A @ c_Product__Type_OSigma ) ) ) @ ( B @ c_lessequals ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( B @ ( C @ ( C @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__Xrefl__onI__1__1 ) ) @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__Xrefl__onI__1__1 ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( B @ ( A @ c_Relation_Orefl__on ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__onI_1) ).
thf(1049,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ c_COMBK ) ) @ ( A @ c_Product__Type_OSigma ) ) ) @ ( B @ c_lessequals ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( B @ ( C @ ( C @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__Xrefl__onI__1__1 ) ) @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__Xrefl__onI__1__1 ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( B @ ( A @ c_Relation_Orefl__on ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(1,negated_conjecture,
! [A: $i] :
( ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( A @ c_in ) ) )
| ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( A @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( v_b @ ( v_a @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(531,plain,
! [A: $i] :
( ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( A @ c_in ) ) )
| ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( A @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( v_b @ ( v_a @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(189,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( D @ tc_prod ) @ ( B @ ( D @ ( D @ ( C @ ( G @ c_Pair ) ) ) @ c_in ) ) )
| ( ( G @ ( A @ hAPP ) )
= ( G @ ( F @ hAPP ) ) )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Recdef_Ocut ) ) ) ) )
!= ( E @ ( D @ ( C @ ( B @ ( F @ c_Recdef_Ocut ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cuts__eq_0) ).
thf(944,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( D @ tc_prod ) @ ( B @ ( D @ ( D @ ( C @ ( G @ c_Pair ) ) ) @ c_in ) ) )
| ( ( G @ ( A @ hAPP ) )
= ( G @ ( F @ hAPP ) ) )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Recdef_Ocut ) ) ) ) )
!= ( E @ ( D @ ( C @ ( B @ ( F @ c_Recdef_Ocut ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(123,axiom,
! [A: $i] :
( ( A @ ( tc_bool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Transitive__Closure_Otrancl ) )
= ( tc_bool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__empty_0) ).
thf(795,plain,
! [A: $i] :
( ( A @ ( tc_bool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Transitive__Closure_Otrancl ) )
= ( tc_bool @ ( A @ ( A @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(70,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_Osym ) )
| ( B @ ( A @ c_Relation_Osym ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__converse_0) ).
thf(680,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_Osym ) )
| ( B @ ( A @ c_Relation_Osym ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(200,axiom,
! [B: $i,A: $i] :
( ~ ( A @ class_Finite__Set_Ofinite_Ofinite )
| ~ ( B @ class_Finite__Set_Ofinite_Ofinite )
| ( B @ ( A @ tc_prod ) @ class_Finite__Set_Ofinite_Ofinite ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_prod__Finite__Set_Ofinite_Ofinite) ).
thf(968,plain,
! [B: $i,A: $i] :
( ~ ( A @ class_Finite__Set_Ofinite_Ofinite )
| ~ ( B @ class_Finite__Set_Ofinite_Ofinite )
| ( B @ ( A @ tc_prod ) @ class_Finite__Set_Ofinite_Ofinite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(298,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ ( C @ tc_prod ) @ tc_fun ) @ ( F @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( E @ ( D @ tc_prod ) @ tc_fun ) @ ( G @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( E @ ( C @ tc_prod ) @ tc_fun ) @ ( E @ ( D @ ( C @ ( G @ ( F @ c_Relation_Orel__comp ) ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Relation_Orel__comp ) ) ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__comp__mono_0) ).
thf(1181,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ ( C @ tc_prod ) @ tc_fun ) @ ( F @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( E @ ( D @ tc_prod ) @ tc_fun ) @ ( G @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( E @ ( C @ tc_prod ) @ tc_fun ) @ ( E @ ( D @ ( C @ ( G @ ( F @ c_Relation_Orel__comp ) ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Relation_Orel__comp ) ) ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(23,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_Relation_Otrans ) )
| ( ( B @ ( A @ c_Transitive__Closure_Otrancl ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__id_0) ).
thf(580,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_Relation_Otrans ) )
| ( ( B @ ( A @ c_Transitive__Closure_Otrancl ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(227,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( B @ ( A @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_r__into__rtrancl_0) ).
thf(1025,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( B @ ( A @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(471,axiom,
tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1 @ c_in ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linear__alt_0) ).
thf(1566,plain,
tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( v_sko__Arrow__Order__Mirabelle__Xlinear__alt__1 @ c_in ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
thf(332,axiom,
tc_bool @ class_Complete__Lattice_Ocomplete__lattice,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Complete__Lattice_Ocomplete__lattice) ).
thf(1252,plain,
tc_bool @ class_Complete__Lattice_Ocomplete__lattice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[332]) ).
thf(340,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( F @ c_in ) ) )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( E @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ ( D @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_COMBK ) ) @ ( E @ c_Product__Type_OSigma ) ) ) @ ( C @ ( D @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_COMBK ) ) @ ( A @ c_Product__Type_OSigma ) ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Times__subset__cancel2_1) ).
thf(1267,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( F @ c_in ) ) )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( E @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ ( C @ ( D @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_COMBK ) ) @ ( E @ c_Product__Type_OSigma ) ) ) @ ( C @ ( D @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_COMBK ) ) @ ( A @ c_Product__Type_OSigma ) ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(259,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Complete__Lattice__XInterI__1__1 ) ) @ ( A @ c_in ) ) )
| ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_Complete__Lattice_OInf__class_OInf ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_InterI_1) ).
thf(1098,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Complete__Lattice__XInterI__1__1 ) ) @ ( A @ c_in ) ) )
| ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_Complete__Lattice_OInf__class_OInf ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(13,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
= ( D @ ( D @ ( C @ ( A @ c_Set_Oinsert ) ) @ ( B @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__commute_0) ).
thf(557,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
= ( D @ ( D @ ( C @ ( A @ c_Set_Oinsert ) ) @ ( B @ c_Set_Oinsert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(216,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_Equiv__Relations_Oequiv ) ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( B @ ( A @ c_Equiv__Relations_Oquotient ) ) @ c_Complete__Lattice_OSup__class_OSup ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Union__quotient_0) ).
thf(1003,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_Equiv__Relations_Oequiv ) ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( B @ ( A @ c_Equiv__Relations_Oquotient ) ) @ c_Complete__Lattice_OSup__class_OSup ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(245,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D = E )
| ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
| ( A = B )
| ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( A = D )
| ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( E @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__below_10) ).
thf(1070,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D = E )
| ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
| ( A = B )
| ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( A = D )
| ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( E @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(157,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ c_COMBK ) ) @ ( A @ c_Product__Type_OSigma ) ) ) @ ( B @ c_lessequals ) ) )
| ( C @ ( A @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__Xrefl__onI__1__1 ) ) @ c_in ) ) )
| ( C @ ( B @ ( A @ c_Relation_Orefl__on ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__onI_0) ).
thf(872,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ c_COMBK ) ) @ ( A @ c_Product__Type_OSigma ) ) ) @ ( B @ c_lessequals ) ) )
| ( C @ ( A @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__Xrefl__onI__1__1 ) ) @ c_in ) ) )
| ( C @ ( B @ ( A @ c_Relation_Orefl__on ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(491,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( E @ c_Equiv__Relations_Oequiv ) ) )
| ~ ( B @ ( E @ ( A @ c_in ) ) )
| ~ ( B @ ( E @ ( D @ c_in ) ) )
| ~ ( B @ ( B @ tc_prod ) @ ( C @ ( B @ ( B @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( ( B @ ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ c_Equiv__Relations_Oquotient ) ) )
= ( B @ ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ c_Equiv__Relations_Oquotient ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__equiv__class__iff2_1) ).
thf(1611,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( E @ c_Equiv__Relations_Oequiv ) ) )
| ~ ( B @ ( E @ ( A @ c_in ) ) )
| ~ ( B @ ( E @ ( D @ c_in ) ) )
| ~ ( B @ ( B @ tc_prod ) @ ( C @ ( B @ ( B @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( ( B @ ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ c_Equiv__Relations_Oquotient ) ) )
= ( B @ ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ c_Equiv__Relations_Oquotient ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).
thf(288,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__left__absorb_0) ).
thf(1156,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(319,axiom,
! [B: $i,A: $i] :
( ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( A @ c_in ) ) )
| ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( B @ ( A @ c_Arrow__Order__Mirabelle_Omktop ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mktop__Lin_0) ).
thf(1225,plain,
! [B: $i,A: $i] :
( ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( A @ c_in ) ) )
| ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( B @ ( A @ c_Arrow__Order__Mirabelle_Omktop ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(398,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( B @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) )
| ( A = D )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertE_0) ).
thf(1400,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( B @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) )
| ( A = D )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(238,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( C @ ( C @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ c_COMBK ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Product__Type_OSigma ) ) ) )
= ( tc_bool @ ( E @ ( C @ tc_prod ) @ tc_fun ) @ ( E @ ( C @ ( C @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ c_COMBK ) ) @ ( B @ c_Product__Type_OSigma ) ) ) @ ( E @ ( C @ ( C @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ c_COMBK ) ) @ ( A @ c_Product__Type_OSigma ) ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Times__Int__distrib1_0) ).
thf(1053,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( C @ ( C @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ c_COMBK ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Product__Type_OSigma ) ) ) )
= ( tc_bool @ ( E @ ( C @ tc_prod ) @ tc_fun ) @ ( E @ ( C @ ( C @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ c_COMBK ) ) @ ( B @ c_Product__Type_OSigma ) ) ) @ ( E @ ( C @ ( C @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ c_COMBK ) ) @ ( A @ c_Product__Type_OSigma ) ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(67,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__inf__iff_0) ).
thf(673,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(90,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( C @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_ODomain ) ) )
= ( C @ ( B @ ( A @ c_Relation_ORange ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__converse_0) ).
thf(717,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( C @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_ODomain ) ) )
= ( C @ ( B @ ( A @ c_Relation_ORange ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(143,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( C @ ( C @ ( D @ c_Relation_Oconverse ) ) @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__converseD_0) ).
thf(840,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( C @ ( C @ ( D @ c_Relation_Oconverse ) ) @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(337,axiom,
! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__lower2_0) ).
thf(1262,plain,
! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(362,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__subset__iff_2) ).
thf(1317,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[362]) ).
thf(253,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
| ~ ( B @ ( C @ c_Finite__Set_Ofinite ) )
| ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__subset_0) ).
thf(1085,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
| ~ ( B @ ( C @ c_Finite__Set_Ofinite ) )
| ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(316,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ tc_prod ) @ ( B @ ( E @ ( D @ ( A @ ( C @ c_Pair ) ) ) @ c_in ) ) )
| ( E @ ( E @ ( D @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__singleton__iff_1) ).
thf(1218,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ tc_prod ) @ ( B @ ( E @ ( D @ ( A @ ( C @ c_Pair ) ) ) @ c_in ) ) )
| ( E @ ( E @ ( D @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[316]) ).
thf(54,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__left__idem_0) ).
thf(643,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(317,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Lattices_Olattice )
| ( B @ ( A @ tc_fun ) @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olattice) ).
thf(1220,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Lattices_Olattice )
| ( B @ ( A @ tc_fun ) @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(354,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ c_in ) ) )
| ( D @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertCI_0) ).
thf(1300,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( A @ c_in ) ) )
| ( D @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(502,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( D @ c_Pair ) ) ) @ c_in ) ) )
| ( D = A )
| ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
| ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( A @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__above_1) ).
thf(1637,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( D @ c_Pair ) ) ) @ c_in ) ) )
| ( D = A )
| ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
| ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( A @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[502]) ).
thf(458,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_in ) ) )
| ~ ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bex__empty_0) ).
thf(1538,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_in ) ) )
| ~ ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).
thf(128,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
= ( tc_bool @ ( C @ ( B @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( ( C @ ( B @ ( A @ c_Relation_ORange ) ) )
!= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__empty__iff_0) ).
thf(808,plain,
! [C: $i,B: $i,A: $i] :
( ( A
= ( tc_bool @ ( C @ ( B @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( ( C @ ( B @ ( A @ c_Relation_ORange ) ) )
!= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(381,axiom,
! [B: $i,A: $i] : ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equalityE_0) ).
thf(1358,plain,
! [B: $i,A: $i] : ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(102,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_Otrans ) )
| ( B @ ( A @ c_Relation_Otrans ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__converse_0) ).
thf(744,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_Otrans ) )
| ( B @ ( A @ c_Relation_Otrans ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(335,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( E @ c_Equiv__Relations_Oequiv ) ) )
| ~ ( C @ ( E @ ( B @ c_in ) ) )
| ~ ( C @ ( E @ ( D @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( A @ ( C @ ( C @ ( D @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ( ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) )
= ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__equiv__class__iff_1) ).
thf(1257,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( E @ c_Equiv__Relations_Oequiv ) ) )
| ~ ( C @ ( E @ ( B @ c_in ) ) )
| ~ ( C @ ( E @ ( D @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( A @ ( C @ ( C @ ( D @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ( ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) )
= ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(348,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( E @ c_in ) ) )
| ( ( B @ ( C @ ( D @ ( C @ ( B @ ( A @ c_COMBK ) ) @ c_Set_Oimage ) ) ) )
= ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__constant_0) ).
thf(1284,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( E @ c_in ) ) )
| ( ( B @ ( C @ ( D @ ( C @ ( B @ ( A @ c_COMBK ) ) @ c_Set_Oimage ) ) ) )
= ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[348]) ).
thf(32,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__greatest_0) ).
thf(600,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(434,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ c_Complete__Lattice_OSup__class_OSup ) )
= B )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sup__singleton_0) ).
thf(1485,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ c_Complete__Lattice_OSup__class_OSup ) )
= B )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(408,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( G @ ( H @ ( F @ c_Equiv__Relations_Oequiv ) ) )
| ~ ( E @ ( D @ ( G @ ( B @ ( A @ ( H @ c_Equiv__Relations_Ocongruent2 ) ) ) ) ) )
| ~ ( G @ ( F @ ( C @ c_in ) ) )
| ( E @ ( D @ ( C @ ( B @ hAPP ) @ ( A @ c_Equiv__Relations_Ocongruent ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_congruent2__implies__congruent_0) ).
thf(1427,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( G @ ( H @ ( F @ c_Equiv__Relations_Oequiv ) ) )
| ~ ( E @ ( D @ ( G @ ( B @ ( A @ ( H @ c_Equiv__Relations_Ocongruent2 ) ) ) ) ) )
| ~ ( G @ ( F @ ( C @ c_in ) ) )
| ( E @ ( D @ ( C @ ( B @ hAPP ) @ ( A @ c_Equiv__Relations_Ocongruent ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(517,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ c_Relation_Oantisym ) )
| ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__def_0) ).
thf(1670,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ c_Relation_Oantisym ) )
| ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).
thf(218,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ c_Finite__Set_Ofinite ) )
| ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Int_0) ).
thf(1008,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ c_Finite__Set_Ofinite ) )
| ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Finite__Set_Ofinite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(39,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( A @ ( B @ ( A @ c_Relation_OId @ c_Relation_Orel__comp ) ) ) ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Id__O__R_0) ).
thf(612,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( A @ ( B @ ( A @ c_Relation_OId @ c_Relation_Orel__comp ) ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(159,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Orderings_Opreorder )
| ( B @ ( A @ tc_fun ) @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Opreorder) ).
thf(876,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Orderings_Opreorder )
| ( B @ ( A @ tc_fun ) @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(279,axiom,
! [B: $i,A: $i] : ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( B @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ ( B @ ( A @ c_Relation_OField ) @ c_COMBK ) ) @ ( B @ ( A @ c_Relation_OField ) @ c_Product__Type_OSigma ) ) ) @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__subset__Field2_0) ).
thf(1141,plain,
! [B: $i,A: $i] : ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( B @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ ( B @ ( A @ c_Relation_OField ) @ c_COMBK ) ) @ ( B @ ( A @ c_Relation_OField ) @ c_Product__Type_OSigma ) ) ) @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(457,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Relation_OImage ) ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__empty_0) ).
thf(1536,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Relation_OImage ) ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(59,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_Relation_Oantisym ) )
| ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_Oantisym ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_antisym__converse_1) ).
thf(656,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_Relation_Oantisym ) )
| ( B @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_Oantisym ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(226,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( C @ tc_fun ) @ ( F @ ( C @ ( E @ ( B @ c_FuncSet_OPi ) ) ) @ ( D @ c_in ) ) )
| ( F @ ( A @ ( E @ hAPP ) @ ( A @ ( D @ hAPP ) @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_PiE_0) ).
thf(1023,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( C @ tc_fun ) @ ( F @ ( C @ ( E @ ( B @ c_FuncSet_OPi ) ) ) @ ( D @ c_in ) ) )
| ( F @ ( A @ ( E @ hAPP ) @ ( A @ ( D @ hAPP ) @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(205,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_HOL_Oord )
| ( B @ ( A @ tc_fun ) @ class_HOL_Oord ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__HOL_Oord) ).
thf(978,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_HOL_Oord )
| ( B @ ( A @ tc_fun ) @ class_HOL_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(278,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( tc_bool @ ( E @ tc_fun ) @ ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( D @ ( C @ ( A @ c_Relation_OImage ) ) ) @ ( E @ ( D @ ( B @ ( A @ c_Relation_OImage ) ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Relation_OImage ) ) ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__Int__subset_0) ).
thf(1140,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( tc_bool @ ( E @ tc_fun ) @ ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( D @ ( C @ ( A @ c_Relation_OImage ) ) ) @ ( E @ ( D @ ( B @ ( A @ c_Relation_OImage ) ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Relation_OImage ) ) ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(388,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( B @ ( A @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( A = B )
| ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
| ( A = B )
| ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__above_11) ).
thf(1372,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( B @ ( A @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( A = B )
| ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
| ( A = B )
| ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(30,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__refl_0) ).
thf(595,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(326,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__trans_0) ).
thf(1240,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(211,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( D @ tc_prod ) @ ( B @ ( D @ ( D @ ( C @ ( F @ c_Pair ) ) ) @ c_in ) ) )
| ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Recdef_Ocut ) ) ) ) @ hAPP ) )
= ( F @ ( A @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tfl__cut__apply_0) ).
thf(991,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( D @ tc_prod ) @ ( B @ ( D @ ( D @ ( C @ ( F @ c_Pair ) ) ) @ c_in ) ) )
| ( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Recdef_Ocut ) ) ) ) @ hAPP ) )
= ( F @ ( A @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(405,axiom,
! [B: $i,A: $i] : ( A @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Relation_Ototal__on ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_total__on__empty_0) ).
thf(1421,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Relation_Ototal__on ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(252,axiom,
! [B: $i,A: $i] : ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__subsetI_0) ).
thf(1084,plain,
! [B: $i,A: $i] : ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(523,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( F @ c_in ) ) )
| ~ ( E @ ( D @ tc_prod ) @ ( B @ ( E @ ( D @ ( A @ ( F @ c_Pair ) ) ) @ c_in ) ) )
| ( E @ ( E @ ( D @ ( C @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__ImageI_0) ).
thf(1685,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( F @ c_in ) ) )
| ~ ( E @ ( D @ tc_prod ) @ ( B @ ( E @ ( D @ ( A @ ( F @ c_Pair ) ) ) @ c_in ) ) )
| ( E @ ( E @ ( D @ ( C @ ( B @ c_Relation_OImage ) ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).
thf(464,axiom,
! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( A @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insertI_0) ).
thf(1553,plain,
! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( A @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(66,axiom,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ ( A @ c_Relation_OId__on ) @ c_Relation_Oconverse ) ) )
= ( B @ ( A @ c_Relation_OId__on ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__Id__on_0) ).
thf(671,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ ( A @ c_Relation_OId__on ) @ c_Relation_Oconverse ) ) )
= ( B @ ( A @ c_Relation_OId__on ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(364,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Lattices_Olattice )
| ( B @ ( A @ tc_fun ) @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Olower__semilattice) ).
thf(1321,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Lattices_Olattice )
| ( B @ ( A @ tc_fun ) @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(510,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( A @ c_in ) ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Set_Oinsert ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__insert__left_0) ).
thf(1654,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( A @ c_in ) ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Set_Oinsert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[510]) ).
thf(271,axiom,
tc_bool @ class_Orderings_Opreorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Opreorder) ).
thf(1126,plain,
tc_bool @ class_Orderings_Opreorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(219,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_in ) ) )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntE_1) ).
thf(1010,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_in ) ) )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(204,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( D @ ( F @ ( E @ ( A @ c_Set_Oimage ) ) ) @ c_lessequals ) ) )
| ~ ( F @ ( E @ ( B @ c_in ) ) )
| ( D @ ( C @ ( B @ ( A @ hAPP ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__subset__iff_0) ).
thf(976,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( D @ ( F @ ( E @ ( A @ c_Set_Oimage ) ) ) @ c_lessequals ) ) )
| ~ ( F @ ( E @ ( B @ c_in ) ) )
| ( D @ ( C @ ( B @ ( A @ hAPP ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(74,axiom,
! [A: $i] : ( A @ ( A @ c_Relation_OId @ c_Relation_Osym ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__Id_0) ).
thf(688,plain,
! [A: $i] : ( A @ ( A @ c_Relation_OId @ c_Relation_Osym ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(315,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__trancl__trancl_0) ).
thf(1216,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[315]) ).
thf(166,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( E @ ( D @ ( A @ ( C @ ( B @ c_FuncSet_Osko__FuncSet__XPi__I_H__1__1 ) ) ) ) @ ( C @ hAPP ) @ ( E @ ( D @ ( A @ ( C @ ( B @ c_FuncSet_Osko__FuncSet__XPi__I_H__1__1 ) ) ) ) @ ( A @ hAPP ) @ c_in ) ) )
| ( E @ ( D @ tc_fun ) @ ( E @ ( D @ ( C @ ( B @ c_FuncSet_OPi ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Pi__I_H_1) ).
thf(891,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( E @ ( D @ ( A @ ( C @ ( B @ c_FuncSet_Osko__FuncSet__XPi__I_H__1__1 ) ) ) ) @ ( C @ hAPP ) @ ( E @ ( D @ ( A @ ( C @ ( B @ c_FuncSet_Osko__FuncSet__XPi__I_H__1__1 ) ) ) ) @ ( A @ hAPP ) @ c_in ) ) )
| ( E @ ( D @ tc_fun ) @ ( E @ ( D @ ( C @ ( B @ c_FuncSet_OPi ) ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(417,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( D @ ( B @ c_Relation_ORange ) ) @ ( A @ c_in ) ) )
| ( C @ ( D @ tc_prod ) @ ( B @ ( C @ ( D @ ( A @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__XRange__iff__1__1 ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__iff_0) ).
thf(1448,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( D @ ( B @ c_Relation_ORange ) ) @ ( A @ c_in ) ) )
| ( C @ ( D @ tc_prod ) @ ( B @ ( C @ ( D @ ( A @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__XRange__iff__1__1 ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(302,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_lessequals ) ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__absorb1_0) ).
thf(1189,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_lessequals ) ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(145,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oimage ) ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__empty_0) ).
thf(844,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oimage ) ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(420,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl_Or__into__trancl_0) ).
thf(1453,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(506,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ c_Wellfounded_Owf ) )
| ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__asym_0) ).
thf(1646,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ c_Wellfounded_Owf ) )
| ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[506]) ).
thf(328,axiom,
! [B: $i,A: $i] :
( ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__absorb_0) ).
thf(1244,plain,
! [B: $i,A: $i] :
( ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[328]) ).
thf(452,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( A = D )
| ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Omkbot ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__mkbot_3) ).
thf(1523,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( A = D )
| ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Omkbot ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(96,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
| ( D @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__imageI_0) ).
thf(731,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
| ( D @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_Finite__Set_Ofinite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(118,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( B @ ( A @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( A = B )
| ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
| ( A = B )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__above_5) ).
thf(781,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( B @ ( A @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( A = B )
| ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(467,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( E @ c_Equiv__Relations_Oequiv ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( A @ ( C @ ( C @ ( D @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ( ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) )
= ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__class__eq_0) ).
thf(1558,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( E @ c_Equiv__Relations_Oequiv ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( A @ ( C @ ( C @ ( D @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ( ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) )
= ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_Relation_OImage ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[467]) ).
thf(27,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ ( B @ ( B @ ( A @ ( A @ c_Relation_Orel__comp ) ) ) ) @ c_Wellfounded_Owf ) )
| ( B @ ( A @ c_Wellfounded_Owf ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__comp__self_1) ).
thf(588,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ ( B @ ( B @ ( A @ ( A @ c_Relation_Orel__comp ) ) ) ) @ c_Wellfounded_Owf ) )
| ( B @ ( A @ c_Wellfounded_Owf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(333,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtrancl__into__trancl2_0) ).
thf(1253,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( E @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( E @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(81,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( B @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__commute_0) ).
thf(699,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( B @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(197,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( A = B )
| ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rtranclD_0) ).
thf(961,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( A = B )
| ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(130,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ hAPP ) @ hBOOL )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_lessequals ) ) )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__predicate1D_0) ).
thf(813,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ hAPP ) @ hBOOL )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_lessequals ) ) )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(393,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( C @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( B @ ( A @ ( D @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( C @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( A = B )
| ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( D @ c_in ) ) )
| ( A = C )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__above_6) ).
thf(1385,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( D @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( C @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( B @ ( A @ ( D @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( C @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( A = B )
| ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( D @ c_in ) ) )
| ( A = C )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(373,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( A @ c_Equiv__Relations_Oquotient ) ) @ ( B @ c_in ) ) )
| ( D @ ( A @ ( D @ ( C @ ( B @ ( A @ c_List_Osko__Equiv__Relations__XquotientE__1__1 ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_quotientE_1) ).
thf(1341,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( A @ c_Equiv__Relations_Oquotient ) ) @ ( B @ c_in ) ) )
| ( D @ ( A @ ( D @ ( C @ ( B @ ( A @ c_List_Osko__Equiv__Relations__XquotientE__1__1 ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[373]) ).
thf(168,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( A @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( D @ c_Pair ) ) ) @ c_in ) ) )
| ( D = A )
| ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
| ( D = B )
| ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( D @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__below_13) ).
thf(896,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( A @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( D @ c_Pair ) ) ) @ c_in ) ) )
| ( D = A )
| ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
| ( D = B )
| ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( D @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(104,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__le1_0) ).
thf(748,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(229,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_Set_Oinsert ) ) @ c_Relation_ORange ) ) )
= ( D @ ( D @ ( C @ ( E @ c_Relation_ORange ) ) @ ( B @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__insert_0) ).
thf(1030,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( C @ ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_Set_Oinsert ) ) @ c_Relation_ORange ) ) )
= ( D @ ( D @ ( C @ ( E @ c_Relation_ORange ) ) @ ( B @ c_Set_Oinsert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(525,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( E @ c_Equiv__Relations_Oequiv ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( D @ c_Relation_OImage ) ) ) @ ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( D @ c_Relation_OImage ) ) ) @ c_lessequals ) ) )
| ~ ( C @ ( E @ ( B @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__equiv__class_0) ).
thf(1689,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( E @ c_Equiv__Relations_Oequiv ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( D @ c_Relation_OImage ) ) ) @ ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( D @ c_Relation_OImage ) ) ) @ c_lessequals ) ) )
| ~ ( C @ ( E @ ( B @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[525]) ).
thf(18,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__inf__iff_2) ).
thf(568,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(248,axiom,
! [A: $i] : ( tc_bool @ ( A @ tc_fun ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__empty_1) ).
thf(1077,plain,
! [A: $i] : ( tc_bool @ ( A @ tc_fun ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(489,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( C @ ( D @ ( A @ c_Set_Oinsert ) ) @ c_lessequals ) ) )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_0) ).
thf(1607,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( C @ ( D @ ( A @ c_Set_Oinsert ) ) @ c_lessequals ) ) )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).
thf(448,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( E @ ( B @ c_Equiv__Relations_Oequiv ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( E @ ( C @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_equiv__class__eq__iff_1) ).
thf(1513,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( E @ ( B @ c_Equiv__Relations_Oequiv ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( E @ ( C @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).
thf(358,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( D @ ( C @ c_Wellfounded_Oacc ) @ ( B @ c_in ) ) )
| ~ ( D @ ( C @ ( A @ c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 ) ) @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__induct_2) ).
thf(1309,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( D @ ( C @ c_Wellfounded_Oacc ) @ ( B @ c_in ) ) )
| ~ ( D @ ( C @ ( A @ c_ATP__Linkup_Osko__Wellfounded__Xacc__induct__1__1 ) ) @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[358]) ).
thf(9,axiom,
! [A: $i] : ( A @ ( A @ c_Relation_OId @ c_Relation_Otrans ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trans__Id_0) ).
thf(549,plain,
! [A: $i] : ( A @ ( A @ c_Relation_OId @ c_Relation_Otrans ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(169,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ tc_prod ) @ ( B @ c_Relation_OId @ ( A @ c_in ) ) )
| ( A
= ( B @ ( B @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__XIdE__1__1 ) @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__XIdE__1__1 ) @ c_Pair ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IdE_0) ).
thf(899,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( B @ tc_prod ) @ ( B @ c_Relation_OId @ ( A @ c_in ) ) )
| ( A
= ( B @ ( B @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__XIdE__1__1 ) @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__XIdE__1__1 ) @ c_Pair ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(512,axiom,
tc_bool @ class_Orderings_Oorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Oorder) ).
thf(1661,plain,
tc_bool @ class_Orderings_Oorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).
thf(139,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B
= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) )
!= ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__is__empty_0) ).
thf(832,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B
= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) )
!= ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(72,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oimage ) ) ) )
= ( E @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__insert_0) ).
thf(684,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oimage ) ) ) )
= ( E @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_Set_Oinsert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(492,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( B @ c_in ) ) )
| ( E @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__eqI_0) ).
thf(1614,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( B @ c_in ) ) )
| ( E @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( B @ ( A @ hAPP ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).
thf(125,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ tc_prod ) @ ( B @ ( D @ ( D @ ( C @ ( E @ ( D @ ( C @ ( B @ ( F @ ( A @ c_List_Osko__Recdef__Xcuts__eq__1__1 ) ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Recdef_Ocut ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ ( F @ c_Recdef_Ocut ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cuts__eq_1) ).
thf(800,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ tc_prod ) @ ( B @ ( D @ ( D @ ( C @ ( E @ ( D @ ( C @ ( B @ ( F @ ( A @ c_List_Osko__Recdef__Xcuts__eq__1__1 ) ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Recdef_Ocut ) ) ) ) )
= ( E @ ( D @ ( C @ ( B @ ( F @ c_Recdef_Ocut ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(267,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( B @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ ( D @ c_COMBK ) ) @ ( C @ c_Product__Type_OSigma ) ) ) @ ( A @ c_lessequals ) ) )
| ( B @ ( C @ ( B @ ( A @ ( D @ ( C @ c_ATP__Linkup_Osko__Wellfounded__XwfI__1__1 ) ) ) @ c_in ) ) )
| ( B @ ( A @ c_Wellfounded_Owf ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wfI_2) ).
thf(1116,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( B @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ ( D @ c_COMBK ) ) @ ( C @ c_Product__Type_OSigma ) ) ) @ ( A @ c_lessequals ) ) )
| ( B @ ( C @ ( B @ ( A @ ( D @ ( C @ c_ATP__Linkup_Osko__Wellfounded__XwfI__1__1 ) ) ) @ c_in ) ) )
| ( B @ ( A @ c_Wellfounded_Owf ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(275,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_in ) ) )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntE_0) ).
thf(1133,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_in ) ) )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(376,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Orderings_Oorder )
| ( B @ ( A @ tc_fun ) @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Orderings_Oorder) ).
thf(1348,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Orderings_Oorder )
| ( B @ ( A @ tc_fun ) @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(106,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Transitive__Closure_Otrancl ) )
= ( B @ ( B @ ( B @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ ( A @ c_Relation_Orel__comp ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__unfold__left_0) ).
thf(752,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Transitive__Closure_Otrancl ) )
= ( B @ ( B @ ( B @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ ( A @ c_Relation_Orel__comp ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(447,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( tc_bool @ ( E @ tc_fun ) @ ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( E @ ( D @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Set_Oimage ) ) ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__Int__subset_0) ).
thf(1512,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( tc_bool @ ( E @ tc_fun ) @ ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( E @ ( D @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Set_Oimage ) ) ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(520,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( E @ ( D @ ( A @ ( C @ ( B @ c_FuncSet_Osko__FuncSet__XPi__I_H__1__1 ) ) ) ) @ c_in ) ) )
| ( E @ ( D @ tc_fun ) @ ( E @ ( D @ ( C @ ( B @ c_FuncSet_OPi ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Pi__I_H_0) ).
thf(1678,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ ( E @ ( D @ ( A @ ( C @ ( B @ c_FuncSet_Osko__FuncSet__XPi__I_H__1__1 ) ) ) ) @ c_in ) ) )
| ( E @ ( D @ tc_fun ) @ ( E @ ( D @ ( C @ ( B @ c_FuncSet_OPi ) ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).
thf(140,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ tc_prod ) @ ( D @ ( C @ ( E @ c_Relation_Oconverse ) ) @ ( C @ ( D @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converseD_0) ).
thf(835,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ tc_prod ) @ ( D @ ( C @ ( E @ c_Relation_Oconverse ) ) @ ( C @ ( D @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ( D @ ( C @ tc_prod ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(321,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ c_Finite__Set_Ofinite ) )
| ~ ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
| ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__finite__subset_0) ).
thf(1229,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ c_Finite__Set_Ofinite ) )
| ~ ( tc_bool @ ( B @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
| ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(496,axiom,
v_a != v_b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_assms_0) ).
thf(1625,plain,
v_a != v_b,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).
thf(132,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( D @ tc_prod ) @ ( D @ ( B @ c_Transitive__Closure_Otrancl ) @ ( D @ ( D @ ( C @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( D @ ( D @ tc_prod ) @ ( B @ ( D @ ( D @ ( D @ ( C @ ( A @ ( B @ c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1 ) ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tranclD_0) ).
thf(818,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( D @ tc_prod ) @ ( D @ ( B @ c_Transitive__Closure_Otrancl ) @ ( D @ ( D @ ( C @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( D @ ( D @ tc_prod ) @ ( B @ ( D @ ( D @ ( D @ ( C @ ( A @ ( B @ c_ATP__Linkup_Osko__Transitive__Closure__XtranclD__1__1 ) ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(482,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( D @ tc_prod ) @ ( D @ ( B @ c_Transitive__Closure_Otrancl ) @ ( D @ ( D @ ( C @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( D @ ( D @ tc_prod ) @ ( D @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( D @ ( D @ ( D @ ( C @ ( A @ ( B @ c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1 ) ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_tranclD2_0) ).
thf(1593,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( D @ tc_prod ) @ ( D @ ( B @ c_Transitive__Closure_Otrancl ) @ ( D @ ( D @ ( C @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( D @ ( D @ tc_prod ) @ ( D @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( D @ ( D @ ( D @ ( C @ ( A @ ( B @ c_ATP__Linkup_Osko__Transitive__Closure__XtranclD2__1__1 ) ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).
thf(330,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ tc_prod ) @ ( E @ ( C @ ( D @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ( D @ ( C @ tc_prod ) @ ( C @ ( D @ ( E @ c_Relation_Oconverse ) ) @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__iff_1) ).
thf(1248,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ tc_prod ) @ ( E @ ( C @ ( D @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ( D @ ( C @ tc_prod ) @ ( C @ ( D @ ( E @ c_Relation_Oconverse ) ) @ ( D @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(98,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( B @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I1_J_0) ).
thf(735,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( B @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(214,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( D @ c_in ) ) )
| ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__downwards__aux_0) ).
thf(999,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( B @ c_Transitive__Closure_Ortrancl ) @ ( C @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( D @ c_in ) ) )
| ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(43,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__le2_0) ).
thf(620,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(284,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ~ ( D @ ( B @ hAPP ) @ hBOOL )
| ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf1I_0) ).
thf(1148,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ~ ( D @ ( B @ hAPP ) @ hBOOL )
| ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(518,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( B @ c_in ) ) )
| ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( D @ ( C @ ( B @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__below_0) ).
thf(1673,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( B @ c_in ) ) )
| ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( D @ ( C @ ( B @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).
thf(154,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( B @ tc_prod ) @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ ( B @ ( B @ ( C @ ( C @ c_Pair ) ) ) @ c_in ) ) )
| ( ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
!= ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_irrefl__tranclI_0) ).
thf(865,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( B @ tc_prod ) @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ ( B @ ( B @ ( C @ ( C @ c_Pair ) ) ) @ c_in ) ) )
| ( ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ c_Transitive__Closure_Ortrancl ) @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
!= ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(432,axiom,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ ( C @ tc_prod ) @ tc_fun ) @ ( D @ ( C @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( H @ c_COMBK ) ) @ ( F @ c_Product__Type_OSigma ) ) ) @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( E @ ( D @ tc_prod ) @ tc_fun ) @ ( E @ ( D @ ( D @ ( tc_bool @ ( E @ tc_fun ) @ ( G @ c_COMBK ) ) @ ( H @ c_Product__Type_OSigma ) ) ) @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( E @ ( C @ tc_prod ) @ tc_fun ) @ ( E @ ( C @ ( C @ ( tc_bool @ ( E @ tc_fun ) @ ( G @ c_COMBK ) ) @ ( F @ c_Product__Type_OSigma ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Relation_Orel__comp ) ) ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__comp__subset__Sigma_0) ).
thf(1480,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ ( C @ tc_prod ) @ tc_fun ) @ ( D @ ( C @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( H @ c_COMBK ) ) @ ( F @ c_Product__Type_OSigma ) ) ) @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( E @ ( D @ tc_prod ) @ tc_fun ) @ ( E @ ( D @ ( D @ ( tc_bool @ ( E @ tc_fun ) @ ( G @ c_COMBK ) ) @ ( H @ c_Product__Type_OSigma ) ) ) @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( E @ ( C @ tc_prod ) @ tc_fun ) @ ( E @ ( C @ ( C @ ( tc_bool @ ( E @ tc_fun ) @ ( G @ c_COMBK ) ) @ ( F @ c_Product__Type_OSigma ) ) ) @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Relation_Orel__comp ) ) ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(16,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I1_J_0) ).
thf(564,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(413,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D = E )
| ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
| ( A = B )
| ( A = E )
| ( B = E )
| ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( E @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__above_4) ).
thf(1436,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D = E )
| ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
| ( A = B )
| ( A = E )
| ( B = E )
| ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( E @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[413]) ).
thf(384,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Complete__Lattice_Ocomplete__lattice )
| ( B @ ( A @ tc_fun ) @ class_Complete__Lattice_Ocomplete__lattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Complete__Lattice_Ocomplete__lattice) ).
thf(1363,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Complete__Lattice_Ocomplete__lattice )
| ( B @ ( A @ tc_fun ) @ class_Complete__Lattice_Ocomplete__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[384]) ).
thf(511,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( A @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( D @ c_Pair ) ) ) @ c_in ) ) )
| ( D = A )
| ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
| ( D = B )
| ( B = D )
| ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__below_7) ).
thf(1657,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( A @ ( D @ ( C @ c_Arrow__Order__Mirabelle_Obelow ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( D @ c_Pair ) ) ) @ c_in ) ) )
| ( D = A )
| ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
| ( D = B )
| ( B = D )
| ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).
thf(371,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
!= ( A @ ( C @ ( B @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__not__insert_0) ).
thf(1335,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
!= ( A @ ( C @ ( B @ c_Set_Oinsert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(468,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( F @ tc_fun ) @ ( D @ ( F @ ( C @ ( E @ c_FuncSet_OPi ) ) ) @ ( A @ c_in ) ) )
| ~ ( F @ ( E @ ( B @ c_in ) ) )
| ( D @ ( B @ ( C @ hAPP ) @ ( B @ ( A @ hAPP ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Pi__mem_0) ).
thf(1561,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( F @ tc_fun ) @ ( D @ ( F @ ( C @ ( E @ c_FuncSet_OPi ) ) ) @ ( A @ c_in ) ) )
| ~ ( F @ ( E @ ( B @ c_in ) ) )
| ( D @ ( B @ ( C @ hAPP ) @ ( B @ ( A @ hAPP ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
thf(137,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ c_Relation_ODomain ) ) @ ( D @ ( C @ ( A @ c_Relation_ODomain ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( D @ ( C @ ( tc_bool @ ( D @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Relation_ODomain ) ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__Int__subset_0) ).
thf(828,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ c_Relation_ODomain ) ) @ ( D @ ( C @ ( A @ c_Relation_ODomain ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( D @ ( C @ ( tc_bool @ ( D @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Relation_ODomain ) ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(194,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ c_Finite__Set_Ofinite ) )
| ~ ( tc_bool @ ( B @ tc_fun ) @ ( B @ ( E @ ( D @ ( C @ c_Set_Oimage ) ) ) @ ( A @ c_lessequals ) ) )
| ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__surj_0) ).
thf(955,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ c_Finite__Set_Ofinite ) )
| ~ ( tc_bool @ ( B @ tc_fun ) @ ( B @ ( E @ ( D @ ( C @ c_Set_Oimage ) ) ) @ ( A @ c_lessequals ) ) )
| ( B @ ( A @ c_Finite__Set_Ofinite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(164,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( E @ ( D @ ( A @ ( C @ ( B @ c_FuncSet_Osko__FuncSet__XPi__I__1__1 ) ) ) ) @ ( C @ hAPP ) @ ( E @ ( D @ ( A @ ( C @ ( B @ c_FuncSet_Osko__FuncSet__XPi__I__1__1 ) ) ) ) @ ( A @ hAPP ) @ c_in ) ) )
| ( E @ ( D @ tc_fun ) @ ( E @ ( D @ ( C @ ( B @ c_FuncSet_OPi ) ) ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Pi__I_1) ).
thf(886,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( E @ ( D @ ( A @ ( C @ ( B @ c_FuncSet_Osko__FuncSet__XPi__I__1__1 ) ) ) ) @ ( C @ hAPP ) @ ( E @ ( D @ ( A @ ( C @ ( B @ c_FuncSet_Osko__FuncSet__XPi__I__1__1 ) ) ) ) @ ( A @ hAPP ) @ c_in ) ) )
| ( E @ ( D @ tc_fun ) @ ( E @ ( D @ ( C @ ( B @ c_FuncSet_OPi ) ) ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(401,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Relation_OId__on ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Id__on__iff_0) ).
thf(1410,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( D @ c_Relation_OId__on ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[401]) ).
thf(112,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Relation_Osym ) )
| ( ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) )
!= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__conv__converse__eq_1) ).
thf(767,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Relation_Osym ) )
| ( ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) )
!= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(324,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
| ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Finite__Set_Ofinite ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_finite__Int_1) ).
thf(1236,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ c_Finite__Set_Ofinite ) )
| ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Finite__Set_Ofinite ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(378,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( t_a @ ( t_a @ ( D @ c_Wellfounded_Oacc ) @ ( B @ c_in ) ) )
| ~ ( t_a @ ( t_a @ tc_prod ) @ ( D @ ( t_a @ ( t_a @ ( D @ ( A @ v_sko__Wellfounded__Xacc__Xinducts__1 ) @ ( C @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc_Oinducts_1) ).
thf(1352,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( t_a @ ( t_a @ ( D @ c_Wellfounded_Oacc ) @ ( B @ c_in ) ) )
| ~ ( t_a @ ( t_a @ tc_prod ) @ ( D @ ( t_a @ ( t_a @ ( D @ ( A @ v_sko__Wellfounded__Xacc__Xinducts__1 ) @ ( C @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( A @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(273,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
= ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( B @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_doubleton__eq__iff_4) ).
thf(1129,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Oinsert ) ) )
= ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( B @ c_Set_Oinsert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(21,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_Orderings_Obot__class_Obot @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Lattices_Obounded__lattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__bot__left_0) ).
thf(575,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_Orderings_Obot__class_Obot @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Lattices_Obounded__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(286,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( D @ ( tc_bool @ ( C @ ( B @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Relation_Orel__comp ) ) ) ) )
= ( tc_bool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rel__comp__empty2_0) ).
thf(1152,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( D @ ( tc_bool @ ( C @ ( B @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Relation_Orel__comp ) ) ) ) )
= ( tc_bool @ ( C @ ( D @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(390,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( C @ c_Relation_OId @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pair__in__Id__conv_0) ).
thf(1378,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( C @ c_Relation_OId @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[390]) ).
thf(478,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__trans_0) ).
thf(1582,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[478]) ).
thf(463,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ c_Complete__Lattice_OInf__class_OInf ) )
= B )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Inf__singleton_0) ).
thf(1550,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ c_Complete__Lattice_OInf__class_OInf ) )
= B )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(173,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( D @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( B @ ( C @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_acc__downward_0) ).
thf(908,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( D @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( B @ ( C @ ( C @ ( D @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ ( B @ c_Wellfounded_Oacc ) @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(134,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ c_in ) ) )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_0) ).
thf(822,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ ( B @ c_in ) ) )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(76,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( C @ ( B @ c_Relation_Oconverse ) ) @ ( A @ c_Relation_Ototal__on ) ) )
| ( C @ ( B @ ( A @ c_Relation_Ototal__on ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_total__on__converse_0) ).
thf(691,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ ( C @ ( B @ c_Relation_Oconverse ) ) @ ( A @ c_Relation_Ototal__on ) ) )
| ( C @ ( B @ ( A @ c_Relation_Ototal__on ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(36,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( A @ c_Relation_OId @ c_Relation_OImage ) ) ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__Id_0) ).
thf(607,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( A @ c_Relation_OId @ c_Relation_OImage ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(257,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( C @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ c_Relation_Oconverse ) ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( C @ ( C @ ( C @ ( D @ c_Relation_Oconverse ) ) @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_trancl__converseI_0) ).
thf(1093,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( C @ tc_prod ) @ ( C @ ( C @ ( C @ ( D @ c_Transitive__Closure_Otrancl ) @ c_Relation_Oconverse ) ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( C @ ( C @ ( C @ ( D @ c_Relation_Oconverse ) ) @ c_Transitive__Closure_Otrancl ) @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(45,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ c_Relation_Osym ) )
| ( D @ ( D @ ( C @ ( B @ ( A @ c_Relation_Oinv__image ) ) ) @ c_Relation_Osym ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__inv__image_0) ).
thf(624,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( A @ c_Relation_Osym ) )
| ( D @ ( D @ ( C @ ( B @ ( A @ c_Relation_Oinv__image ) ) ) @ c_Relation_Osym ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(142,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Relation_ORange ) ) @ ( D @ ( C @ ( A @ c_Relation_ORange ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( D @ ( C @ ( tc_bool @ ( D @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Relation_ORange ) ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Range__Int__subset_0) ).
thf(839,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Relation_ORange ) ) @ ( D @ ( C @ ( A @ c_Relation_ORange ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( D @ ( C @ ( tc_bool @ ( D @ ( C @ tc_prod ) @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Relation_ORange ) ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(95,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__assoc_0) ).
thf(728,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(100,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( D @ ( C @ ( B @ ( A @ c_Relation_Oinv__image ) ) ) @ c_Relation_Oconverse ) ) )
= ( D @ ( C @ ( B @ ( C @ ( C @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_Oinv__image ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__inv__image_0) ).
thf(740,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( D @ ( D @ ( C @ ( B @ ( A @ c_Relation_Oinv__image ) ) ) @ c_Relation_Oconverse ) ) )
= ( D @ ( C @ ( B @ ( C @ ( C @ ( A @ c_Relation_Oconverse ) ) @ c_Relation_Oinv__image ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(441,axiom,
! [B: $i,A: $i] : ( B @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Relation_Osym ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__Int__converse_0) ).
thf(1500,plain,
! [B: $i,A: $i] : ( B @ ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( B @ ( A @ c_Relation_Oconverse ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Relation_Osym ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[441]) ).
thf(93,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( A @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__left__commute_0) ).
thf(723,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( A @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(484,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ ( tc_bool @ ( B @ ( A @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Relation_ODomain ) ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Domain__empty_0) ).
thf(1597,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ( tc_bool @ ( B @ ( A @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Relation_ODomain ) ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).
thf(207,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
| ~ ( C @ ( D @ ( A @ c_in ) ) )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__mp_0) ).
thf(982,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
| ~ ( C @ ( D @ ( A @ c_in ) ) )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(410,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__mono_0) ).
thf(1431,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(444,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
| ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Lin__irrefl_0) ).
thf(1505,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
| ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(495,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( D @ ( A @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( A = D )
| ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
| ( A = B )
| ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_in__above_12) ).
thf(1621,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( D @ ( A @ ( C @ c_Arrow__Order__Mirabelle_Oabove ) ) @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ( A = D )
| ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( C @ c_in ) ) )
| ( A = B )
| ~ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ ( C @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).
thf(126,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__commute_0) ).
thf(803,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(184,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( A @ c_in ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__rev__mp_0) ).
thf(935,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( A @ c_in ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(300,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_lessequals ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__eq__subset_2) ).
thf(1184,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_lessequals ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[300]) ).
thf(6,axiom,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_Relation_Osym ) )
| ( B @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_Relation_Osym ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__trancl_0) ).
thf(543,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ c_Relation_Osym ) )
| ( B @ ( B @ ( A @ c_Transitive__Closure_Otrancl ) @ c_Relation_Osym ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(403,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( F @ tc_fun ) @ ( D @ ( F @ ( F @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ c_COMBK ) ) @ ( E @ c_FuncSet_OPi ) ) ) @ ( A @ c_in ) ) )
| ~ ( F @ ( E @ ( B @ c_in ) ) )
| ( D @ ( C @ ( B @ ( A @ hAPP ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_funcset__mem_0) ).
thf(1416,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( F @ tc_fun ) @ ( D @ ( F @ ( F @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ c_COMBK ) ) @ ( E @ c_FuncSet_OPi ) ) ) @ ( A @ c_in ) ) )
| ~ ( F @ ( E @ ( B @ c_in ) ) )
| ( D @ ( C @ ( B @ ( A @ hAPP ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[403]) ).
thf(52,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__infE_0) ).
thf(639,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(309,axiom,
tc_bool @ class_Lattices_Olower__semilattice,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olower__semilattice) ).
thf(1204,plain,
tc_bool @ class_Lattices_Olower__semilattice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(85,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__eq__iff_0) ).
thf(708,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(162,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( E @ ( C @ ( B @ ( D @ c_Set_Oimage ) ) ) @ ( A @ ( D @ hAPP ) @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__image__eqI_0) ).
thf(882,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( E @ ( C @ ( B @ ( D @ c_Set_Oimage ) ) ) @ ( A @ ( D @ hAPP ) @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(369,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Product__Type_OSigma ) ) ) )
= ( tc_bool @ ( C @ ( A @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sigma__empty1_0) ).
thf(1331,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Product__Type_OSigma ) ) ) )
= ( tc_bool @ ( C @ ( A @ tc_prod ) @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(488,axiom,
! [B: $i,A: $i] : ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( B @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ ( A @ c_COMBK ) ) @ ( A @ c_Product__Type_OSigma ) ) ) @ ( B @ ( A @ c_Relation_OId__on ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Id__on__subset__Times_0) ).
thf(1606,plain,
! [B: $i,A: $i] : ( tc_bool @ ( B @ ( B @ tc_prod ) @ tc_fun ) @ ( B @ ( B @ ( B @ ( tc_bool @ ( B @ tc_fun ) @ ( A @ c_COMBK ) ) @ ( A @ c_Product__Type_OSigma ) ) ) @ ( B @ ( A @ c_Relation_OId__on ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).
thf(386,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( E @ ( D @ ( A @ ( C @ c_Relation_OImage ) ) ) @ ( B @ c_in ) ) )
| ( E @ ( D @ tc_prod ) @ ( C @ ( E @ ( D @ ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__XImage__iff__1__1 ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Image__iff_1) ).
thf(1367,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( E @ ( D @ ( A @ ( C @ c_Relation_OImage ) ) ) @ ( B @ c_in ) ) )
| ( E @ ( D @ tc_prod ) @ ( C @ ( E @ ( D @ ( B @ ( E @ ( D @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__XImage__iff__1__1 ) ) ) ) @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[386]) ).
thf(187,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_1) ).
thf(940,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(436,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ tc_prod ) @ ( B @ ( C @ c_Transitive__Closure_Otrancl ) @ ( B @ ( B @ ( B @ ( C @ c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1 ) @ ( B @ ( C @ c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1 ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( B @ ( B @ tc_prod ) @ ( C @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_irrefl__trancl__rD_0) ).
thf(1490,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ tc_prod ) @ ( B @ ( C @ c_Transitive__Closure_Otrancl ) @ ( B @ ( B @ ( B @ ( C @ c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1 ) @ ( B @ ( C @ c_ATP__Linkup_Osko__Transitive__Closure__Xirrefl__trancl__rD__1__1 ) @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( B @ ( B @ tc_prod ) @ ( C @ ( B @ ( B @ ( A @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(232,axiom,
! [A: $i] :
( ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ c_Relation_Oconverse ) ) @ c_in ) ) )
| ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_converse__in__Lin_0) ).
thf(1037,plain,
! [A: $i] :
( ~ ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( A @ c_Relation_Oconverse ) ) @ c_in ) ) )
| ( tc_bool @ ( tc_Arrow__Order__Mirabelle_Oalt @ ( tc_Arrow__Order__Mirabelle_Oalt @ tc_prod ) @ tc_fun ) @ ( c_Arrow__Order__Mirabelle_OLin @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(115,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ c_Relation_Osym ) )
| ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sym__def_0) ).
thf(775,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ c_Relation_Osym ) )
| ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( A @ ( B @ c_Pair ) ) ) @ c_in ) ) )
| ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( B @ ( A @ c_Pair ) ) ) @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(221,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ c_Wellfounded_Owf ) )
| ~ ( C @ ( B @ ( E @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( C @ ( D @ ( B @ c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_wf__eq__minimal_1) ).
thf(1014,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ c_Wellfounded_Owf ) )
| ~ ( C @ ( B @ ( E @ c_in ) ) )
| ~ ( C @ ( C @ tc_prod ) @ ( D @ ( C @ ( C @ ( C @ ( D @ ( B @ c_ATP__Linkup_Osko__Wellfounded__Xwf__eq__minimal__1__1 ) ) @ ( A @ c_Pair ) ) ) @ c_in ) ) )
| ~ ( C @ ( B @ ( A @ c_in ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(202,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ c_COMBK ) ) @ ( A @ c_Product__Type_OSigma ) ) ) @ ( B @ c_lessequals ) ) )
| ( C @ ( A @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__Xrefl__on__def__1__1 ) ) @ c_in ) ) )
| ( C @ ( B @ ( A @ c_Relation_Orefl__on ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_refl__on__def_2) ).
thf(972,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ ( C @ tc_prod ) @ tc_fun ) @ ( C @ ( C @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ c_COMBK ) ) @ ( A @ c_Product__Type_OSigma ) ) ) @ ( B @ c_lessequals ) ) )
| ( C @ ( A @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Relation__Xrefl__on__def__1__1 ) ) @ c_in ) ) )
| ( C @ ( B @ ( A @ c_Relation_Orefl__on ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(1771,plain,
$false,
inference(e,[status(thm)],[1665,1469,1369,1105,846,628,893,1315,1179,1295,1586,1501,1168,760,777,555,1554,1110,1211,1290,1068,1443,1618,994,1073,1205,1591,878,1533,1158,762,1422,1569,1142,1269,614,1692,1305,597,1041,861,1078,533,550,715,1327,1640,1354,1164,797,1260,698,1507,1222,930,1196,1001,1127,1576,1046,1359,1482,651,829,1095,1650,1645,1518,1265,1628,1055,1287,570,1298,719,785,1323,1455,1462,949,917,702,1313,1279,1545,902,559,853,1087,1147,1609,606,770,1398,1494,1100,1319,870,924,1302,789,1450,1418,646,937,966,1051,1109,1632,1383,1020,1183,1283,602,634,1526,660,1433,1201,1600,1521,1696,1564,1345,988,1242,849,920,942,678,1691,1199,1338,1311,1274,910,957,746,1343,1021,952,1580,1255,1123,820,815,1238,1174,1676,693,630,566,1032,1365,665,583,1027,757,1281,1634,710,842,1012,1687,1457,682,1407,1573,974,1350,1121,1064,1227,1425,1138,593,1118,742,578,697,1234,874,1143,980,1498,1540,1006,1567,1683,1082,1361,933,537,669,1584,1446,547,706,884,1329,686,1075,1016,1207,590,1039,970,1114,1263,1530,1231,1131,1192,984,721,1429,779,1393,622,837,1150,1478,1451,738,1599,1246,1333,805,1563,1187,1515,1616,953,586,1202,792,662,888,906,618,1680,824,1548,856,1595,689,733,1135,1648,750,1510,1698,1103,1389,772,1652,1403,584,1154,562,904,826,711,545,1488,641,1503,1669,572,1271,713,1635,1092,1090,704,1356,540,611,787,1058,1107,1464,947,1194,1209,996,1542,1144,880,616,1307,863,764,604,1492,1603,1571,1376,1439,1667,811,1080,631,858,535,609,1630,1325,964,1381,1061,1162,726,626,915,1556,1460,1293,668,1396,1474,959,1213,1643,1176,986,1435,1477,1250,1496,851,653,658,912,1171,636,695,1066,1528,868,1694,922,1413,1034,675,1662,1166,1467,927,1277,648,939,1472,1018,754,553,1049,531,944,795,680,968,1181,580,1025,1566,1252,1267,1098,557,1003,1070,872,1611,1156,1225,1400,1053,673,717,840,1262,1317,1085,1218,643,1220,1300,1637,1538,808,1358,744,1257,1284,600,1485,1427,1670,1008,612,876,1141,1536,656,1023,978,1140,1372,595,1240,991,1421,1084,1685,1553,671,1321,1654,1126,1010,976,688,1216,891,1448,1189,844,1453,1646,1244,1523,731,781,1558,588,1253,699,961,813,1385,1341,896,748,1030,1689,568,1077,1607,1513,1309,549,899,1661,832,684,1614,800,1116,1133,1348,752,1512,1678,835,1229,1625,818,1593,1248,735,999,620,1148,1673,865,1480,564,1436,1363,1657,1335,1561,828,955,886,1410,767,1236,1352,1129,575,1152,1378,1582,1550,908,822,691,607,1093,624,839,728,740,1500,723,1597,982,1431,1505,1621,803,935,1184,543,1416,639,1204,708,882,1331,1606,1367,940,1490,1037,775,1014,972]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SCT026-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.14/0.41 % Computer : n026.cluster.edu
% 0.14/0.41 % Model : x86_64 x86_64
% 0.14/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.41 % Memory : 8046.5625MB
% 0.14/0.41 % OS : Linux 6.8.0-71-generic
% 0.14/0.42 % CPULimit : 300
% 0.14/0.42 % WCLimit : 300
% 0.14/0.42 % DateTime : Sat Sep 26 06:22:40 UTC 2026
% 0.14/0.42 % CPUTime :
% 0.14/0.42 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 1.25/1.25 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.98/1.82 % [INFO] Parsing done (564ms).
% 2.98/1.84 % [INFO] Running in sequential loop mode.
% 4.24/2.41 % [INFO] eprover registered as external prover.
% 4.24/2.42 % [INFO] Scanning for conjecture ...
% 5.12/2.72 % [INFO] Found a conjecture (or negated_conjecture) and 531 axioms. Running axiom selection ...
% 6.61/3.06 % [INFO] Axiom selection finished. Selected 529 axioms (removed 2 axioms).
% 8.34/3.51 % [INFO] Problem is propositional (TPTP CNF).
% 8.34/3.55 % [INFO] Type checking passed.
% 8.34/3.56 % [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 ...
% 23.72/7.00 % External prover 'e' found a proof!
% 23.72/7.01 % [INFO] Killing All external provers ...
% 23.72/7.01 % Time passed: 6381ms (effective reasoning time: 5155ms)
% 23.72/7.01 % Axioms used in derivation (529): clsarity_fun__Lattices_Olower__semilattice, cls_trancl__converseD_0, cls_inf__sup__aci_I2_J_0, cls_wfI_3, cls_in__mktop_1, cls_subset__insert_1, cls_rtrancl__idemp_0, cls_sym__conv__converse__eq_1, cls_cuts__eq_1, cls_PiE_0, cls_Int__absorb2_0, cls_sym__Int__converse_0, cls_Inter__lower_0, cls_equiv__class__eq__iff_0, cls_image__constant_0, cls_in__above_11, cls_insertE_0, cls_congruent_Ocongruent_0, cls_Pi__I_0, cls_wf__subset_0, cls_insert__inter__insert_0, cls_rtrancl__converseD_0, cls_in__below_14, cls_order__eq__iff_0, cls_total__on__def_0, cls_converseI_0, cls_InterI_1, cls_equalityI_0, cls_Id__onE_0, cls_funcsetI_0, cls_subset__image__iff_2, cls_trancl__subset__Sigma__aux_0, cls_finite__insert_0, cls_funcset__image_0, cls_empty__is__image_1, cls_insert__code_1, cls_wfE__min_0, cls_le__funD_0, cls_subset__empty_1, cls_Pi__mem_0, cls_rel__comp__empty1_0, cls_Image__singleton__iff_0, cls_image__mono_0, cls_tranclD2_0, cls_assms_0, clsarity_bool__Lattices_Olower__semilattice, cls_Int__mono_0, cls_le__iff__inf_1, cls_finite__Inter_0, cls_acc_Oinduct_2, clsarity_fun__Orderings_Oorder, cls_COMBK__def_0, cls_acc__wfD_0, cls_in__below_3, cls_tranclD_0, cls_Id__O__R_0, cls_mkbot__Lin_0, cls_Range__def_0, cls_Id__on__eqI_0, cls_Sigma__empty1_0, cls_Int__insert__left_0, cls_comp__equivI_0, cls_empty__iff_0, cls_in__above_7, cls_le__inf__iff_1, cls_rtrancl__trans_0, cls_mem__def_1, cls_wf__inv__image_0, cls_Inf__lower_0, cls_insert__absorb_0, cls_equiv__class__self_0, cls_Int__subset__iff_2, cls_in__below_2, cls_Domain__iff_0, cls_wf__no__loop_0, cls_inf1E_1, cls_in__mkbot_4, cls_Domain__empty_0, cls_insert__iff_1, cls_insert__subset_0, cls_wf__empty_0, cls_Int__absorb1_0, cls_in__above_4, cls_Field__converse_0, cls_antisymD_0, cls_refl__on__converse_0, cls_in__below_7, cls_set__rev__mp_0, cls_inf__left__commute_0, cls_Range__empty__iff_0, cls_Times__subset__cancel2_1, cls_acc_Oinducts_0, cls_congruent2_Ocongruent2_0, cls_inf__commute_0, cls_trans__converse_1, cls_DomainE_0, cls_subset__insert__iff_2, cls_Range__Id__on_0, cls_refl__on__Id__on_0, cls_rtrancl__trancl__absorb_0, clsarity_bool__Finite__Set_Ofinite_Ofinite, cls_rtrancl__into__trancl1_0, cls_finite__insert_1, cls_trancl__subset__Field2_0, clsarity_bool__HOL_Oord, cls_set__mp_0, cls_cut__apply_0, cls_Pi__I_H_1, cls_wf__converse__trancl_0, cls_wfI_2, cls_finite__Int_1, cls_Int__empty__right_0, cls_trans__Int_0, cls_Image__iff_0, cls_in__below_11, cls_sym__Id__on_0, cls_sym__Id_0, cls_equiv__class__eq__iff_3, cls_Inf__singleton_0, cls_rtrancl__mono_0, cls_Inf__binary_0, cls_Union__disjoint_0, cls_rel__compEpair_0, cls_antisym__converse_0, cls_Image__subset_0, cls_wf__insert_0, cls_empty__is__image_0, cls_converse__rtrancl__into__rtrancl_0, cls_wfE__min_1, cls_rev__image__eqI_0, cls_Image__empty_0, cls_eq__equiv__class__iff2_1, clsarity_fun__Orderings_Obot, cls_Image__iff_1, cls_in__mktop_3, cls_Sigma__empty2_0, cls_order__eq__refl_0, cls_in__below_9, cls_insert__ident_0, cls_wf__acc__iff_1, cls_sym__trancl_0, cls_cuts__eq_0, cls_acc__wfI_0, cls_SigmaI_0, cls_Union__upper_0, cls_finite__Int_0, cls_trancl__into__trancl2_0, cls_trancl__empty_0, cls_notin__Lin__iff_0, cls_less__by__empty_0, cls_image__constant__conv_1, cls_Image__Id__on_0, cls_Range__converse_0, cls_refl__on__empty_0, cls_r__into__trancl_H_0, clsarity_bool__Orderings_Oorder, cls_bot__least_0, cls_rtrancl__eq__or__trancl_0, cls_in__above_6, cls_Range__Int__subset_0, cls_antisym__Id__on_0, cls_Int__insert__right_1, cls_r__r__into__trancl_0, cls_wf__trancl_0, cls_rtrancl__converse_0, cls_Sup__singleton_0, cls_trans__rtrancl_0, cls_refl__on__def_1, cls_in__below_6, cls_RangeE_0, cls_Range__def__raw_0, cls_Lin__irrefl_0, cls_not__acc__down_1, cls_finite_0, cls_subset__iff_0, cls_insert__code_2, cls_wf__comp__self_0, cls_trans__O__subset_0, clsarity_fun__HOL_Oord, cls_subset__empty_0, cls_in__mkbot_3, cls_equiv__class__eq_0, cls_rev__predicate1D_0, cls_singleton__iff_1, cls_r__comp__rtrancl__eq_0, cls_sym__converse_1, cls_wf__eq__minimal_0, cls_image__insert_0, cls_equiv_Otrans_0, cls_acc__downwards__aux_0, cls_wf__comp__self_1, cls_tranclD_1, cls_Range__iff_0, cls_acc__induct_2, cls_inf__sup__ord_I2_J_0, cls_doubleton__eq__iff_2, clsarity_fun__Finite__Set_Ofinite_Ofinite, cls_Range__iff_1, cls_Domain__Int__subset_0, cls_inf__absorb2_0, cls_Inf__insert_0, cls_pair__in__Id__conv_0, cls_wf__irrefl_0, cls_Id__on__iff_0, cls_ex__in__conv_0, cls_IdE_0, cls_finite__surj_0, cls_SigmaD2_0, cls_inf__sup__aci_I3_J_0, cls_set__eq__subset_2, cls_Int__insert__left_1, cls_insert__subset_1, cls_Int__empty__left_0, cls_Image__singleton__iff_1, cls_Range__insert_0, cls_sym__inv__image_0, cls_trancl__domain_0, cls_converse__Id__on_0, cls_le__inf__iff_0, cls_Int__subset__iff_1, cls_linorder__linear_0, cls_irrefl__tranclI_0, clsarity_prod__Finite__Set_Ofinite_Ofinite, cls_in__above_1, cls_DomainI_0, clsarity_fun__Lattices_Olattice, cls_in__below_10, 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% 23.72/7.01 % No. of inferences in proof: 1061
% 23.72/7.01 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 6381 ms resp. 5155 ms w/o parsing
% 25.78/7.33 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 25.78/7.34 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------