%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWV857-1 : 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 09:00:48 AM UTC 2026
% Result : Unsatisfiable 25.96s 7.25s
% Output : Refutation 28.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 2
% Number of leaves : 579
% Syntax : Number of formulae : 1159 ( 301 unt; 0 typ; 0 def)
% Number of atoms : 2615 ( 614 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 18138 (1374 ~;1456 |; 0 &;15308 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 69 ( 67 usr; 8 con; 0-5 aty)
% Number of variables : 3892 ( 0 ^;3892 !; 0 ?;3892 :)
% Comments :
%------------------------------------------------------------------------------
thf(c_lessequals_decl,type,
c_lessequals: $i > $i > $i > $o ).
thf(v_tsa_decl,type,
v_tsa: $i ).
thf(v_Ga_decl,type,
v_Ga: $i ).
thf(tc_fun_decl,type,
tc_fun: $i > $i > $i ).
thf(tc_Hoare__Mirabelle_Otriple_decl,type,
tc_Hoare__Mirabelle_Otriple: $i > $i ).
thf(t_a_decl,type,
t_a: $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_in_decl,type,
c_in: $i > $i ).
thf(v_xa_decl,type,
v_xa: $i ).
thf(c_Hoare__Mirabelle_Otriple__valid_decl,type,
c_Hoare__Mirabelle_Otriple__valid: $i > $i > $i > $o ).
thf(v_x_decl,type,
v_x: $i ).
thf(class_Orderings_Oorder_decl,type,
class_Orderings_Oorder: $i > $o ).
thf(tc_nat_decl,type,
tc_nat: $i ).
thf(class_Lattices_Odistrib__lattice_decl,type,
class_Lattices_Odistrib__lattice: $i > $o ).
thf(class_Orderings_Opreorder_decl,type,
class_Orderings_Opreorder: $i > $o ).
thf(class_Lattices_Oupper__semilattice_decl,type,
class_Lattices_Oupper__semilattice: $i > $o ).
thf(class_Orderings_Olinorder_decl,type,
class_Orderings_Olinorder: $i > $o ).
thf(class_Lattices_Olattice_decl,type,
class_Lattices_Olattice: $i > $o ).
thf(class_Lattices_Olower__semilattice_decl,type,
class_Lattices_Olower__semilattice: $i > $o ).
thf(class_HOL_Oord_decl,type,
class_HOL_Oord: $i > $o ).
thf(class_Ring__and__Field_Oordered__idom_decl,type,
class_Ring__and__Field_Oordered__idom: $i > $o ).
thf(c_HOL_Oord__class_Oless_decl,type,
c_HOL_Oord__class_Oless: $i > $i > $i > $o ).
thf(class_Lattices_Obounded__lattice_decl,type,
class_Lattices_Obounded__lattice: $i > $o ).
thf(c_Lattices_Olower__semilattice__class_Oinf_decl,type,
c_Lattices_Olower__semilattice__class_Oinf: $i > $i > $i > $i ).
thf(c_Orderings_Obot__class_Obot_decl,type,
c_Orderings_Obot__class_Obot: $i > $i ).
thf(class_OrderedGroup_Olordered__ab__group__add_decl,type,
class_OrderedGroup_Olordered__ab__group__add: $i > $o ).
thf(c_HOL_Ouminus__class_Ouminus_decl,type,
c_HOL_Ouminus__class_Ouminus: $i > $i > $i ).
thf(c_Lattices_Oupper__semilattice__class_Osup_decl,type,
c_Lattices_Oupper__semilattice__class_Osup: $i > $i > $i > $i ).
thf(class_Lattices_Oboolean__algebra_decl,type,
class_Lattices_Oboolean__algebra: $i > $o ).
thf(c_Suc_decl,type,
c_Suc: $i > $i ).
thf(c_Set_Ovimage_decl,type,
c_Set_Ovimage: $i > $i > $i > $i > $i ).
thf(c_Fun_Ocomp_decl,type,
c_Fun_Ocomp: $i > $i > $i > $i > $i > $i ).
thf(c_Set_Oinsert_decl,type,
c_Set_Oinsert: $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_Fun_Ofcomp_decl,type,
c_Fun_Ofcomp: $i > $i > $i > $i > $i > $i ).
thf(c_Fun_Oid_decl,type,
c_Fun_Oid: $i > $i ).
thf(class_OrderedGroup_Opordered__ab__group__add_decl,type,
class_OrderedGroup_Opordered__ab__group__add: $i > $o ).
thf(c_SetInterval_Oord__class_OatLeast_decl,type,
c_SetInterval_Oord__class_OatLeast: $i > $i > $i ).
thf(class_OrderedGroup_Oab__group__add_decl,type,
class_OrderedGroup_Oab__group__add: $i > $o ).
thf(c_HOL_Ominus__class_Ominus_decl,type,
c_HOL_Ominus__class_Ominus: $i > $i > $i > $i ).
thf(c_Complete__Lattice_OSup__class_OSup_decl,type,
c_Complete__Lattice_OSup__class_OSup: $i > $i > $i ).
thf(class_Orderings_Obot_decl,type,
class_Orderings_Obot: $i > $o ).
thf(c_SetInterval_Oord__class_OgreaterThan_decl,type,
c_SetInterval_Oord__class_OgreaterThan: $i > $i > $i ).
thf(c_SetInterval_Oord__class_OatMost_decl,type,
c_SetInterval_Oord__class_OatMost: $i > $i > $i ).
thf(c_SetInterval_Oord__class_OlessThan_decl,type,
c_SetInterval_Oord__class_OlessThan: $i > $i > $i ).
thf(class_HOL_Ominus_decl,type,
class_HOL_Ominus: $i > $o ).
thf(c_Set_Oimage_decl,type,
c_Set_Oimage: $i > $i > $i > $i > $i ).
thf(c_Hoare__Mirabelle_Ohoare__derivs_decl,type,
c_Hoare__Mirabelle_Ohoare__derivs: $i > $i > $i > $o ).
thf(c_COMBC_decl,type,
c_COMBC: $i > $i > $i > $i > $i > $i ).
thf(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR_decl,type,
c_Complete__Lattice_Ocomplete__lattice__class_OSUPR: $i > $i > $i > $i > $i ).
thf(c_SetInterval_Oord__class_OatLeastAtMost_decl,type,
c_SetInterval_Oord__class_OatLeastAtMost: $i > $i > $i > $i ).
thf(c_SetInterval_Oord__class_OatLeastLessThan_decl,type,
c_SetInterval_Oord__class_OatLeastLessThan: $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Orderings__Xle__fun__def__1__1_decl,type,
c_ATP__Linkup_Osko__Orderings__Xle__fun__def__1__1: $i > $i > $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Set__Xsubset__iff__1__1_decl,type,
c_ATP__Linkup_Osko__Set__Xsubset__iff__1__1: $i > $i > $i > $i ).
thf(c_Complete__Lattice_Ocomplete__lattice__class_OINFI_decl,type,
c_Complete__Lattice_Ocomplete__lattice__class_OINFI: $i > $i > $i > $i > $i ).
thf(class_HOL_Ouminus_decl,type,
class_HOL_Ouminus: $i > $o ).
thf(c_ATP__Linkup_Osko__Set__XsubsetI__1__1_decl,type,
c_ATP__Linkup_Osko__Set__XsubsetI__1__1: $i > $i > $i > $i ).
thf(v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1_decl,type,
v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1: $i > $i > $i ).
thf(c_Inductive_Ocomplete__lattice__class_Ogfp_decl,type,
c_Inductive_Ocomplete__lattice__class_Ogfp: $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Predicate__Xpredicate1I__1__1_decl,type,
c_ATP__Linkup_Osko__Predicate__Xpredicate1I__1__1: $i > $i > $i > $i ).
thf(c_Hoare__Mirabelle_Ohoare__valids_decl,type,
c_Hoare__Mirabelle_Ohoare__valids: $i > $i > $i > $o ).
thf(v_sko__Hoare__Mirabelle__Xhoare__valids__def__2_decl,type,
v_sko__Hoare__Mirabelle__Xhoare__valids__def__2: $i > $i > $i ).
thf(v_sko__Hoare__Mirabelle__Xhoare__valids__def__1_decl,type,
v_sko__Hoare__Mirabelle__Xhoare__valids__def__1: $i > $i > $i ).
thf(c_ATP__Linkup_Osko__Orderings__Xle__funI__1__1_decl,type,
c_ATP__Linkup_Osko__Orderings__Xle__funI__1__1: $i > $i > $i > $i > $i ).
thf(447,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ~ ( C @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_6) ).
thf(1586,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ~ ( C @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[447]) ).
thf(506,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(1718,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)],[506]) ).
thf(371,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__le_0) ).
thf(1411,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[371]) ).
thf(24,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( E @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ocomp ) ) ) ) @ c_Set_Ovimage ) ) ) )
= ( C @ ( E @ ( D @ ( C @ ( F @ ( A @ c_Set_Ovimage ) ) ) @ ( B @ c_Set_Ovimage ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__compose_0) ).
thf(629,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( E @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ocomp ) ) ) ) @ c_Set_Ovimage ) ) ) )
= ( C @ ( E @ ( D @ ( C @ ( F @ ( A @ c_Set_Ovimage ) ) ) @ ( B @ c_Set_Ovimage ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(397,axiom,
! [B: $i,A: $i] :
( ( ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( B @ c_SetInterval_Oord__class_OatLeast ) @ c_HOL_Ouminus__class_Ouminus ) )
= ( A @ ( B @ c_SetInterval_Oord__class_OlessThan ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__atLeast_0) ).
thf(1469,plain,
! [B: $i,A: $i] :
( ( ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( B @ c_SetInterval_Oord__class_OatLeast ) @ c_HOL_Ouminus__class_Ouminus ) )
= ( A @ ( B @ c_SetInterval_Oord__class_OlessThan ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[397]) ).
thf(391,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(1454,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)],[391]) ).
thf(528,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertCI_0) ).
thf(1767,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[528]) ).
thf(511,axiom,
! [B: $i,A: $i] :
( ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__absorb_0) ).
thf(1729,plain,
! [B: $i,A: $i] :
( ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[511]) ).
thf(194,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Ovimage ) ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__empty_0) ).
thf(1031,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Ovimage ) ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(152,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( C @ c_SetInterval_Oord__class_OatLeast ) @ ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__int_I8_J_0) ).
thf(941,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( C @ c_SetInterval_Oord__class_OatLeast ) @ ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(551,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_0) ).
thf(1818,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[551]) ).
thf(431,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Set_Oinsert ) ) )
= ( C @ ( B @ ( A @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff__single_0) ).
thf(1549,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Set_Oinsert ) ) )
= ( C @ ( B @ ( A @ c_Set_Oinsert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[431]) ).
thf(231,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__iff__psubset__eq_0) ).
thf(1110,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(330,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( v_x @ ( D @ ( C @ ( t_a @ ( B @ ( A @ c_Fun_Ofcomp ) ) ) ) @ hAPP ) )
= ( v_x @ ( A @ hAPP ) @ ( B @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fcomp__def_0) ).
thf(1322,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( v_x @ ( D @ ( C @ ( t_a @ ( B @ ( A @ c_Fun_Ofcomp ) ) ) ) @ hAPP ) )
= ( v_x @ ( A @ hAPP ) @ ( B @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[330]) ).
thf(482,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( D @ ( C @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__int_I15_J_0) ).
thf(1665,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( D @ ( C @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[482]) ).
thf(258,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ouminus__class_Ouminus ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ c_HOL_Ouminus__class_Ouminus ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__Diff__eq_0) ).
thf(1168,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ouminus__class_Ouminus ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ c_HOL_Ouminus__class_Ouminus ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(73,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_Orderings_Obot__class_Obot @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= B )
| ~ ( A @ class_Lattices_Obounded__lattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__bot__right_0) ).
thf(760,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ c_Orderings_Obot__class_Obot @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= B )
| ~ ( A @ class_Lattices_Obounded__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(130,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ c_SetInterval_Oord__class_OatMost ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_HOL_Oord ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atMost__iff_1) ).
thf(893,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ c_SetInterval_Oord__class_OatMost ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_HOL_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(562,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(1840,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)],[562]) ).
thf(218,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( D @ c_lessequals ) ) )
| ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__mp_0) ).
thf(1083,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( D @ c_lessequals ) ) )
| ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(161,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( C @ hAPP ) @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( A @ ( D @ ( C @ c_Set_Ovimage ) ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__eq_1) ).
thf(962,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( C @ hAPP ) @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( A @ ( D @ ( C @ c_Set_Ovimage ) ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(520,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( E @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( E @ ( B @ hAPP ) )
= ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ ( A @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) )
!= ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UNION__empty__conv_I2_J_0) ).
thf(1750,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( E @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( E @ ( B @ hAPP ) )
= ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ ( A @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) )
!= ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[520]) ).
thf(419,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( C @ c_SetInterval_Oord__class_OlessThan ) @ ( A @ ( B @ c_SetInterval_Oord__class_OlessThan ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lessThan__subset__iff_1) ).
thf(1522,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( C @ c_SetInterval_Oord__class_OlessThan ) @ ( A @ ( B @ c_SetInterval_Oord__class_OlessThan ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[419]) ).
thf(441,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(1569,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)],[441]) ).
thf(213,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Set__XsubsetI__1__1 ) ) @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subsetI_1) ).
thf(1073,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Set__XsubsetI__1__1 ) ) @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(14,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(597,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)],[14]) ).
thf(383,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff1_0) ).
thf(1437,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[383]) ).
thf(115,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(861,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)],[115]) ).
thf(260,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(1173,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)],[260]) ).
thf(253,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofcomp ) ) ) ) @ hAPP ) )
= ( F @ ( A @ hAPP ) @ ( B @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fcomp__apply_0) ).
thf(1158,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ofcomp ) ) ) ) @ hAPP ) )
= ( F @ ( A @ hAPP ) @ ( B @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(3,negated_conjecture,
~ ( t_a @ ( v_xa @ ( v_x @ c_Hoare__Mirabelle_Otriple__valid ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_2) ).
thf(582,plain,
~ ( t_a @ ( v_xa @ ( v_x @ c_Hoare__Mirabelle_Otriple__valid ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(540,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__subset__iff_2) ).
thf(1793,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[540]) ).
thf(424,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ ( A @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distrib__inf__le_0) ).
thf(1533,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ ( A @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[424]) ).
thf(500,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( E @ ( A @ ( F @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ c_lessequals ) ) )
| ~ ( F @ ( B @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ ( A @ hAPP ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__subset__iff_0) ).
thf(1705,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( E @ ( A @ ( F @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ c_lessequals ) ) )
| ~ ( F @ ( B @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ ( A @ hAPP ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[500]) ).
thf(457,axiom,
tc_bool @ class_HOL_Ouminus,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__HOL_Ouminus) ).
thf(1608,plain,
tc_bool @ class_HOL_Ouminus,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[457]) ).
thf(243,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( tc_bool @ ( E @ tc_fun ) @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ ( A @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( B @ ( A @ hAPP ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( E @ tc_fun ) @ ( D @ ( A @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__absorb_0) ).
thf(1137,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( tc_bool @ ( E @ tc_fun ) @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ ( A @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( B @ ( A @ hAPP ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( E @ tc_fun ) @ ( D @ ( A @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(56,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__infI2_0) ).
thf(715,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(94,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__asym_H_0) ).
thf(814,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(139,axiom,
! [B: $i,A: $i] :
( ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__empty_0) ).
thf(913,plain,
! [B: $i,A: $i] :
( ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(538,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ hAPP ) @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ c_Inductive_Ocomplete__lattice__class_Ogfp ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_gfp__upperbound_0) ).
thf(1788,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ hAPP ) @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ c_Inductive_Ocomplete__lattice__class_Ogfp ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[538]) ).
thf(378,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( C @ hAPP ) @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( A @ ( D @ ( C @ c_Set_Ovimage ) ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimageI_0) ).
thf(1426,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( C @ hAPP ) @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( A @ ( D @ ( C @ c_Set_Ovimage ) ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[378]) ).
thf(522,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Int__distrib_0) ).
thf(1756,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[522]) ).
thf(325,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( A @ tc_fun ) @ ( E @ ( C @ ( F @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( F @ ( D @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ hAPP ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__iff_0) ).
thf(1310,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( A @ tc_fun ) @ ( E @ ( C @ ( F @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( F @ ( D @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ hAPP ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[325]) ).
thf(256,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( E @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Set_Ovimage ) ) ) )
= ( tc_bool @ ( E @ tc_fun ) @ ( D @ ( E @ ( C @ ( A @ c_Set_Ovimage ) ) ) @ ( D @ ( E @ ( B @ ( A @ c_Set_Ovimage ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__Un_0) ).
thf(1164,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( E @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Set_Ovimage ) ) ) )
= ( tc_bool @ ( E @ tc_fun ) @ ( D @ ( E @ ( C @ ( A @ c_Set_Ovimage ) ) ) @ ( D @ ( E @ ( B @ ( A @ c_Set_Ovimage ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(87,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__supI1_0) ).
thf(797,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(303,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( 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(1260,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
!= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[303]) ).
thf(50,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Odistrib__lattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__inf__distrib2_0) ).
thf(698,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Odistrib__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(284,axiom,
! [B: $i,A: $i] :
( ( ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( B @ c_SetInterval_Oord__class_OgreaterThan ) @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( B @ c_SetInterval_Oord__class_OatLeast ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__un_I1_J_0) ).
thf(1222,plain,
! [B: $i,A: $i] :
( ( ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( B @ c_SetInterval_Oord__class_OgreaterThan ) @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( B @ c_SetInterval_Oord__class_OatLeast ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(147,axiom,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( I @ ( B @ hAPP ) @ ( A @ hAPP ) )
= ( I @ ( G @ hAPP ) @ ( F @ hAPP ) ) )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ocomp ) ) ) ) )
!= ( E @ ( D @ ( H @ ( G @ ( F @ c_Fun_Ocomp ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__eq__dest_0) ).
thf(930,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( I @ ( B @ hAPP ) @ ( A @ hAPP ) )
= ( I @ ( G @ hAPP ) @ ( F @ hAPP ) ) )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ocomp ) ) ) ) )
!= ( E @ ( D @ ( H @ ( G @ ( F @ c_Fun_Ocomp ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(224,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnE_0) ).
thf(1095,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(272,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( C @ c_SetInterval_Oord__class_OgreaterThan ) @ ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( B @ c_SetInterval_Oord__class_OatLeast ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__un_I13_J_0) ).
thf(1196,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( C @ c_SetInterval_Oord__class_OgreaterThan ) @ ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( B @ c_SetInterval_Oord__class_OatLeast ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(180,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__ge1_0) ).
thf(1001,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(362,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(1391,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)],[362]) ).
thf(81,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= B )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__absorb_0) ).
thf(782,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= B )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(54,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I8_J_0) ).
thf(709,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(106,axiom,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_Orderings_Obot__class_Obot ) )
| ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
!= ( A @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Lattices_Obounded__lattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__eq__bot__eq2_0) ).
thf(841,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ c_Orderings_Obot__class_Obot ) )
| ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
!= ( A @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Lattices_Obounded__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(126,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DiffI_0) ).
thf(885,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(460,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(1613,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)],[460]) ).
thf(473,axiom,
! [C: $i,B: $i,A: $i] : ( A @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertCI_1) ).
thf(1645,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[473]) ).
thf(454,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Fun_Oid @ hAPP ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_id__apply_0) ).
thf(1601,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ c_Fun_Oid @ hAPP ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[454]) ).
thf(399,axiom,
! [B: $i,A: $i] :
( ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ ( A @ c_HOL_Ouminus__class_Ouminus ) @ ( 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_Compl__disjoint_0) ).
thf(1475,plain,
! [B: $i,A: $i] :
( ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ ( A @ c_HOL_Ouminus__class_Ouminus ) @ ( 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)],[399]) ).
thf(544,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__ge2_0) ).
thf(1803,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[544]) ).
thf(33,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Ouminus__class_Ouminus ) )
= B )
| ~ ( A @ class_Lattices_Oboolean__algebra ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__compl_0) ).
thf(651,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Ouminus__class_Ouminus ) )
= B )
| ~ ( A @ class_Lattices_Oboolean__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(518,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( E @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( A @ ( D @ ( C @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__subset__iff_0) ).
thf(1746,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( E @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( A @ ( D @ ( C @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[518]) ).
thf(132,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ c_lessequals ) ) )
| ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_1) ).
thf(898,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ c_lessequals ) ) )
| ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(417,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(1518,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Orderings_Oorder )
| ( B @ ( A @ tc_fun ) @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[417]) ).
thf(305,axiom,
! [C: $i,B: $i,A: $i] : ( A @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__iff_1) ).
thf(1265,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[305]) ).
thf(499,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( t_a @ ( C @ ( D @ c_Hoare__Mirabelle_Ohoare__valids ) ) )
| ~ ( t_a @ ( A @ ( D @ v_sko__Hoare__Mirabelle__Xhoare__valids__def__1 ) @ ( A @ c_Hoare__Mirabelle_Otriple__valid ) ) )
| ~ ( C @ ( B @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( t_a @ ( B @ ( A @ c_Hoare__Mirabelle_Otriple__valid ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hoare__valids__def_1) ).
thf(1703,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( t_a @ ( C @ ( D @ c_Hoare__Mirabelle_Ohoare__valids ) ) )
| ~ ( t_a @ ( A @ ( D @ v_sko__Hoare__Mirabelle__Xhoare__valids__def__1 ) @ ( A @ c_Hoare__Mirabelle_Otriple__valid ) ) )
| ~ ( C @ ( B @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( t_a @ ( B @ ( A @ c_Hoare__Mirabelle_Otriple__valid ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[499]) ).
thf(286,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__le__iff__le_0) ).
thf(1228,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(300,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(1254,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)],[300]) ).
thf(315,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(1287,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)],[315]) ).
thf(502,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(1709,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)],[502]) ).
thf(380,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(1430,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)],[380]) ).
thf(480,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( C @ ( F @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( F @ ( E @ ( B @ c_Set_Oimage ) ) ) @ ( D @ hAPP ) @ ( A @ ( F @ ( E @ ( B @ c_Set_Oimage ) ) ) @ c_lessequals ) ) )
| ( tc_bool @ ( A @ tc_fun ) @ ( D @ c_Inductive_Ocomplete__lattice__class_Ogfp ) @ ( C @ ( B @ hAPP ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_weak__coinduct__image_0) ).
thf(1660,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( C @ ( F @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( F @ ( E @ ( B @ c_Set_Oimage ) ) ) @ ( D @ hAPP ) @ ( A @ ( F @ ( E @ ( B @ c_Set_Oimage ) ) ) @ c_lessequals ) ) )
| ( tc_bool @ ( A @ tc_fun ) @ ( D @ c_Inductive_Ocomplete__lattice__class_Ogfp ) @ ( C @ ( B @ hAPP ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[480]) ).
thf(82,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( B @ c_SetInterval_Oord__class_OlessThan ) )
!= ( A @ ( C @ c_SetInterval_Oord__class_OlessThan ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lessThan__eq__iff_0) ).
thf(785,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( B @ c_SetInterval_Oord__class_OlessThan ) )
!= ( A @ ( C @ c_SetInterval_Oord__class_OlessThan ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(577,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( C @ c_SetInterval_Oord__class_OlessThan ) @ ( A @ ( B @ c_SetInterval_Oord__class_OlessThan ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lessThan__subset__iff_0) ).
thf(1871,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( C @ c_SetInterval_Oord__class_OlessThan ) @ ( A @ ( B @ c_SetInterval_Oord__class_OlessThan ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[577]) ).
thf(6,axiom,
tc_nat @ class_Lattices_Odistrib__lattice,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Odistrib__lattice) ).
thf(587,plain,
tc_nat @ class_Lattices_Odistrib__lattice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(141,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( A @ ( E @ ( D @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__psubset__iff_3) ).
thf(917,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( A @ ( E @ ( D @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(89,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__less__iff_0) ).
thf(802,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(444,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( A @ ( B @ c_SetInterval_Oord__class_OlessThan ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__int_I4_J_0) ).
thf(1577,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( A @ ( B @ c_SetInterval_Oord__class_OlessThan ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[444]) ).
thf(155,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 ) ) @ c_HOL_Ouminus__class_Ouminus ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ c_HOL_Ouminus__class_Ouminus ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__Int_0) ).
thf(949,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_HOL_Ouminus__class_Ouminus ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ c_HOL_Ouminus__class_Ouminus ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(205,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( D @ c_lessequals ) ) )
| ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_set__rev__mp_0) ).
thf(1055,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( D @ c_lessequals ) ) )
| ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(370,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__is__Un_0) ).
thf(1409,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[370]) ).
thf(558,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Predicate__Xpredicate1I__1__1 ) ) @ ( A @ hAPP ) @ hBOOL )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_predicate1I_0) ).
thf(1832,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Predicate__Xpredicate1I__1__1 ) ) @ ( A @ hAPP ) @ hBOOL )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[558]) ).
thf(269,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__iff_2) ).
thf(1191,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(394,axiom,
! [B: $i,A: $i] :
( ( ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( B @ c_SetInterval_Oord__class_OlessThan ) @ c_HOL_Ouminus__class_Ouminus ) )
= ( A @ ( B @ c_SetInterval_Oord__class_OatLeast ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__lessThan_0) ).
thf(1462,plain,
! [B: $i,A: $i] :
( ( ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( B @ c_SetInterval_Oord__class_OlessThan ) @ c_HOL_Ouminus__class_Ouminus ) )
= ( A @ ( B @ c_SetInterval_Oord__class_OatLeast ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[394]) ).
thf(207,axiom,
! [B: $i,A: $i] :
( ( ( v_x @ ( A @ ( t_a @ tc_fun ) @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ hAPP ) )
= ( A @ ( v_x @ ( B @ hAPP ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_HOL_Ouminus ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__Compl__def_0) ).
thf(1059,plain,
! [B: $i,A: $i] :
( ( ( v_x @ ( A @ ( t_a @ tc_fun ) @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ hAPP ) )
= ( A @ ( v_x @ ( B @ hAPP ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_HOL_Ouminus ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(241,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(1132,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)],[241]) ).
thf(429,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__sup__iff_0) ).
thf(1545,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[429]) ).
thf(134,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I4_J_0) ).
thf(902,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(111,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__imp__le_0) ).
thf(853,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(296,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( A @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( C @ hAPP ) @ c_Set_Oinsert ) ) @ ( C @ c_Set_Ovimage ) ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__singleton__eq_1) ).
thf(1247,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( A @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( C @ hAPP ) @ c_Set_Oinsert ) ) @ ( C @ c_Set_Ovimage ) ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[296]) ).
thf(17,axiom,
! [C: $i,B: $i,A: $i] :
( ( C = B )
| ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE_0) ).
thf(606,plain,
! [C: $i,B: $i,A: $i] :
( ( C = B )
| ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(185,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__minus__iff_1) ).
thf(1013,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(471,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ c_SetInterval_Oord__class_OgreaterThan ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_HOL_Oord ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_greaterThan__iff_1) ).
thf(1641,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ c_SetInterval_Oord__class_OgreaterThan ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_HOL_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[471]) ).
thf(531,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( A @ ( E @ ( B @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( C @ ( B @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__SUPI_0) ).
thf(1773,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( A @ ( E @ ( B @ ( D @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( C @ ( B @ hAPP ) @ c_lessequals ) ) )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[531]) ).
thf(408,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( E @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Set_Ovimage ) ) ) )
= ( tc_bool @ ( E @ tc_fun ) @ ( D @ ( E @ ( C @ ( A @ c_Set_Ovimage ) ) ) @ ( D @ ( E @ ( B @ ( A @ c_Set_Ovimage ) ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__Int_0) ).
thf(1494,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( E @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Set_Ovimage ) ) ) )
= ( tc_bool @ ( E @ tc_fun ) @ ( D @ ( E @ ( C @ ( A @ c_Set_Ovimage ) ) ) @ ( D @ ( E @ ( B @ ( A @ c_Set_Ovimage ) ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[408]) ).
thf(226,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( D @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( tc_bool @ ( C @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ ( A @ ( D @ c_lessequals ) ) )
| ( C @ ( B @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_thin_0) ).
thf(1100,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( D @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( tc_bool @ ( C @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ ( A @ ( D @ c_lessequals ) ) )
| ( C @ ( B @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(288,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
!= ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastLessThan ) ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastLessThan__empty__iff2_0) ).
thf(1232,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
!= ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastLessThan ) ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(566,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ hAPP ) @ ( A @ hAPP ) )
= ( C @ ( F @ ( E @ ( D @ ( B @ ( A @ c_Fun_Ocomp ) ) ) ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__eq__dest__lhs_0) ).
thf(1847,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ hAPP ) @ ( A @ hAPP ) )
= ( C @ ( F @ ( E @ ( D @ ( B @ ( A @ c_Fun_Ocomp ) ) ) ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[566]) ).
thf(329,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( 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(1319,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( 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)],[329]) ).
thf(119,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Diff_0) ).
thf(870,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(401,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(1479,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)],[401]) ).
thf(458,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_4) ).
thf(1609,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[458]) ).
thf(516,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(1741,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)],[516]) ).
thf(365,axiom,
! [B: $i,A: $i] :
~ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ex__in__conv_0) ).
thf(1398,plain,
! [B: $i,A: $i] :
~ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[365]) ).
thf(124,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( E @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Ovimage ) ) ) )
= ( tc_bool @ ( E @ tc_fun ) @ ( D @ ( E @ ( C @ ( A @ c_Set_Ovimage ) ) ) @ ( D @ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Ovimage ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__insert_0) ).
thf(881,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( E @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Ovimage ) ) ) )
= ( tc_bool @ ( E @ tc_fun ) @ ( D @ ( E @ ( C @ ( A @ c_Set_Ovimage ) ) ) @ ( D @ ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Set_Ovimage ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(406,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__absorb1_0) ).
thf(1489,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[406]) ).
thf(144,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(924,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Orderings_Opreorder )
| ( B @ ( A @ tc_fun ) @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(395,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__ord_I3_J_0) ).
thf(1465,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[395]) ).
thf(84,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( E @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eqI_0) ).
thf(789,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( E @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(548,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(1811,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)],[548]) ).
thf(10,axiom,
tc_nat @ class_Lattices_Olattice,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Olattice) ).
thf(591,plain,
tc_nat @ class_Lattices_Olattice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(22,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_Orderings_Obot__class_Obot ) )
| ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
!= ( A @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Lattices_Obounded__lattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__eq__bot__eq1_0) ).
thf(623,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( A @ c_Orderings_Obot__class_Obot ) )
| ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
!= ( A @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Lattices_Obounded__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(31,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( A @ ( B @ ( A @ c_Fun_Oid @ c_Fun_Ofcomp ) ) ) ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_id__fcomp_0) ).
thf(646,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( A @ ( B @ ( A @ c_Fun_Oid @ c_Fun_Ofcomp ) ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(358,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(1383,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)],[358]) ).
thf(91,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I9_J_0) ).
thf(806,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(163,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( C @ ( E @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( A @ ( B @ ( D @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( D @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__psubset__iff_1) ).
thf(966,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( C @ ( E @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( A @ ( B @ ( D @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( D @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(313,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(1283,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)],[313]) ).
thf(203,axiom,
! [B: $i,A: $i] :
~ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__iff_0) ).
thf(1051,plain,
! [B: $i,A: $i] :
~ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(198,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(1040,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)],[198]) ).
thf(468,axiom,
! [A: $i] :
( ( ( v_x @ ( A @ ( t_a @ tc_fun ) @ c_Orderings_Obot__class_Obot @ hAPP ) )
= ( A @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Orderings_Obot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot__fun__eq_0) ).
thf(1632,plain,
! [A: $i] :
( ( ( v_x @ ( A @ ( t_a @ tc_fun ) @ c_Orderings_Obot__class_Obot @ hAPP ) )
= ( A @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Orderings_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[468]) ).
thf(46,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( G @ ( E @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Fun_Ocomp ) ) ) ) @ ( A @ c_Fun_Ocomp ) ) ) ) )
= ( F @ ( G @ ( D @ ( C @ ( D @ ( G @ ( E @ ( B @ ( A @ c_Fun_Ocomp ) ) ) ) @ c_Fun_Ocomp ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__assoc_0) ).
thf(687,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( G @ ( E @ ( F @ ( E @ ( D @ ( C @ ( B @ c_Fun_Ocomp ) ) ) ) @ ( A @ c_Fun_Ocomp ) ) ) ) )
= ( F @ ( G @ ( D @ ( C @ ( D @ ( G @ ( E @ ( B @ ( A @ c_Fun_Ocomp ) ) ) ) @ c_Fun_Ocomp ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(281,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__empty__iff_1) ).
thf(1215,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(64,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_HOL_Ouminus__class_Ouminus ) )
= ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__inf__eq__sup_0) ).
thf(734,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_HOL_Ouminus__class_Ouminus ) )
= ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(387,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( tc_bool @ ( E @ tc_fun ) @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ ( A @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( B @ ( A @ hAPP ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__upper_0) ).
thf(1447,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( tc_bool @ ( E @ tc_fun ) @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ ( A @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( B @ ( A @ hAPP ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[387]) ).
thf(117,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(866,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)],[117]) ).
thf(464,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ hAPP ) @ hBOOL )
| ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup1CI_0) ).
thf(1622,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ hAPP ) @ hBOOL )
| ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[464]) ).
thf(421,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntI_0) ).
thf(1526,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[421]) ).
thf(342,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(1351,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Lattices_Olattice )
| ( B @ ( A @ tc_fun ) @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[342]) ).
thf(340,axiom,
! [B: $i,A: $i] :
( ( ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( B @ c_SetInterval_Oord__class_OgreaterThan ) @ c_HOL_Ouminus__class_Ouminus ) )
= ( A @ ( B @ c_SetInterval_Oord__class_OatMost ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__greaterThan_0) ).
thf(1345,plain,
! [B: $i,A: $i] :
( ( ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( B @ c_SetInterval_Oord__class_OgreaterThan ) @ c_HOL_Ouminus__class_Ouminus ) )
= ( A @ ( B @ c_SetInterval_Oord__class_OatMost ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[340]) ).
thf(381,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Set__Xsubset__iff__1__1 ) ) @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__iff_2) ).
thf(1433,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Set__Xsubset__iff__1__1 ) ) @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[381]) ).
thf(368,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ ( A @ ( B @ c_lessequals ) ) )
| ( C @ ( B @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_asm_0) ).
thf(1405,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ ( A @ ( B @ c_lessequals ) ) )
| ( C @ ( B @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[368]) ).
thf(274,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Predicate__Xpredicate1I__1__1 ) ) @ ( B @ hAPP ) @ hBOOL )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_predicate1I_1) ).
thf(1201,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Predicate__Xpredicate1I__1__1 ) ) @ ( B @ hAPP ) @ hBOOL )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(496,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_COMBC ) ) ) ) @ hAPP ) )
= ( B @ ( F @ ( A @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_COMBC__def_0) ).
thf(1696,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_COMBC ) ) ) ) @ hAPP ) )
= ( B @ ( F @ ( A @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[496]) ).
thf(438,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__insert2_0) ).
thf(1564,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[438]) ).
thf(122,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__left__absorb_0) ).
thf(877,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(48,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Oboolean__algebra ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__eq_0) ).
thf(692,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Oboolean__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(228,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__disjoint_0) ).
thf(1104,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(293,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ tc_fun ) @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ tc_fun ) @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_HOL_Oord ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__fun__def_1) ).
thf(1242,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ tc_fun ) @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ tc_fun ) @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_HOL_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[293]) ).
thf(109,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( B @ ( C @ c_in @ c_COMBC ) ) ) ) @ ( tc_bool @ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( A @ ( C @ c_in @ c_COMBC ) ) ) ) @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pred__subset__eq_0) ).
thf(849,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( B @ ( C @ c_in @ c_COMBC ) ) ) ) @ ( tc_bool @ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( A @ ( C @ c_in @ c_COMBC ) ) ) ) @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(574,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( C @ ( B @ c_ATP__Linkup_Osko__Orderings__Xle__funI__1__1 ) ) ) @ ( C @ hAPP ) @ ( A @ ( D @ ( C @ ( B @ c_ATP__Linkup_Osko__Orderings__Xle__funI__1__1 ) ) ) @ ( B @ hAPP ) @ c_lessequals ) ) )
| ( A @ ( D @ tc_fun ) @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_HOL_Oord ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__funI_0) ).
thf(1863,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( C @ ( B @ c_ATP__Linkup_Osko__Orderings__Xle__funI__1__1 ) ) ) @ ( C @ hAPP ) @ ( A @ ( D @ ( C @ ( B @ c_ATP__Linkup_Osko__Orderings__Xle__funI__1__1 ) ) ) @ ( B @ hAPP ) @ c_lessequals ) ) )
| ( A @ ( D @ tc_fun ) @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_HOL_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[574]) ).
thf(476,axiom,
tc_bool @ class_HOL_Oord,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__HOL_Oord) ).
thf(1651,plain,
tc_bool @ class_HOL_Oord,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[476]) ).
thf(277,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( C @ ( E @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( A @ ( B @ ( D @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ c_lessequals ) ) )
| ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastLessThan__subset__iff_1) ).
thf(1206,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( C @ ( E @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( A @ ( B @ ( D @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ c_lessequals ) ) )
| ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(43,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( B @ c_SetInterval_Oord__class_OatLeast ) )
!= ( A @ ( C @ c_SetInterval_Oord__class_OatLeast ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeast__eq__iff_0) ).
thf(678,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( B @ c_SetInterval_Oord__class_OatLeast ) )
!= ( A @ ( C @ c_SetInterval_Oord__class_OatLeast ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(494,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( 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(1691,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( 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)],[494]) ).
thf(323,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( F @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( F @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ ( A @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SUP1__iff_2) ).
thf(1306,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( F @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( F @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ ( A @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[323]) ).
thf(273,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( C @ c_SetInterval_Oord__class_OatMost ) @ ( A @ ( B @ c_SetInterval_Oord__class_OatMost ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atMost__subset__iff_1) ).
thf(1199,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( C @ c_SetInterval_Oord__class_OatMost ) @ ( A @ ( B @ c_SetInterval_Oord__class_OatMost ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(337,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__insert__absorb_0) ).
thf(1338,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[337]) ).
thf(536,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ( ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( D @ ( C @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( D @ ( B @ c_SetInterval_Oord__class_OatLeastLessThan ) ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__un_I17_J_0) ).
thf(1783,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ( ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( D @ ( C @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( D @ ( B @ c_SetInterval_Oord__class_OatLeastLessThan ) ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[536]) ).
thf(576,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastLessThan ) ) )
!= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastLessThan__empty__iff_0) ).
thf(1868,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastLessThan ) ) )
!= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[576]) ).
thf(210,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( D @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_0) ).
thf(1067,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( D @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(514,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
= ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__empty__iff2_1) ).
thf(1736,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
= ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[514]) ).
thf(201,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(1047,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)],[201]) ).
thf(206,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__least_0) ).
thf(1057,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(310,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
!= ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__empty__iff2_0) ).
thf(1274,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
!= ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[310]) ).
thf(508,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_5) ).
thf(1723,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[508]) ).
thf(159,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( B = C )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le_2) ).
thf(957,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( B = C )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(199,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
= ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastLessThan ) ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastLessThan__empty__iff2_1) ).
thf(1042,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
= ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastLessThan ) ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(301,axiom,
! [B: $i,A: $i] :
( ( ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( B @ c_SetInterval_Oord__class_OatMost ) @ c_HOL_Ouminus__class_Ouminus ) )
= ( A @ ( B @ c_SetInterval_Oord__class_OgreaterThan ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__atMost_0) ).
thf(1255,plain,
! [B: $i,A: $i] :
( ( ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( B @ c_SetInterval_Oord__class_OatMost ) @ c_HOL_Ouminus__class_Ouminus ) )
= ( A @ ( B @ c_SetInterval_Oord__class_OgreaterThan ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[301]) ).
thf(487,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) )
= ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastAtMost__singleton_0) ).
thf(1676,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) )
= ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[487]) ).
thf(405,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__le__iff_1) ).
thf(1487,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[405]) ).
thf(291,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__insert__right_0) ).
thf(1238,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Set_Oinsert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(436,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnCI_1) ).
thf(1560,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[436]) ).
thf(68,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(746,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)],[68]) ).
thf(222,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( 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(1091,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( D @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( 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)],[222]) ).
thf(99,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Odistrib__lattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__inf__distrib1_0) ).
thf(825,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Odistrib__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(339,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ tc_fun ) @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_HOL_Oord ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__fun__def_0) ).
thf(1343,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ tc_fun ) @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_HOL_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[339]) ).
thf(189,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_distrib__sup__le_0) ).
thf(1021,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( A @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(79,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_1) ).
thf(778,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(344,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( tc_bool @ ( F @ tc_fun ) @ ( D @ ( A @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) ) ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INF1__D_0) ).
thf(1355,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( tc_bool @ ( F @ tc_fun ) @ ( D @ ( A @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) ) ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[344]) ).
thf(445,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( D @ ( B @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ ( C @ ( D @ c_SetInterval_Oord__class_OatLeastLessThan ) ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__diff_0) ).
thf(1580,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( D @ ( B @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ ( C @ ( D @ c_SetInterval_Oord__class_OatLeastLessThan ) ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[445]) ).
thf(411,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( 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(1502,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( 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)],[411]) ).
thf(97,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__minus__iff_1) ).
thf(820,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(83,axiom,
tc_nat @ class_HOL_Ominus,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__HOL_Ominus) ).
thf(788,plain,
tc_nat @ class_HOL_Ominus,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(351,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( A @ tc_fun ) @ ( E @ ( C @ ( F @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( F @ ( D @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ hAPP ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__D_0) ).
thf(1370,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( A @ tc_fun ) @ ( E @ ( C @ ( F @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( F @ ( D @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ hAPP ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[351]) ).
thf(376,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( C @ c_lessequals ) ) )
| ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( tc_bool @ ( B @ tc_fun ) @ ( A @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__subset__Compl__iff_1) ).
thf(1423,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( C @ c_lessequals ) ) )
| ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( tc_bool @ ( B @ tc_fun ) @ ( A @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[376]) ).
thf(108,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ hAPP ) @ hBOOL )
| ( B @ ( C @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup1E_0) ).
thf(847,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ hAPP ) @ hBOOL )
| ( B @ ( C @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(349,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= B )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__absorb1_0) ).
thf(1365,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= B )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[349]) ).
thf(123,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(879,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)],[123]) ).
thf(263,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( B @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( B @ ( D @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( D @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_2) ).
thf(1178,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( B @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( B @ ( D @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( D @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(465,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( D @ c_lessequals ) ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
!= ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__assoc__eq_0) ).
thf(1624,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( D @ c_lessequals ) ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
!= ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[465]) ).
thf(128,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I8_J_0) ).
thf(889,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(560,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__le__iff_0) ).
thf(1836,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[560]) ).
thf(279,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( E @ ( D @ c_lessequals ) ) )
| ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( E @ ( D @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__psubset__iff_4) ).
thf(1210,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( E @ ( D @ c_lessequals ) ) )
| ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( E @ ( D @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(72,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__eq__neg__sup_0) ).
thf(757,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(369,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( B @ c_SetInterval_Oord__class_OgreaterThan ) @ ( A @ ( C @ c_SetInterval_Oord__class_OgreaterThan ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_greaterThan__subset__iff_0) ).
thf(1407,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( B @ c_SetInterval_Oord__class_OgreaterThan ) @ ( A @ ( C @ c_SetInterval_Oord__class_OgreaterThan ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[369]) ).
thf(239,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_0) ).
thf(1128,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(317,axiom,
! [C: $i,B: $i,A: $i] :
( ( C = B )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I12_J_0) ).
thf(1291,plain,
! [C: $i,B: $i,A: $i] :
( ( C = B )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[317]) ).
thf(167,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( E @ ( B @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( A @ ( D @ ( C @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( D @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastLessThan__subset__iff_0) ).
thf(974,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( E @ ( B @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( A @ ( D @ ( C @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( D @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(229,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(1106,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Orderings_Obot )
| ( B @ ( A @ tc_fun ) @ class_Orderings_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(319,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Set_Oinsert ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff__if_1) ).
thf(1296,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Set_Oinsert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[319]) ).
thf(38,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( B @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__commute_0) ).
thf(665,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( B @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(492,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__le_1) ).
thf(1687,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[492]) ).
thf(392,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(1457,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)],[392]) ).
thf(4,negated_conjecture,
! [A: $i] :
( ~ ( v_Ga @ ( A @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( t_a @ ( A @ ( v_x @ c_Hoare__Mirabelle_Otriple__valid ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_3) ).
thf(583,plain,
! [A: $i] :
( ~ ( v_Ga @ ( A @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( t_a @ ( A @ ( v_x @ c_Hoare__Mirabelle_Otriple__valid ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(101,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(830,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)],[101]) ).
thf(216,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( C @ c_SetInterval_Oord__class_OatLeast ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_HOL_Oord ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeast__iff_1) ).
thf(1079,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( C @ c_SetInterval_Oord__class_OatLeast ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_HOL_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(192,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(1027,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)],[192]) ).
thf(367,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(1402,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)],[367]) ).
thf(347,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_lessequals ) ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__absorb2_0) ).
thf(1360,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_lessequals ) ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[347]) ).
thf(525,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(1762,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)],[525]) ).
thf(20,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Suc )
!= ( B @ c_Suc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__inject_0) ).
thf(615,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Suc )
!= ( B @ c_Suc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(209,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__absorb_0) ).
thf(1064,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(170,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__distrib_0) ).
thf(980,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(377,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(1425,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)],[377]) ).
thf(485,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( E @ tc_fun ) @ ( C @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) )
= ( tc_bool @ ( E @ tc_fun ) @ ( tc_bool @ ( E @ tc_fun ) @ ( C @ ( D @ ( B @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( A @ ( D @ hAPP ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__insert_0) ).
thf(1672,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( E @ tc_fun ) @ ( C @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) )
= ( tc_bool @ ( E @ tc_fun ) @ ( tc_bool @ ( E @ tc_fun ) @ ( C @ ( D @ ( B @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( A @ ( D @ hAPP ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[485]) ).
thf(182,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(1006,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)],[182]) ).
thf(12,axiom,
tc_nat @ class_HOL_Oord,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__HOL_Oord) ).
thf(593,plain,
tc_nat @ class_HOL_Oord,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(235,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(1118,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)],[235]) ).
thf(174,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(989,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)],[174]) ).
thf(113,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Un_0) ).
thf(857,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(121,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( v_x @ ( A @ ( t_a @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ hAPP ) )
= ( A @ ( v_x @ ( C @ hAPP ) @ ( v_x @ ( B @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_HOL_Ominus ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fun__diff__def_0) ).
thf(874,plain,
! [C: $i,B: $i,A: $i] :
( ( ( v_x @ ( A @ ( t_a @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ hAPP ) )
= ( A @ ( v_x @ ( C @ hAPP ) @ ( v_x @ ( B @ hAPP ) @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_HOL_Ominus ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(245,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_HOL_Ouminus )
| ( B @ ( A @ tc_fun ) @ class_HOL_Ouminus ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__HOL_Ouminus) ).
thf(1143,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_HOL_Ouminus )
| ( B @ ( A @ tc_fun ) @ class_HOL_Ouminus ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(308,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(1270,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)],[308]) ).
thf(568,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__eq_0) ).
thf(1851,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[568]) ).
thf(530,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(1772,plain,
! [B: $i,A: $i] : ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[530]) ).
thf(571,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( tc_bool @ ( E @ tc_fun ) @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ ( A @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) ) ) @ ( B @ ( A @ hAPP ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( E @ tc_fun ) @ ( D @ ( A @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__absorb_0) ).
thf(1856,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( tc_bool @ ( E @ tc_fun ) @ ( tc_bool @ ( E @ tc_fun ) @ ( D @ ( A @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) ) ) @ ( B @ ( A @ hAPP ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( E @ tc_fun ) @ ( D @ ( A @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[571]) ).
thf(61,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ouminus__class_Ouminus ) )
= ( A @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__diff__eq_0) ).
thf(725,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ouminus__class_Ouminus ) )
= ( A @ ( B @ ( C @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(440,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( A @ hAPP ) @ ( B @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( C @ ( B @ ( A @ c_Set_Ovimage ) ) ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__code_1) ).
thf(1567,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( A @ hAPP ) @ ( B @ hAPP ) @ hBOOL )
| ( E @ ( D @ ( C @ ( B @ ( A @ c_Set_Ovimage ) ) ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[440]) ).
thf(490,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( E @ ( D @ ( A @ ( B @ c_Set_Ovimage ) ) ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ hAPP ) @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__code_0) ).
thf(1683,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( E @ ( D @ ( A @ ( B @ c_Set_Ovimage ) ) ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ hAPP ) @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[490]) ).
thf(333,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( E @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( E @ ( A @ c_Set_Ovimage ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Ovimage ) ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__mono_0) ).
thf(1329,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( E @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( E @ ( A @ c_Set_Ovimage ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Ovimage ) ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[333]) ).
thf(254,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__subset__iff_1) ).
thf(1160,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(148,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(933,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)],[148]) ).
thf(265,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( B @ ( A @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
!= ( C @ ( D @ ( A @ c_Set_Oinsert ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__ident_0) ).
thf(1182,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = D )
| ( B @ ( A @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( A @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( C @ ( B @ ( A @ c_Set_Oinsert ) ) )
!= ( C @ ( D @ ( A @ c_Set_Oinsert ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(515,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( tc_bool @ ( F @ tc_fun ) @ ( D @ ( A @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) ) ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INF1__iff_0) ).
thf(1739,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( tc_bool @ ( F @ tc_fun ) @ ( D @ ( A @ ( E @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) ) ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[515]) ).
thf(214,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( 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_3) ).
thf(1075,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(563,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__eq_0) ).
thf(1842,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[563]) ).
thf(165,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__less_1) ).
thf(970,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(517,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Int2_0) ).
thf(1744,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[517]) ).
thf(53,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__left__commute_0) ).
thf(706,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(374,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( tc_bool @ ( A @ tc_fun ) @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ComplI_0) ).
thf(1419,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( tc_bool @ ( A @ tc_fun ) @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[374]) ).
thf(187,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastLessThan ) ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastLessThan__empty__iff_1) ).
thf(1016,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastLessThan ) ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(9,axiom,
tc_nat @ class_Orderings_Olinorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Olinorder) ).
thf(590,plain,
tc_nat @ class_Orderings_Olinorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(104,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( A @ ( B @ ( A @ c_Fun_Oid @ c_Fun_Ocomp ) ) ) ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_id__o_0) ).
thf(837,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ ( A @ ( B @ ( A @ c_Fun_Oid @ c_Fun_Ocomp ) ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(448,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__le__not__le_2) ).
thf(1588,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[448]) ).
thf(51,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le_1) ).
thf(701,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(249,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__crazy_0) ).
thf(1150,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(389,axiom,
tc_bool @ class_HOL_Ominus,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__HOL_Ominus) ).
thf(1451,plain,
tc_bool @ class_HOL_Ominus,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[389]) ).
thf(34,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__minus__iff_0) ).
thf(654,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(483,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( t_a @ ( C @ ( D @ c_Hoare__Mirabelle_Ohoare__valids ) ) )
| ( D @ ( A @ ( D @ v_sko__Hoare__Mirabelle__Xhoare__valids__def__1 ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( B @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( t_a @ ( B @ ( A @ c_Hoare__Mirabelle_Otriple__valid ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hoare__valids__def_0) ).
thf(1668,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( t_a @ ( C @ ( D @ c_Hoare__Mirabelle_Ohoare__valids ) ) )
| ( D @ ( A @ ( D @ v_sko__Hoare__Mirabelle__Xhoare__valids__def__1 ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( B @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( t_a @ ( B @ ( A @ c_Hoare__Mirabelle_Otriple__valid ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[483]) ).
thf(59,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__less__iff__less_1) ).
thf(721,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(579,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ tc_fun ) @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( D @ tc_fun ) @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_HOL_Oord ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__fun__def_2) ).
thf(1874,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ tc_fun ) @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( D @ tc_fun ) @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_HOL_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[579]) ).
thf(453,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_7) ).
thf(1599,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[453]) ).
thf(504,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(1715,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)],[504]) ).
thf(507,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( 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(1720,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( 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)],[507]) ).
thf(466,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(1627,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)],[466]) ).
thf(554,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( A @ tc_fun ) @ ( tc_bool @ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( C @ ( A @ c_in @ c_COMBC ) ) ) ) @ ( tc_bool @ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( B @ ( A @ c_in @ c_COMBC ) ) ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pred__subset__eq_1) ).
thf(1825,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( A @ tc_fun ) @ ( tc_bool @ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( C @ ( A @ c_in @ c_COMBC ) ) ) ) @ ( tc_bool @ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( B @ ( A @ c_in @ c_COMBC ) ) ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[554]) ).
thf(331,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_4) ).
thf(1324,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[331]) ).
thf(304,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Compl_0) ).
thf(1263,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[304]) ).
thf(178,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( 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(997,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( 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)],[178]) ).
thf(423,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( E @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( E @ ( C @ hAPP ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
!= ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ ( B @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UNION__empty__conv_I1_J_0) ).
thf(1530,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( E @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( E @ ( C @ hAPP ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot )
!= ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ ( B @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[423]) ).
thf(427,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( D @ ( C @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__int_I11_J_0) ).
thf(1539,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( D @ ( C @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[427]) ).
thf(306,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(1266,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)],[306]) ).
thf(557,axiom,
! [A: $i] : ( tc_bool @ ( A @ tc_fun ) @ ( tc_bool @ ( A @ tc_fun ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_HOL_Ouminus__class_Ouminus ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__Compl__self__eq_1) ).
thf(1831,plain,
! [A: $i] : ( tc_bool @ ( A @ tc_fun ) @ ( tc_bool @ ( A @ tc_fun ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_HOL_Ouminus__class_Ouminus ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[557]) ).
thf(172,axiom,
! [B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty__left_0) ).
thf(984,plain,
! [B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(138,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__le__trans_0) ).
thf(911,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( D @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(524,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(1759,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)],[524]) ).
thf(363,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(1393,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)],[363]) ).
thf(335,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( t_a @ ( C @ ( B @ ( A @ v_sko__Hoare__Mirabelle__Xhoare__valids__def__2 ) @ c_Hoare__Mirabelle_Otriple__valid ) ) )
| ( t_a @ ( B @ ( A @ c_Hoare__Mirabelle_Ohoare__valids ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_hoare__valids__def_2) ).
thf(1333,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( t_a @ ( C @ ( B @ ( A @ v_sko__Hoare__Mirabelle__Xhoare__valids__def__2 ) @ c_Hoare__Mirabelle_Otriple__valid ) ) )
| ( t_a @ ( B @ ( A @ c_Hoare__Mirabelle_Ohoare__valids ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[335]) ).
thf(85,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__supI2_0) ).
thf(792,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(143,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( D @ ( E @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__eqI_0) ).
thf(921,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( D @ ( E @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(259,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(1170,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)],[259]) ).
thf(196,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= C )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__sup_0) ).
thf(1035,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= C )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(212,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( C @ c_lessequals ) ) )
| ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( tc_bool @ ( B @ tc_fun ) @ ( A @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__anti__mono_0) ).
thf(1071,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( C @ c_lessequals ) ) )
| ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( tc_bool @ ( B @ tc_fun ) @ ( A @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(267,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(1187,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)],[267]) ).
thf(416,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( v_x @ ( A @ ( t_a @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ hAPP ) )
= ( A @ ( v_x @ ( C @ hAPP ) @ ( v_x @ ( B @ hAPP ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__fun__eq_0) ).
thf(1515,plain,
! [C: $i,B: $i,A: $i] :
( ( ( v_x @ ( A @ ( t_a @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ hAPP ) )
= ( A @ ( v_x @ ( C @ hAPP ) @ ( v_x @ ( B @ hAPP ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[416]) ).
thf(145,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( E @ ( D @ ( B @ c_Set_Ovimage ) ) ) @ ( C @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ hAPP ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimageE_0) ).
thf(926,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( E @ ( D @ ( B @ c_Set_Ovimage ) ) ) @ ( C @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ hAPP ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(549,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(1814,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)],[549]) ).
thf(150,axiom,
! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__subset_0) ).
thf(938,plain,
! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(26,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(633,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)],[26]) ).
thf(534,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(1779,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)],[534]) ).
thf(503,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( A @ ( B @ c_SetInterval_Oord__class_OlessThan ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( C @ c_SetInterval_Oord__class_OatMost ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__un_I10_J_0) ).
thf(1712,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( A @ ( B @ c_SetInterval_Oord__class_OlessThan ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( C @ c_SetInterval_Oord__class_OatMost ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[503]) ).
thf(565,axiom,
tc_bool @ class_Lattices_Oboolean__algebra,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oboolean__algebra) ).
thf(1846,plain,
tc_bool @ class_Lattices_Oboolean__algebra,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[565]) ).
thf(157,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Un__distrib_0) ).
thf(953,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(266,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__sup__iff_2) ).
thf(1185,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(77,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( C @ ( B @ c_Fun_Oid @ ( A @ c_Fun_Ofcomp ) ) ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fcomp__id_0) ).
thf(773,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( B @ ( C @ ( B @ c_Fun_Oid @ ( A @ c_Fun_Ofcomp ) ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(86,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( E @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__eqI_1) ).
thf(794,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( E @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(5,axiom,
tc_nat @ class_Orderings_Oorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Oorder) ).
thf(586,plain,
tc_nat @ class_Orderings_Oorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(37,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( A @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Odistrib__lattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__distrib1_0) ).
thf(662,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( A @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Odistrib__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(58,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv3_0) ).
thf(718,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(136,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( C @ hAPP ) @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( A @ ( D @ ( C @ c_Set_Ovimage ) ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimageI2_0) ).
thf(906,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( C @ hAPP ) @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( A @ ( D @ ( C @ c_Set_Ovimage ) ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(247,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( B @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supE_1) ).
thf(1146,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( B @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(497,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( 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(1698,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( 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)],[497]) ).
thf(403,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(1483,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)],[403]) ).
thf(47,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( B @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I5_J_0) ).
thf(689,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( B @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(353,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(1374,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)],[353]) ).
thf(510,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(1727,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)],[510]) ).
thf(414,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__subset__conv_1) ).
thf(1510,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[414]) ).
thf(321,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastLessThan ) ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastLessThan__empty_0) ).
thf(1301,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastLessThan ) ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[321]) ).
thf(451,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( E @ ( D @ ( B @ c_Set_Ovimage ) ) ) @ ( C @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ hAPP ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimageD_0) ).
thf(1595,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( E @ ( D @ ( B @ c_Set_Ovimage ) ) ) @ ( C @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ hAPP ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[451]) ).
thf(251,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(1154,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)],[251]) ).
thf(135,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(904,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)],[135]) ).
thf(461,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( B @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__sup__iff_1) ).
thf(1615,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( B @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[461]) ).
thf(238,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( A @ ( B @ c_SetInterval_Oord__class_OlessThan ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__int_I2_J_0) ).
thf(1125,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( A @ ( B @ c_SetInterval_Oord__class_OlessThan ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(463,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( E @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( A @ ( D @ ( C @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__psubset__iff_0) ).
thf(1620,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( E @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( A @ ( D @ ( C @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[463]) ).
thf(477,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(1652,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)],[477]) ).
thf(360,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( B @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) )
| ( A @ ( D @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__insert__iff_1) ).
thf(1388,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( B @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) )
| ( A @ ( D @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[360]) ).
thf(67,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( B @ c_SetInterval_Oord__class_OgreaterThan ) )
!= ( A @ ( C @ c_SetInterval_Oord__class_OgreaterThan ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_greaterThan__eq__iff_0) ).
thf(743,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( B @ c_SetInterval_Oord__class_OgreaterThan ) )
!= ( A @ ( C @ c_SetInterval_Oord__class_OgreaterThan ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(425,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( F @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( F @ ( D @ hAPP ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( tc_bool @ ( A @ tc_fun ) @ ( E @ ( D @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__iff_2) ).
thf(1535,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( F @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( F @ ( D @ hAPP ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( tc_bool @ ( A @ tc_fun ) @ ( E @ ( D @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[425]) ).
thf(418,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ ( C @ ( E @ c_Set_Oimage ) ) ) @ ( B @ ( E @ hAPP ) @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_rev__image__eqI_0) ).
thf(1520,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ ( C @ ( E @ c_Set_Oimage ) ) ) @ ( B @ ( E @ hAPP ) @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[418]) ).
thf(541,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( E @ ( tc_bool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( A @ c_Set_Ovimage ) ) ) @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( B @ ( A @ hAPP ) )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__singleton__eq_0) ).
thf(1795,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( D @ ( E @ ( tc_bool @ ( E @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( A @ c_Set_Ovimage ) ) ) @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( B @ ( A @ hAPP ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[541]) ).
thf(498,axiom,
! [B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_empty__Diff_0) ).
thf(1701,plain,
! [B: $i,A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[498]) ).
thf(537,axiom,
! [B: $i,A: $i] :
( ( v_x @ ( tc_bool @ ( t_a @ tc_fun ) @ ( tc_bool @ ( tc_bool @ ( t_a @ tc_fun ) @ ( t_a @ ( B @ ( t_a @ c_in @ c_COMBC ) ) ) ) @ ( tc_bool @ ( tc_bool @ ( t_a @ tc_fun ) @ ( t_a @ ( A @ ( t_a @ c_in @ c_COMBC ) ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ hAPP ) )
= ( tc_bool @ ( t_a @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( v_x @ ( t_a @ c_in @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__Un__eq_0) ).
thf(1786,plain,
! [B: $i,A: $i] :
( ( v_x @ ( tc_bool @ ( t_a @ tc_fun ) @ ( tc_bool @ ( tc_bool @ ( t_a @ tc_fun ) @ ( t_a @ ( B @ ( t_a @ c_in @ c_COMBC ) ) ) ) @ ( tc_bool @ ( tc_bool @ ( t_a @ tc_fun ) @ ( t_a @ ( A @ ( t_a @ c_in @ c_COMBC ) ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ hAPP ) )
= ( tc_bool @ ( t_a @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( v_x @ ( t_a @ c_in @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[537]) ).
thf(501,axiom,
! [B: $i,A: $i] :
( ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ ( A @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Ouminus__class_Ouminus ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__complement_0) ).
thf(1707,plain,
! [B: $i,A: $i] :
( ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ ( A @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Ouminus__class_Ouminus ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[501]) ).
thf(326,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ c_SetInterval_Oord__class_OatMost ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_HOL_Oord ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atMost__iff_0) ).
thf(1312,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ c_SetInterval_Oord__class_OatMost ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_HOL_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[326]) ).
thf(575,axiom,
! [C: $i,B: $i,A: $i] :
( ( A
= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
!= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty_0) ).
thf(1865,plain,
! [C: $i,B: $i,A: $i] :
( ( A
= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
!= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[575]) ).
thf(302,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UnCI_0) ).
thf(1258,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[302]) ).
thf(470,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
!= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_disjoint__iff__not__equal_0) ).
thf(1638,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
!= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[470]) ).
thf(29,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__asym_0) ).
thf(641,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(379,axiom,
! [B: $i,A: $i] :
( ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( tc_bool @ ( B @ tc_fun ) @ ( A @ c_HOL_Ouminus__class_Ouminus ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__disjoint2_0) ).
thf(1428,plain,
! [B: $i,A: $i] :
( ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( tc_bool @ ( B @ tc_fun ) @ ( A @ c_HOL_Ouminus__class_Ouminus ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[379]) ).
thf(469,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( E @ c_lessequals ) ) )
| ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__eqI_1) ).
thf(1635,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( E @ c_lessequals ) ) )
| ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[469]) ).
thf(513,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
!= C )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__iff__sup_1) ).
thf(1733,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
!= C )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[513]) ).
thf(527,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ocomp ) ) ) ) @ hAPP ) )
= ( F @ ( B @ hAPP ) @ ( A @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__apply_0) ).
thf(1765,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ocomp ) ) ) ) @ hAPP ) )
= ( F @ ( B @ hAPP ) @ ( A @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[527]) ).
thf(221,axiom,
! [C: $i,B: $i,A: $i] : ( A @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertI1_0) ).
thf(1090,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(142,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__assoc_0) ).
thf(919,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(90,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_minus__less__iff_1) ).
thf(804,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(271,axiom,
! [B: $i,A: $i] :
( ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty__right_0) ).
thf(1194,plain,
! [B: $i,A: $i] :
( ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(133,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(900,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)],[133]) ).
thf(234,axiom,
tc_bool @ class_Orderings_Obot,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Obot) ).
thf(1117,plain,
tc_bool @ class_Orderings_Obot,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(443,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singletonE_0) ).
thf(1574,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[443]) ).
thf(420,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( E @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( E @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( E @ ( D @ c_lessequals ) ) )
| ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( E @ ( D @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__psubset__iff_6) ).
thf(1524,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( E @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( E @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( E @ ( D @ c_lessequals ) ) )
| ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( E @ ( D @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[420]) ).
thf(428,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_OSup__class_OSup ) )
= ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sup__binary_0) ).
thf(1542,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_OSup__class_OSup ) )
= ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[428]) ).
thf(65,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Lattices_Oboolean__algebra ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_compl__inf__bot_0) ).
thf(737,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Lattices_Oboolean__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(543,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_HOL_Oord__class_Oless ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__psubset__trans_0) ).
thf(1801,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_HOL_Oord__class_Oless ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[543]) ).
thf(237,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__less_0) ).
thf(1122,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(261,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( E @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( E @ ( C @ hAPP ) @ ( A @ ( D @ ( C @ ( B @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INF__leI_0) ).
thf(1175,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( E @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( E @ ( C @ hAPP ) @ ( A @ ( D @ ( C @ ( B @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(44,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( D @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__eqI_1) ).
thf(681,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( D @ ( D @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(569,axiom,
tc_bool @ class_Orderings_Oorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Oorder) ).
thf(1853,plain,
tc_bool @ class_Orderings_Oorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[569]) ).
thf(407,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__commute_0) ).
thf(1492,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[407]) ).
thf(455,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( D @ c_lessequals ) ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__assoc__eq_1) ).
thf(1603,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( D @ c_lessequals ) ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[455]) ).
thf(442,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) )
!= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__empty__iff_0) ).
thf(1571,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) )
!= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[442]) ).
thf(354,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( F @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( F @ ( D @ hAPP ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( tc_bool @ ( A @ tc_fun ) @ ( E @ ( D @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__I_0) ).
thf(1376,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( F @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( F @ ( D @ hAPP ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( tc_bool @ ( A @ tc_fun ) @ ( E @ ( D @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[354]) ).
thf(93,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(811,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)],[93]) ).
thf(25,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(631,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)],[25]) ).
thf(435,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( C @ c_SetInterval_Oord__class_OatLeast ) @ ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( B @ c_SetInterval_Oord__class_OatLeast ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__un_I14_J_0) ).
thf(1557,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( C @ c_SetInterval_Oord__class_OatLeast ) @ ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( B @ c_SetInterval_Oord__class_OatLeast ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[435]) ).
thf(95,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( A @ c_Fun_Oid @ c_Set_Ovimage ) ) ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__id_0) ).
thf(816,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( A @ c_Fun_Oid @ c_Set_Ovimage ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(18,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__less__iff__gr__or__eq_0) ).
thf(609,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(561,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( 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(1838,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( 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)],[561]) ).
thf(162,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__idemp_0) ).
thf(964,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(434,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(1556,plain,
! [B: $i,A: $i] : ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[434]) ).
thf(39,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) )
!= ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_Lattices_Oboolean__algebra ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_compl__eq__compl__iff_0) ).
thf(668,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) )
!= ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_Lattices_Oboolean__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(552,axiom,
! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__upper1_0) ).
thf(1821,plain,
! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[552]) ).
thf(512,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ c_HOL_Ouminus__class_Ouminus ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__subset__Compl__iff_0) ).
thf(1731,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ c_HOL_Ouminus__class_Ouminus ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[512]) ).
thf(13,axiom,
! [C: $i,B: $i,A: $i] :
( ( C = B )
| ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neqE__ordered__idom_0) ).
thf(594,plain,
! [C: $i,B: $i,A: $i] :
( ( C = B )
| ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Ring__and__Field_Oordered__idom ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(88,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(799,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)],[88]) ).
thf(255,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__less__trans_0) ).
thf(1162,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(193,axiom,
( ( v_x @ ( tc_bool @ ( t_a @ tc_fun ) @ c_Orderings_Obot__class_Obot @ hAPP ) )
= ( tc_bool @ ( t_a @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( v_x @ ( t_a @ c_in @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bot__empty__eq_0) ).
thf(1029,plain,
( ( v_x @ ( tc_bool @ ( t_a @ tc_fun ) @ c_Orderings_Obot__class_Obot @ hAPP ) )
= ( tc_bool @ ( t_a @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( v_x @ ( t_a @ c_in @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(131,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(895,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)],[131]) ).
thf(23,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__eq__neg__inf_0) ).
thf(626,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_HOL_Ouminus__class_Ouminus ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(140,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(915,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)],[140]) ).
thf(262,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(1177,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)],[262]) ).
thf(357,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__trans_0) ).
thf(1381,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[357]) ).
thf(364,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Un__distrib2_0) ).
thf(1396,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[364]) ).
thf(75,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_HOL_Ouminus__class_Ouminus ) )
= ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Oboolean__algebra ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_compl__inf_0) ).
thf(768,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_HOL_Ouminus__class_Ouminus ) )
= ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Oboolean__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(125,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ c_SetInterval_Oord__class_OlessThan ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_HOL_Oord ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lessThan__iff_1) ).
thf(883,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ c_SetInterval_Oord__class_OlessThan ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ class_HOL_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(186,axiom,
tc_bool @ class_Lattices_Obounded__lattice,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Obounded__lattice) ).
thf(1015,plain,
tc_bool @ class_Lattices_Obounded__lattice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(173,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ( ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( D @ ( C @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( D @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__un_I21_J_0) ).
thf(986,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ( ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( D @ ( C @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( D @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(232,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( tc_bool @ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( B @ ( A @ c_in @ c_COMBC ) ) ) ) )
!= ( tc_bool @ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( C @ ( A @ c_in @ c_COMBC ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_pred__equals__eq_0) ).
thf(1113,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( tc_bool @ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( B @ ( A @ c_in @ c_COMBC ) ) ) ) )
!= ( tc_bool @ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( C @ ( A @ c_in @ c_COMBC ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(400,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( E @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( E @ ( D @ c_lessequals ) ) )
| ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( E @ ( D @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__psubset__iff_5) ).
thf(1477,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( E @ ( C @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( E @ ( D @ c_lessequals ) ) )
| ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( E @ ( D @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[400]) ).
thf(298,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_8) ).
thf(1250,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[298]) ).
thf(409,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(1496,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)],[409]) ).
thf(495,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supE_0) ).
thf(1694,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[495]) ).
thf(545,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= D ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__extend__simps_I1_J_0) ).
thf(1805,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= D ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[545]) ).
thf(437,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( 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(1562,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( 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)],[437]) ).
thf(27,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Lattices_Oboolean__algebra ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__compl__bot_0) ).
thf(636,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Lattices_Oboolean__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(49,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Set_Oinsert ) ) @ c_Complete__Lattice_OSup__class_OSup ) )
= ( A @ ( A @ ( C @ c_Complete__Lattice_OSup__class_OSup ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Sup__insert_0) ).
thf(695,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Set_Oinsert ) ) @ c_Complete__Lattice_OSup__class_OSup ) )
= ( A @ ( A @ ( C @ c_Complete__Lattice_OSup__class_OSup ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Complete__Lattice_Ocomplete__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(295,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( E @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( tc_bool @ ( D @ tc_fun ) @ ( E @ ( B @ hAPP ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ ( A @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__lower_0) ).
thf(1245,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( E @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( tc_bool @ ( D @ tc_fun ) @ ( E @ ( B @ hAPP ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ ( A @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[295]) ).
thf(118,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( D @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( D @ ( B @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ ( B @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_1) ).
thf(868,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( D @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ( D @ ( B @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ ( B @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(386,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(1445,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)],[386]) ).
thf(422,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( E @ ( C @ c_lessequals ) ) )
| ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( E @ ( D @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__subset__iff_3) ).
thf(1528,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( D @ c_lessequals ) ) )
| ~ ( A @ ( E @ ( C @ c_lessequals ) ) )
| ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( E @ ( D @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[422]) ).
thf(80,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(780,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)],[80]) ).
thf(472,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Int_0) ).
thf(1643,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[472]) ).
thf(532,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__leE_0) ).
thf(1775,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[532]) ).
thf(382,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntE_0) ).
thf(1435,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[382]) ).
thf(110,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(851,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)],[110]) ).
thf(227,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( A @ c_Set_Oinsert ) ) )
= ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__extend__simps_I1_J_0) ).
thf(1102,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( A @ c_Set_Oinsert ) ) )
= ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(372,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(1413,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)],[372]) ).
thf(547,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Int__distrib2_0) ).
thf(1809,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[547]) ).
thf(481,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(1662,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)],[481]) ).
thf(153,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_HOL_Ominus )
| ( B @ ( A @ tc_fun ) @ class_HOL_Ominus ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__HOL_Ominus) ).
thf(944,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_HOL_Ominus )
| ( B @ ( A @ tc_fun ) @ class_HOL_Ominus ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(396,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DiffE_0) ).
thf(1467,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[396]) ).
thf(311,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( A @ ( B @ c_SetInterval_Oord__class_OlessThan ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( C @ c_SetInterval_Oord__class_OlessThan ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__un_I8_J_0) ).
thf(1277,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ ( A @ ( B @ c_SetInterval_Oord__class_OlessThan ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( C @ c_SetInterval_Oord__class_OlessThan ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[311]) ).
thf(151,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_Suc @ c_Hoare__Mirabelle_Otriple__valid ) ) )
| ( C @ ( B @ ( A @ c_Hoare__Mirabelle_Otriple__valid ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_triple__valid__Suc_0) ).
thf(939,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_Suc @ c_Hoare__Mirabelle_Otriple__valid ) ) )
| ( C @ ( B @ ( A @ c_Hoare__Mirabelle_Otriple__valid ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(398,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv1_0) ).
thf(1472,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( B = C )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[398]) ).
thf(246,axiom,
! [B: $i,A: $i] : ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_singleton__iff_1) ).
thf(1145,plain,
! [B: $i,A: $i] : ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(71,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( B @ c_SetInterval_Oord__class_OatMost ) )
!= ( A @ ( C @ c_SetInterval_Oord__class_OatMost ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atMost__eq__iff_0) ).
thf(754,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ( ( A @ ( B @ c_SetInterval_Oord__class_OatMost ) )
!= ( A @ ( C @ c_SetInterval_Oord__class_OatMost ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(164,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( tc_bool @ ( C @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
| ( C @ ( B @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_weaken_0) ).
thf(968,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( tc_bool @ ( C @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ ( D @ ( B @ c_lessequals ) ) )
| ( C @ ( B @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(432,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( C @ c_SetInterval_Oord__class_OgreaterThan ) @ ( A @ ( B @ c_SetInterval_Oord__class_OgreaterThan ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_greaterThan__subset__iff_1) ).
thf(1551,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( C @ c_SetInterval_Oord__class_OgreaterThan ) @ ( A @ ( B @ c_SetInterval_Oord__class_OgreaterThan ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[432]) ).
thf(202,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Int__Diff_0) ).
thf(1049,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(42,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(675,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)],[42]) ).
thf(446,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__empty_0) ).
thf(1583,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[446]) ).
thf(322,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(1304,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)],[322]) ).
thf(578,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( E @ ( A @ c_Set_Oimage ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__diff__subset_0) ).
thf(1873,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] : ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Set_Oimage ) ) ) @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( E @ ( A @ c_Set_Oimage ) ) ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[578]) ).
thf(523,axiom,
tc_bool @ class_Lattices_Oupper__semilattice,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Oupper__semilattice) ).
thf(1758,plain,
tc_bool @ class_Lattices_Oupper__semilattice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[523]) ).
thf(257,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I7_J_0) ).
thf(1166,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(275,axiom,
tc_bool @ class_Lattices_Olattice,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olattice) ).
thf(1203,plain,
tc_bool @ class_Lattices_Olattice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(278,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_HOL_Ouminus__class_Ouminus ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ c_HOL_Ouminus__class_Ouminus ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__Un_0) ).
thf(1208,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_HOL_Ouminus__class_Ouminus ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ c_HOL_Ouminus__class_Ouminus ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(8,axiom,
tc_nat @ class_Lattices_Oupper__semilattice,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Oupper__semilattice) ).
thf(589,plain,
tc_nat @ class_Lattices_Oupper__semilattice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(242,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Set_Oinsert ) ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__Diff_0) ).
thf(1134,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_Set_Oinsert ) ) @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Set_Oinsert ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(32,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(648,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)],[32]) ).
thf(217,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Diff__cancel_0) ).
thf(1081,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(69,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_eq__eqI_0) ).
thf(749,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C = D )
| ( ( A @ ( B @ ( B @ c_HOL_Ominus__class_Ominus ) ) )
!= ( A @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) ) )
| ~ ( A @ class_OrderedGroup_Oab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(542,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_lessequals ) ) )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_double__diff_0) ).
thf(1798,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( C @ c_lessequals ) ) )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[542]) ).
thf(191,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__antisym__conv2_1) ).
thf(1025,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(120,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(872,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)],[120]) ).
thf(127,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( E @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__mono_0) ).
thf(887,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( E @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( D @ c_HOL_Ominus__class_Ominus ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(439,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(1566,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[439]) ).
thf(299,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(1252,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)],[299]) ).
thf(350,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( v_x @ ( t_a @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ocomp ) ) ) ) @ hAPP ) )
= ( v_x @ ( B @ hAPP ) @ ( A @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__def_0) ).
thf(1368,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( v_x @ ( t_a @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ocomp ) ) ) ) @ hAPP ) )
= ( v_x @ ( B @ hAPP ) @ ( A @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[350]) ).
thf(521,axiom,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__neq__le__trans_0) ).
thf(1753,plain,
! [C: $i,B: $i,A: $i] :
( ( B = C )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[521]) ).
thf(287,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( C @ ( D @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( A @ ( B @ ( E @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( E @ c_lessequals ) ) )
| ( A @ ( E @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__psubset__iff_2) ).
thf(1230,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( C @ ( D @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( A @ ( B @ ( E @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( B @ ( E @ c_lessequals ) ) )
| ( A @ ( E @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(176,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( A @ ( E @ ( F @ ( B @ c_Set_Oimage ) ) ) @ c_lessequals ) ) )
| ~ ( F @ ( C @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ hAPP ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__subset__iff_0) ).
thf(993,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( A @ ( E @ ( F @ ( B @ c_Set_Oimage ) ) ) @ c_lessequals ) ) )
| ~ ( F @ ( C @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( C @ ( B @ hAPP ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(430,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(1547,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)],[430]) ).
thf(519,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( D @ c_lessequals ) ) )
| ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subsetD_0) ).
thf(1748,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( D @ c_lessequals ) ) )
| ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[519]) ).
thf(55,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I6_J_0) ).
thf(712,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(181,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( C @ c_SetInterval_Oord__class_OgreaterThan ) @ ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__int_I7_J_0) ).
thf(1003,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( C @ c_SetInterval_Oord__class_OgreaterThan ) @ ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(1,negated_conjecture,
tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ ( v_Ga @ ( v_tsa @ c_lessequals ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_0) ).
thf(580,plain,
tc_bool @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ tc_fun ) @ ( v_Ga @ ( v_tsa @ c_lessequals ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(112,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Lattices_Olattice )
| ( B @ ( A @ tc_fun ) @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Oupper__semilattice) ).
thf(855,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Lattices_Olattice )
| ( B @ ( A @ tc_fun ) @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(459,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(1611,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[459]) ).
thf(252,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__least_0) ).
thf(1156,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(285,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(1225,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)],[285]) ).
thf(366,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( E @ ( D @ ( B @ c_Set_Oimage ) ) ) @ ( C @ ( B @ hAPP ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__eqI_0) ).
thf(1400,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( E @ ( D @ ( B @ c_Set_Oimage ) ) ) @ ( C @ ( B @ hAPP ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[366]) ).
thf(41,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__less__iff__less_0) ).
thf(673,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(390,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(1452,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)],[390]) ).
thf(197,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_IntE_1) ).
thf(1038,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( D @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(57,axiom,
tc_nat @ class_Orderings_Obot,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Obot) ).
thf(717,plain,
tc_nat @ class_Orderings_Obot,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(289,axiom,
! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__upper2_0) ).
thf(1235,plain,
! [C: $i,B: $i,A: $i] : ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(526,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ c_SetInterval_Oord__class_OatLeast ) @ ( C @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_HOL_Oord ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeast__iff_0) ).
thf(1763,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ c_SetInterval_Oord__class_OatLeast ) @ ( C @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_HOL_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[526]) ).
thf(219,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(1085,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)],[219]) ).
thf(488,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ball__empty_0) ).
thf(1679,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[488]) ).
thf(240,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(1130,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)],[240]) ).
thf(30,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(643,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)],[30]) ).
thf(283,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__mono_0) ).
thf(1220,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_lessequals ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( E @ ( D @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(204,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( E @ ( B @ ( F @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) ) ) @ ( A @ c_lessequals ) ) )
| ~ ( F @ ( C @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ hAPP ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__subset__iff_0) ).
thf(1053,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( E @ ( B @ ( F @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) ) ) @ ( A @ c_lessequals ) ) )
| ~ ( F @ ( C @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ hAPP ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(410,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
!= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__Un__eq_1) ).
thf(1499,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
!= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[410]) ).
thf(539,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__un_I6_J_0) ).
thf(1790,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( C @ c_Set_Oinsert ) ) @ ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastLessThan ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[539]) ).
thf(505,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( E @ ( D @ ( B @ c_Set_Oimage ) ) ) @ ( C @ ( B @ hAPP ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_imageI_0) ).
thf(1716,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( C @ ( E @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( E @ ( D @ ( B @ c_Set_Oimage ) ) ) @ ( C @ ( B @ hAPP ) @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[505]) ).
thf(156,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(951,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)],[156]) ).
thf(92,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= B )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__idem_0) ).
thf(808,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= B )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(314,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__iff_2) ).
thf(1285,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( D @ ( C @ c_Set_Oinsert ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[314]) ).
thf(282,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supI2_0) ).
thf(1218,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(346,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__subset__iff_0) ).
thf(1358,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[346]) ).
thf(567,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__left__commute_0) ).
thf(1849,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[567]) ).
thf(52,axiom,
! [A: $i] :
( A
!= ( A @ c_Suc ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_n__not__Suc__n_0) ).
thf(703,plain,
! [A: $i] :
( A
!= ( A @ c_Suc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(404,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__extend__simps_I3_J_0) ).
thf(1485,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[404]) ).
thf(116,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( F @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( F @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ ( A @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_SUP1__I_0) ).
thf(864,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( F @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( E @ ( F @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
| ( E @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ ( A @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(484,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supI1_0) ).
thf(1670,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[484]) ).
thf(183,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( D @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_DiffE_1) ).
thf(1008,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( D @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(352,axiom,
( ( v_x @ ( t_a @ c_Fun_Oid @ hAPP ) )
= v_x ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_id__def_0) ).
thf(1372,plain,
( ( v_x @ ( t_a @ c_Fun_Oid @ hAPP ) )
= v_x ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[352]) ).
thf(114,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(859,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)],[114]) ).
thf(35,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Odistrib__lattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__distrib2_0) ).
thf(656,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( A @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Odistrib__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(190,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
| ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__subset__conv_0) ).
thf(1023,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
| ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(343,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(1353,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)],[343]) ).
thf(15,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_HOL_Ouminus__class_Ouminus ) )
= ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_neg__sup__eq__inf_0) ).
thf(600,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_HOL_Ouminus__class_Ouminus ) )
= ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_OrderedGroup_Olordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(169,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( 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(978,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( 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)],[169]) ).
thf(244,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(1140,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)],[244]) ).
thf(309,axiom,
! [B: $i,A: $i] :
~ ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__eq_1) ).
thf(1272,plain,
! [B: $i,A: $i] :
~ ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[309]) ).
thf(19,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_HOL_Ouminus__class_Ouminus ) )
= ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Oboolean__algebra ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_compl__sup_0) ).
thf(612,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_HOL_Ouminus__class_Ouminus ) )
= ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Oboolean__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(292,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ c_SetInterval_Oord__class_OgreaterThan ) @ ( C @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_HOL_Oord ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_greaterThan__iff_0) ).
thf(1240,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ c_SetInterval_Oord__class_OgreaterThan ) @ ( C @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_HOL_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[292]) ).
thf(175,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( A @ ( D @ ( B @ c_Set_Oinsert ) ) @ c_lessequals ) ) )
| ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insert__subset_0) ).
thf(991,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( A @ ( D @ ( B @ c_Set_Oinsert ) ) @ c_lessequals ) ) )
| ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(462,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( v_x @ ( A @ ( t_a @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ hAPP ) )
= ( A @ ( v_x @ ( C @ hAPP ) @ ( v_x @ ( B @ hAPP ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__fun__eq_0) ).
thf(1617,plain,
! [C: $i,B: $i,A: $i] :
( ( ( v_x @ ( A @ ( t_a @ tc_fun ) @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ hAPP ) )
= ( A @ ( v_x @ ( C @ hAPP ) @ ( v_x @ ( B @ hAPP ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[462]) ).
thf(375,axiom,
! [A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty_2) ).
thf(1421,plain,
! [A: $i] :
( ( tc_bool @ ( A @ tc_fun ) @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[375]) ).
thf(393,axiom,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( I @ ( H @ ( G @ ( B @ ( A @ c_Fun_Ocomp ) ) ) ) @ hAPP ) )
= ( F @ ( K @ ( H @ ( J @ ( E @ ( D @ c_Fun_Ocomp ) ) ) ) @ hAPP ) ) )
| ( ( C @ ( B @ hAPP ) @ ( A @ hAPP ) )
!= ( F @ ( E @ hAPP ) @ ( D @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_comp__cong_0) ).
thf(1459,plain,
! [K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( I @ ( H @ ( G @ ( B @ ( A @ c_Fun_Ocomp ) ) ) ) @ hAPP ) )
= ( F @ ( K @ ( H @ ( J @ ( E @ ( D @ c_Fun_Ocomp ) ) ) ) @ hAPP ) ) )
| ( ( C @ ( B @ hAPP ) @ ( A @ hAPP ) )
!= ( F @ ( E @ hAPP ) @ ( D @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[393]) ).
thf(264,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__subset__trans_0) ).
thf(1180,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( D @ c_lessequals ) ) )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(491,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_mem__def_1) ).
thf(1685,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[491]) ).
thf(433,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__partition_0) ).
thf(1553,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[433]) ).
thf(40,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( B @ ( B @ c_Fun_Oid @ ( A @ c_Fun_Ocomp ) ) ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__id_0) ).
thf(671,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ ( B @ ( B @ c_Fun_Oid @ ( A @ c_Fun_Ocomp ) ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(559,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( tc_bool @ ( F @ tc_fun ) @ ( A @ ( D @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) ) ) @ hAPP ) @ hBOOL )
| ( E @ ( B @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INF1__E_0) ).
thf(1834,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ ( tc_bool @ ( F @ tc_fun ) @ ( A @ ( D @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) ) ) @ hAPP ) @ hBOOL )
| ( E @ ( B @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[559]) ).
thf(2,negated_conjecture,
v_tsa @ ( v_xa @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_in @ hAPP ) @ hAPP ) @ hBOOL,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_conjecture_1) ).
thf(581,plain,
v_tsa @ ( v_xa @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_in @ hAPP ) @ hAPP ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(478,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(1654,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)],[478]) ).
thf(268,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( E @ tc_fun ) @ ( C @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) ) ) )
= ( tc_bool @ ( E @ tc_fun ) @ ( tc_bool @ ( E @ tc_fun ) @ ( C @ ( D @ ( B @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) ) ) @ ( tc_bool @ ( E @ tc_fun ) @ ( C @ ( D @ ( A @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__Un_0) ).
thf(1189,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( E @ tc_fun ) @ ( C @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) ) ) )
= ( tc_bool @ ( E @ tc_fun ) @ ( tc_bool @ ( E @ tc_fun ) @ ( C @ ( D @ ( B @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) ) ) @ ( tc_bool @ ( E @ tc_fun ) @ ( C @ ( D @ ( A @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(230,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup1CI_1) ).
thf(1108,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( A @ hAPP ) @ hBOOL )
| ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(328,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(1316,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)],[328]) ).
thf(475,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( C @ c_SetInterval_Oord__class_OatLeast ) @ ( A @ ( B @ c_SetInterval_Oord__class_OatLeast ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeast__subset__iff_1) ).
thf(1649,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( C @ c_SetInterval_Oord__class_OatLeast ) @ ( A @ ( B @ c_SetInterval_Oord__class_OatLeast ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[475]) ).
thf(168,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Set__Xsubset__iff__1__1 ) ) @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__iff_1) ).
thf(976,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Set__Xsubset__iff__1__1 ) ) @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(564,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Diff__cancel2_0) ).
thf(1844,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[564]) ).
thf(535,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubsetD_0) ).
thf(1781,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[535]) ).
thf(129,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__supI_0) ).
thf(891,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_lessequals ) ) )
| ~ ( A @ ( D @ ( C @ c_lessequals ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(184,axiom,
! [B: $i,A: $i] :
( ( ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( B @ c_SetInterval_Oord__class_OatLeast ) @ ( A @ ( B @ c_SetInterval_Oord__class_OatMost ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atMost__Int__atLeast_0) ).
thf(1010,plain,
! [B: $i,A: $i] :
( ( ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( B @ c_SetInterval_Oord__class_OatLeast ) @ ( A @ ( B @ c_SetInterval_Oord__class_OatMost ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(361,axiom,
tc_bool @ class_Complete__Lattice_Ocomplete__lattice,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Complete__Lattice_Ocomplete__lattice) ).
thf(1390,plain,
tc_bool @ class_Complete__Lattice_Ocomplete__lattice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[361]) ).
thf(316,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(1289,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)],[316]) ).
thf(107,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(844,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)],[107]) ).
thf(546,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= D ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__extend__simps_I2_J_0) ).
thf(1807,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( A @ ( B @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= D ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[546]) ).
thf(76,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_Fun_Ofcomp ) ) ) ) @ c_Fun_Ofcomp ) ) ) ) )
= ( G @ ( D @ ( C @ ( G @ ( E @ ( D @ ( F @ ( B @ c_Fun_Ofcomp ) ) ) ) @ ( A @ c_Fun_Ofcomp ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_fcomp__assoc_0) ).
thf(771,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_Fun_Ofcomp ) ) ) ) @ c_Fun_Ofcomp ) ) ) ) )
= ( G @ ( D @ ( C @ ( G @ ( E @ ( D @ ( F @ ( B @ c_Fun_Ofcomp ) ) ) ) @ ( A @ c_Fun_Ofcomp ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(449,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(1590,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)],[449]) ).
thf(474,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ( A = B )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__eq_2) ).
thf(1646,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) )
| ( A = B )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[474]) ).
thf(332,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(1326,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)],[332]) ).
thf(7,axiom,
tc_nat @ class_Orderings_Opreorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Orderings_Opreorder) ).
thf(588,plain,
tc_nat @ class_Orderings_Opreorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(359,axiom,
! [C: $i,B: $i,A: $i] :
( ( B
= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
!= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__empty_1) ).
thf(1385,plain,
! [C: $i,B: $i,A: $i] :
( ( B
= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
!= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[359]) ).
thf(338,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Set_Oinsert ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__insert__left_0) ).
thf(1341,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( C @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Set_Oinsert ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[338]) ).
thf(486,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Un__Diff__Int_0) ).
thf(1674,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[486]) ).
thf(402,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( B @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ~ ( B @ ( D @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_0) ).
thf(1481,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( C @ ( B @ ( D @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ~ ( B @ ( D @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[402]) ).
thf(154,axiom,
! [B: $i,A: $i] :
( ( ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( B @ c_SetInterval_Oord__class_OlessThan ) @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_single__Diff__lessThan_0) ).
thf(946,plain,
! [B: $i,A: $i] :
( ( ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( B @ c_SetInterval_Oord__class_OlessThan ) @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ c_HOL_Ominus__class_Ominus ) ) )
= ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(467,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(1629,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)],[467]) ).
thf(570,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( 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(1854,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( 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)],[570]) ).
thf(63,axiom,
! [A: $i] :
( ( A @ c_Suc )
!= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Suc__n__not__n_0) ).
thf(731,plain,
! [A: $i] :
( ( A @ c_Suc )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(177,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__Int__distrib2_0) ).
thf(995,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( tc_bool @ ( C @ tc_fun ) @ ( D @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(208,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( F @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) ) ) @ ( E @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( F @ hAPP ) @ ( E @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__E_0) ).
thf(1062,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( A @ ( F @ ( C @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) ) ) @ ( E @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( F @ hAPP ) @ ( E @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(413,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(1508,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)],[413]) ).
thf(294,axiom,
tc_bool @ class_Orderings_Opreorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Orderings_Opreorder) ).
thf(1244,plain,
tc_bool @ class_Orderings_Opreorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[294]) ).
thf(553,axiom,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( tc_bool @ ( B @ tc_fun ) @ ( A @ c_HOL_Ouminus__class_Ouminus ) )
!= ( tc_bool @ ( B @ tc_fun ) @ ( C @ c_HOL_Ouminus__class_Ouminus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Compl__eq__Compl__iff_0) ).
thf(1822,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ( ( tc_bool @ ( B @ tc_fun ) @ ( A @ c_HOL_Ouminus__class_Ouminus ) )
!= ( tc_bool @ ( B @ tc_fun ) @ ( C @ c_HOL_Ouminus__class_Ouminus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[553]) ).
thf(573,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( B @ c_SetInterval_Oord__class_OatLeast ) @ ( A @ ( C @ c_SetInterval_Oord__class_OatLeast ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeast__subset__iff_0) ).
thf(1861,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( B @ c_SetInterval_Oord__class_OatLeast ) @ ( A @ ( C @ c_SetInterval_Oord__class_OatLeast ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[573]) ).
thf(493,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__not__less_0) ).
thf(1689,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[493]) ).
thf(533,axiom,
! [B: $i,A: $i] :
~ ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_HOL_Oord__class_Oless ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_not__psubset__empty_0) ).
thf(1777,plain,
! [B: $i,A: $i] :
~ ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( A @ c_HOL_Oord__class_Oless ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[533]) ).
thf(318,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_3) ).
thf(1294,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[318]) ).
thf(384,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(1440,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)],[384]) ).
thf(324,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ c_SetInterval_Oord__class_OlessThan ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_HOL_Oord ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_lessThan__iff_0) ).
thf(1308,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ c_SetInterval_Oord__class_OlessThan ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_HOL_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[324]) ).
thf(270,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(1193,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)],[270]) ).
thf(215,axiom,
! [B: $i,A: $i] :
( ( v_x @ ( tc_bool @ ( t_a @ tc_fun ) @ ( tc_bool @ ( tc_bool @ ( t_a @ tc_fun ) @ ( t_a @ ( B @ ( t_a @ c_in @ c_COMBC ) ) ) ) @ ( tc_bool @ ( tc_bool @ ( t_a @ tc_fun ) @ ( t_a @ ( A @ ( t_a @ c_in @ c_COMBC ) ) ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ hAPP ) )
= ( tc_bool @ ( t_a @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( v_x @ ( t_a @ c_in @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__Int__eq_0) ).
thf(1077,plain,
! [B: $i,A: $i] :
( ( v_x @ ( tc_bool @ ( t_a @ tc_fun ) @ ( tc_bool @ ( tc_bool @ ( t_a @ tc_fun ) @ ( t_a @ ( B @ ( t_a @ c_in @ c_COMBC ) ) ) ) @ ( tc_bool @ ( tc_bool @ ( t_a @ tc_fun ) @ ( t_a @ ( A @ ( t_a @ c_in @ c_COMBC ) ) ) ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ hAPP ) )
= ( tc_bool @ ( t_a @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( v_x @ ( t_a @ c_in @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(280,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( B = C )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__neq__trans_0) ).
thf(1212,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( B = C )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(74,axiom,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Suc )
!= ( B @ c_Suc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_nat_Oinject_0) ).
thf(763,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( ( A @ c_Suc )
!= ( B @ c_Suc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(45,axiom,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_Orderings_Obot__class_Obot @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= B )
| ~ ( A @ class_Lattices_Obounded__lattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__bot__left_0) ).
thf(684,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( A @ c_Orderings_Obot__class_Obot @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= B )
| ~ ( A @ class_Lattices_Obounded__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(385,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= A )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
!= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__triv_0) ).
thf(1442,plain,
! [C: $i,B: $i,A: $i] :
( ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= A )
| ( ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
!= ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[385]) ).
thf(200,axiom,
! [B: $i,A: $i] :
( ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__cancel_0) ).
thf(1045,plain,
! [B: $i,A: $i] :
( ( tc_bool @ ( B @ tc_fun ) @ ( A @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(233,axiom,
tc_bool @ class_Lattices_Odistrib__lattice,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Odistrib__lattice) ).
thf(1116,plain,
tc_bool @ class_Lattices_Odistrib__lattice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(341,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(1348,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)],[341]) ).
thf(70,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__neq__iff_1) ).
thf(752,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(415,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(1512,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)],[415]) ).
thf(102,axiom,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__irrefl_0) ).
thf(833,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(96,axiom,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( A @ c_Fun_Oid @ c_Set_Oimage ) ) ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__id_0) ).
thf(818,plain,
! [B: $i,A: $i] :
( ( A @ ( A @ ( B @ ( A @ c_Fun_Oid @ c_Set_Oimage ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(248,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ hAPP ) @ ( D @ c_lessequals ) ) )
| ( tc_bool @ ( A @ tc_fun ) @ ( C @ c_Inductive_Ocomplete__lattice__class_Ogfp ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_weak__coinduct_0) ).
thf(1148,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ hAPP ) @ ( D @ c_lessequals ) ) )
| ( tc_bool @ ( A @ tc_fun ) @ ( C @ c_Inductive_Ocomplete__lattice__class_Ogfp ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(297,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Lattices_Odistrib__lattice )
| ( B @ ( A @ tc_fun ) @ class_Lattices_Odistrib__lattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Odistrib__lattice) ).
thf(1248,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Lattices_Odistrib__lattice )
| ( B @ ( A @ tc_fun ) @ class_Lattices_Odistrib__lattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[297]) ).
thf(16,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= B )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__inf__absorb_0) ).
thf(603,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= B )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(179,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( E @ tc_fun ) @ ( C @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) )
= ( tc_bool @ ( E @ tc_fun ) @ ( tc_bool @ ( E @ tc_fun ) @ ( C @ ( D @ ( B @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( tc_bool @ ( E @ tc_fun ) @ ( C @ ( D @ ( A @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_UN__Un_0) ).
thf(999,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( E @ tc_fun ) @ ( C @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) )
= ( tc_bool @ ( E @ tc_fun ) @ ( tc_bool @ ( E @ tc_fun ) @ ( C @ ( D @ ( B @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( tc_bool @ ( E @ tc_fun ) @ ( C @ ( D @ ( A @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(21,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_inf__sup__aci_I7_J_0) ).
thf(620,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( A @ ( D @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Olattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(509,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_bex__empty_0) ).
thf(1725,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( B @ ( A @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[509]) ).
thf(312,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( C = B )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I11_J_0) ).
thf(1280,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( C = B )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[312]) ).
thf(225,axiom,
! [B: $i,A: $i] :
( ( ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ ( B @ c_SetInterval_Oord__class_OlessThan ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( B @ c_SetInterval_Oord__class_OatMost ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ivl__disj__un_I2_J_0) ).
thf(1097,plain,
! [B: $i,A: $i] :
( ( ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ ( B @ c_SetInterval_Oord__class_OlessThan ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( B @ c_SetInterval_Oord__class_OatMost ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(103,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__infI1_0) ).
thf(835,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Olower__semilattice__class_Oinf ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Lattices_Olower__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(450,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__iff_2) ).
thf(1593,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( tc_bool @ ( A @ tc_fun ) @ ( D @ ( C @ c_HOL_Ominus__class_Ominus ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[450]) ).
thf(356,axiom,
! [D: $i,C: $i,B: $i,A: $i] : ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_Set_Ovimage ) ) ) @ ( A @ c_Set_Oimage ) ) ) @ c_lessequals ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__vimage__subset_0) ).
thf(1380,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( D @ ( C @ ( D @ ( C @ ( B @ ( A @ c_Set_Ovimage ) ) ) @ ( A @ c_Set_Oimage ) ) ) @ c_lessequals ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[356]) ).
thf(572,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__minus__iff_0) ).
thf(1859,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[572]) ).
thf(550,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( E @ ( D @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__subset__iff_2) ).
thf(1816,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ c_lessequals ) ) )
| ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( E @ ( D @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( A @ ( C @ ( B @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[550]) ).
thf(479,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_Set_Oinsert ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B = D )
| ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_insertE_0) ).
thf(1657,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_Set_Oinsert ) ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( B = D )
| ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[479]) ).
thf(336,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(1335,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)],[336]) ).
thf(195,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__extend__simps_I4_J_0) ).
thf(1033,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Complete__Lattice_Ocomplete__lattice__class_OSUPR ) ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(100,axiom,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( E @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ocomp ) ) ) ) @ c_Set_Oimage ) ) ) )
= ( D @ ( C @ ( C @ ( E @ ( F @ ( B @ c_Set_Oimage ) ) ) @ ( A @ c_Set_Oimage ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__compose_0) ).
thf(828,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( E @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ocomp ) ) ) ) @ c_Set_Oimage ) ) ) )
= ( D @ ( C @ ( C @ ( E @ ( F @ ( B @ c_Set_Oimage ) ) ) @ ( A @ c_Set_Oimage ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(160,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( C @ ( B @ c_ATP__Linkup_Osko__Orderings__Xle__fun__def__1__1 ) ) ) @ ( C @ hAPP ) @ ( A @ ( D @ ( C @ ( B @ c_ATP__Linkup_Osko__Orderings__Xle__fun__def__1__1 ) ) ) @ ( B @ hAPP ) @ c_lessequals ) ) )
| ( A @ ( D @ tc_fun ) @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_HOL_Oord ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__fun__def_1) ).
thf(960,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( A @ ( D @ ( C @ ( B @ c_ATP__Linkup_Osko__Orderings__Xle__fun__def__1__1 ) ) ) @ ( C @ hAPP ) @ ( A @ ( D @ ( C @ ( B @ c_ATP__Linkup_Osko__Orderings__Xle__fun__def__1__1 ) ) ) @ ( B @ hAPP ) @ c_lessequals ) ) )
| ( A @ ( D @ tc_fun ) @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_HOL_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(158,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_Diff__insert_0) ).
thf(955,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) )
= ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(146,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( C @ ( E @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( A @ ( B @ ( D @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( D @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atLeastatMost__subset__iff_1) ).
thf(928,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( C @ ( E @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( A @ ( B @ ( D @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( D @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(348,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(1363,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)],[348]) ).
thf(327,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_le__imp__neg__le_0) ).
thf(1314,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_lessequals ) ) )
| ( A @ ( A @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ c_lessequals ) ) )
| ~ ( A @ class_OrderedGroup_Opordered__ab__group__add ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[327]) ).
thf(290,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ ( C @ ( E @ c_Set_Oimage ) ) ) @ ( B @ ( E @ hAPP ) @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__iff_2) ).
thf(1236,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( A @ ( C @ ( E @ c_Set_Oimage ) ) ) @ ( B @ ( E @ hAPP ) @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(556,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Set__XsubsetI__1__1 ) ) @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subsetI_0) ).
thf(1829,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ ( B @ ( A @ c_ATP__Linkup_Osko__Set__XsubsetI__1__1 ) ) @ ( C @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( tc_bool @ ( C @ tc_fun ) @ ( B @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[556]) ).
thf(555,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( D @ c_lessequals ) ) )
| ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__iff_0) ).
thf(1827,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( A @ tc_fun ) @ ( C @ ( D @ c_lessequals ) ) )
| ~ ( D @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[555]) ).
thf(307,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(1268,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)],[307]) ).
thf(250,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(1152,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(426,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_Set_Ovimage ) ) ) )
= ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( D @ ( B @ ( A @ c_Set_Ovimage ) ) ) @ c_HOL_Ouminus__class_Ouminus ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__Compl_0) ).
thf(1537,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( D @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_Set_Ovimage ) ) ) )
= ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( D @ ( B @ ( A @ c_Set_Ovimage ) ) ) @ c_HOL_Ouminus__class_Ouminus ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[426]) ).
thf(355,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( C @ c_SetInterval_Oord__class_OatMost ) @ ( A @ ( B @ c_SetInterval_Oord__class_OatMost ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_atMost__subset__iff_0) ).
thf(1378,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( A @ tc_fun ) @ ( A @ ( C @ c_SetInterval_Oord__class_OatMost ) @ ( A @ ( B @ c_SetInterval_Oord__class_OatMost ) @ c_lessequals ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[355]) ).
thf(188,axiom,
! [B: $i,A: $i] :
~ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_emptyE_0) ).
thf(1019,plain,
! [B: $i,A: $i] :
~ ( tc_bool @ ( A @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(345,axiom,
tc_bool @ class_Lattices_Olower__semilattice,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_bool__Lattices_Olower__semilattice) ).
thf(1357,plain,
tc_bool @ class_Lattices_Olower__semilattice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[345]) ).
thf(137,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(908,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)],[137]) ).
thf(60,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__less__trans_0) ).
thf(723,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(98,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__assoc_0) ).
thf(822,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( D @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( A @ ( D @ ( C @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(320,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Set_Oimage ) ) ) )
= ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( E @ ( D @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_image__Un_0) ).
thf(1299,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( E @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( A @ c_Set_Oimage ) ) ) )
= ( tc_bool @ ( E @ tc_fun ) @ ( E @ ( D @ ( C @ ( A @ c_Set_Oimage ) ) ) @ ( E @ ( D @ ( B @ ( A @ c_Set_Oimage ) ) ) @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[320]) ).
thf(412,axiom,
! [B: $i,A: $i] :
( ~ ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ ( A @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_lessequals ) ) )
| ( A
= ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_subset__Compl__self__eq_0) ).
thf(1505,plain,
! [B: $i,A: $i] :
( ~ ( tc_bool @ ( B @ tc_fun ) @ ( tc_bool @ ( B @ tc_fun ) @ ( A @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_lessequals ) ) )
| ( A
= ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[412]) ).
thf(236,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( A @ v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1 ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( B @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( t_a @ ( B @ ( A @ c_Hoare__Mirabelle_Otriple__valid ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_triples__valid__Suc_0) ).
thf(1120,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( C @ ( A @ v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1 ) @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( B @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( t_a @ ( B @ ( A @ c_Hoare__Mirabelle_Otriple__valid ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(223,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( E @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Set_Ovimage ) ) ) )
= ( tc_bool @ ( E @ tc_fun ) @ ( D @ ( E @ ( C @ ( A @ c_Set_Ovimage ) ) ) @ ( D @ ( E @ ( B @ ( A @ c_Set_Ovimage ) ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_vimage__Diff_0) ).
thf(1093,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( E @ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( B @ c_HOL_Ominus__class_Ominus ) ) @ ( A @ c_Set_Ovimage ) ) ) )
= ( tc_bool @ ( E @ tc_fun ) @ ( D @ ( E @ ( C @ ( A @ c_Set_Ovimage ) ) ) @ ( D @ ( E @ ( B @ ( A @ c_Set_Ovimage ) ) ) @ c_HOL_Ominus__class_Ominus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(105,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( D @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( C @ ( D @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ( C @ ( B @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_cut_0) ).
thf(839,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( D @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ~ ( C @ ( D @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) )
| ( C @ ( B @ ( A @ c_Hoare__Mirabelle_Ohoare__derivs ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(62,axiom,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( C = B )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_linorder__less__linear_0) ).
thf(728,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ( C = B )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Olinorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(66,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(740,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)],[66]) ).
thf(452,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_less__le__not__le_1) ).
thf(1597,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ ( C @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Opreorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[452]) ).
thf(171,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_diff__single__insert_0) ).
thf(982,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_lessequals ) ) )
| ~ ( A @ ( B @ ( D @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_lessequals ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(149,axiom,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( G @ ( B @ hAPP ) @ ( A @ hAPP ) )
= ( G @ ( F @ hAPP ) ) )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ocomp ) ) ) ) )
!= ( E @ ( D @ ( D @ ( F @ ( D @ c_Fun_Oid @ c_Fun_Ocomp ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_o__eq__id__dest_0) ).
thf(935,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( G @ ( B @ hAPP ) @ ( A @ hAPP ) )
= ( G @ ( F @ hAPP ) ) )
| ( ( E @ ( D @ ( C @ ( B @ ( A @ c_Fun_Ocomp ) ) ) ) )
!= ( E @ ( D @ ( D @ ( F @ ( D @ c_Fun_Oid @ c_Fun_Ocomp ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(489,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_order__le__less_1) ).
thf(1681,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_lessequals ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[489]) ).
thf(36,axiom,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_sup__left__idem_0) ).
thf(659,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) )
= ( A @ ( C @ ( B @ c_Lattices_Oupper__semilattice__class_Osup ) ) ) )
| ~ ( A @ class_Lattices_Oupper__semilattice ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(78,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(775,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)],[78]) ).
thf(373,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_lessequals ) ) )
| ( ( 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_disjoint__eq__subset__Compl_1) ).
thf(1416,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_lessequals ) ) )
| ( ( 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)],[373]) ).
thf(28,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_xt1_I10_J_0) ).
thf(639,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( D @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ ( D @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ( A @ ( C @ ( B @ c_HOL_Oord__class_Oless ) ) )
| ~ ( A @ class_Orderings_Oorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(529,axiom,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_lessequals ) ) )
| ( ( 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_disjoint__eq__subset__Compl_0) ).
thf(1769,plain,
! [C: $i,B: $i,A: $i] :
( ( tc_bool @ ( C @ tc_fun ) @ ( tc_bool @ ( C @ tc_fun ) @ ( B @ c_HOL_Ouminus__class_Ouminus ) @ ( A @ c_lessequals ) ) )
| ( ( 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)],[529]) ).
thf(220,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( t_a @ ( C @ ( A @ v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1 ) @ ( A @ c_Suc @ c_Hoare__Mirabelle_Otriple__valid ) ) )
| ~ ( C @ ( B @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( t_a @ ( B @ ( A @ c_Hoare__Mirabelle_Otriple__valid ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_triples__valid__Suc_1) ).
thf(1088,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( t_a @ ( C @ ( A @ v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1 ) @ ( A @ c_Suc @ c_Hoare__Mirabelle_Otriple__valid ) ) )
| ~ ( C @ ( B @ ( t_a @ tc_Hoare__Mirabelle_Otriple @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ( t_a @ ( B @ ( A @ c_Hoare__Mirabelle_Otriple__valid ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(11,axiom,
tc_nat @ class_Lattices_Olower__semilattice,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_nat__Lattices_Olower__semilattice) ).
thf(592,plain,
tc_nat @ class_Lattices_Olower__semilattice,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(211,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(1069,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_HOL_Oord )
| ( B @ ( A @ tc_fun ) @ class_HOL_Oord ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(166,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_psubset__insert__iff_9) ).
thf(972,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( tc_bool @ ( D @ tc_fun ) @ c_Orderings_Obot__class_Obot @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Ominus__class_Ominus ) ) @ c_HOL_Oord__class_Oless ) ) )
| ~ ( tc_bool @ ( D @ tc_fun ) @ ( C @ ( A @ c_lessequals ) ) )
| ( tc_bool @ ( D @ tc_fun ) @ ( D @ ( C @ ( B @ c_Set_Oinsert ) ) @ ( A @ c_HOL_Oord__class_Oless ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(334,axiom,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__extend__simps_I2_J_0) ).
thf(1331,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( D @ tc_fun ) @ ( tc_bool @ ( D @ tc_fun ) @ ( B @ ( C @ ( tc_bool @ ( B @ tc_fun ) @ c_Orderings_Obot__class_Obot @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) ) ) @ ( A @ c_Lattices_Olower__semilattice__class_Oinf ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[334]) ).
thf(456,axiom,
! [B: $i,A: $i] :
( ~ ( B @ class_Lattices_Oboolean__algebra )
| ( B @ ( A @ tc_fun ) @ class_Lattices_Oboolean__algebra ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',clsarity_fun__Lattices_Oboolean__algebra) ).
thf(1606,plain,
! [B: $i,A: $i] :
( ~ ( B @ class_Lattices_Oboolean__algebra )
| ( B @ ( A @ tc_fun ) @ class_Lattices_Oboolean__algebra ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[456]) ).
thf(276,axiom,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( E @ tc_fun ) @ ( C @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) ) ) )
= ( tc_bool @ ( E @ tc_fun ) @ ( tc_bool @ ( E @ tc_fun ) @ ( C @ ( D @ ( B @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) ) ) @ ( A @ ( D @ hAPP ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_INT__insert_0) ).
thf(1204,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( tc_bool @ ( E @ tc_fun ) @ ( C @ ( D @ ( C @ ( B @ ( A @ c_Set_Oinsert ) ) @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) ) ) )
= ( tc_bool @ ( E @ tc_fun ) @ ( tc_bool @ ( E @ tc_fun ) @ ( C @ ( D @ ( B @ c_Complete__Lattice_Ocomplete__lattice__class_OINFI ) ) ) @ ( A @ ( D @ hAPP ) @ c_Lattices_Olower__semilattice__class_Oinf ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(388,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( A @ tc_fun ) @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cls_ComplD_0) ).
thf(1449,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( tc_bool @ ( A @ tc_fun ) @ ( C @ c_HOL_Ouminus__class_Ouminus ) @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( C @ ( B @ ( A @ c_in @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[388]) ).
thf(2151,plain,
$false,
inference(e,[status(thm)],[1586,1718,1411,629,1469,1454,1767,1729,1031,941,1818,1549,1110,1322,1665,1168,760,893,1840,1083,962,1750,1522,1569,1073,597,1437,861,1173,1158,582,1793,1533,1705,1608,1137,715,814,913,1788,1426,1756,1310,1164,797,1260,698,1222,930,1095,1196,1001,1391,782,709,841,885,1613,1645,1601,1475,1803,651,1746,898,1518,1265,1703,1228,1254,1287,1709,1430,1660,785,1871,587,917,802,1577,949,1055,1409,1832,1191,1462,1059,1132,1545,902,853,1247,606,1013,1641,1773,1494,1100,1232,1847,1319,870,1479,1609,1741,1398,881,1489,924,1465,789,1811,591,623,646,1383,806,966,1283,1051,1040,1632,687,1215,734,1447,866,1622,1526,1351,1345,1433,1405,1201,1696,1564,877,692,1104,1242,849,1863,1651,1206,678,1691,1306,1199,1338,1783,1868,1067,1736,1047,1057,1274,1723,957,1042,1255,1676,1487,1238,1560,746,1091,825,1343,1021,778,1355,1580,1502,820,788,1370,1423,847,1365,879,1178,1624,889,1836,1210,757,1407,1128,1291,974,1106,1296,665,1687,1457,583,830,1079,1027,1402,1360,1762,615,1064,980,1425,1672,1006,593,1118,989,857,874,1143,1270,1851,1772,1856,725,1567,1683,1329,1160,933,1182,1739,1075,1842,970,1744,706,1419,1016,590,837,1588,701,1150,1451,654,1668,721,1874,1599,1715,1720,1627,1825,1324,1263,997,1530,1539,1266,1831,984,911,1759,1393,1333,792,921,1170,1035,1071,1187,1515,926,1814,938,633,1779,1712,1846,953,1185,773,794,586,662,718,906,1146,1698,1483,689,1374,1727,1510,1301,1595,1154,904,1615,1125,1620,1652,1388,743,1535,1520,1795,1701,1786,1707,1312,1865,1258,1638,641,1428,1635,1733,1765,1090,919,804,1194,900,1117,1574,1524,1542,737,1801,1122,1175,681,1853,1492,1603,1571,1376,811,631,1557,816,609,1838,964,1556,668,1821,1731,594,799,1162,1029,895,626,915,1177,1381,1396,768,883,1015,986,1113,1477,1250,1496,1694,1805,1562,636,695,1245,868,1445,1528,780,1643,1775,1435,851,1102,1413,1809,1662,944,1467,1277,939,1472,1145,754,968,1551,1049,675,1583,1304,1873,1758,1166,1203,1208,589,1134,648,1081,749,1798,1025,872,887,1566,1252,1368,1753,1230,993,1547,1748,712,1003,580,855,1611,1156,1225,1400,673,1452,1038,717,1235,1763,1085,1679,1130,643,1220,1053,1499,1790,1716,951,808,1285,1218,1358,1849,703,1485,864,1670,1008,1372,859,656,1023,1353,600,978,1140,1272,612,1240,991,1617,1421,1459,1180,1685,1553,671,1834,581,1654,1189,1108,1316,1649,976,1844,1781,891,1010,1390,1289,844,1807,771,1590,1646,1326,588,1385,1341,1674,1481,946,1629,1854,731,995,1062,1508,1244,1822,1861,1689,1777,1294,1440,1308,1193,1077,1212,763,684,1442,1045,1116,1348,752,1512,833,818,1148,1248,603,999,620,1725,1280,1097,835,1593,1380,1859,1816,1657,1335,1033,828,960,955,928,1363,1314,1236,1829,1827,1268,1152,1537,1378,1019,1357,908,723,822,1299,1505,1120,1093,839,728,740,1597,982,935,1681,659,775,1416,639,1769,1088,592,1069,972,1331,1606,1204,1449]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWV857-1 : TPTP v9.3.1. Released v4.1.0.
% 0.00/0.12 % 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
% 0.24/0.49 % Computer : n026.cluster.edu
% 0.24/0.49 % Model : x86_64 x86_64
% 0.24/0.49 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.24/0.49 % Memory : 8046.5625MB
% 0.24/0.49 % OS : Linux 6.8.0-71-generic
% 0.24/0.49 % CPULimit : 300
% 0.24/0.49 % WCLimit : 300
% 0.24/0.49 % DateTime : Sat Sep 26 15:06:55 UTC 2026
% 0.24/0.49 % CPUTime :
% 0.24/0.49 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
% 1.22/1.10 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.77/1.69 % [INFO] Parsing done (581ms).
% 3.23/1.71 % [INFO] Running in sequential loop mode.
% 4.23/2.28 % [INFO] eprover registered as external prover.
% 4.23/2.29 % [INFO] Scanning for conjecture ...
% 5.33/2.61 % [INFO] Found a conjecture (or negated_conjecture) and 582 axioms. Running axiom selection ...
% 6.57/2.94 % [INFO] Axiom selection finished. Selected 575 axioms (removed 7 axioms).
% 7.97/3.39 % [INFO] Problem is propositional (TPTP CNF).
% 8.39/3.43 % [INFO] Type checking passed.
% 8.39/3.43 % [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 ...
% 25.96/7.23 % External prover 'e' found a proof!
% 25.96/7.23 % [INFO] Killing All external provers ...
% 25.96/7.24 % Time passed: 6594ms (effective reasoning time: 5514ms)
% 25.96/7.25 % Axioms used in derivation (575): cls_inf__sup__aci_I2_J_0, cls_atLeastatMost__subset__iff_2, cls_xt1_I9_J_0, cls_linorder__antisym__conv2_1, cls_Compl__subset__Compl__iff_1, cls_bot__fun__eq_0, cls_order__le__less__trans_0, cls_atLeastatMost__psubset__iff_1, cls_inf__sup__absorb_0, clsarity_nat__HOL_Oord, cls_vimage__code_0, cls_Int__Un__distrib_0, clsarity_fun__Lattices_Olower__semilattice, cls_Diff__cancel_0, cls_INT__extend__simps_I4_J_0, cls_Int__absorb2_0, cls_minus__le__iff_0, cls_asm_0, cls_subset__insert_1, cls_ivl__disj__un_I8_J_0, cls_Diff__iff_2, cls_Compl__Diff__eq_0, cls_compl__sup_0, cls_insertE_0, cls_less__fun__def_1, cls_Un__Diff_0, cls_order__less__le__trans_0, cls_order__eq__iff_0, cls_equalityI_0, cls_insert__inter__insert_0, cls_sup__ge1_0, cls_ivl__disj__un_I21_J_0, cls_Un__subset__iff_0, cls_Suc__inject_0, cls_xt1_I12_J_0, cls_COMBC__def_0, cls_subset__empty_1, cls_subset__image__iff_2, cls_predicate1I_0, cls_empty__is__image_1, cls_image__mono_0, cls_Un__empty__left_0, clsarity_nat__Lattices_Odistrib__lattice, cls_le__funD_0, cls_atLeastatMost__psubset__iff_2, cls_subset__iff_1, cls_hoare__valids__def_2, cls_id__o_0, cls_Diff__eq_0, cls_Suc__n__not__n_0, cls_sup__bot__right_0, cls_insert__code_1, cls_atMost__Int__atLeast_0, cls_atLeastLessThan__subset__iff_1, cls_INT__D_0, clsarity_bool__Lattices_Olower__semilattice, cls_le__SUPI_0, cls_linorder__neqE_0, cls_vimage__Diff_0, cls_inf__sup__aci_I6_J_0, cls_Un__upper1_0, cls_Un__commute_0, cls_fun__Compl__def_0, clsarity_fun__Orderings_Oorder, cls_UnCI_1, cls_distrib__sup__le_0, cls_Int__mono_0, cls_le__iff__inf_1, cls_le__fun__def_1, cls_Diff__Un_0, cls_Int__insert__left_0, cls_empty__iff_0, cls_Int__subset__iff_2, clsarity_bool__HOL_Ominus, cls_o__eq__id__dest_0, cls_Diff__subset__conv_0, cls_mem__def_1, clsarity_nat__Orderings_Olinorder, cls_Inf__lower_0, cls_insert__absorb_0, cls_atLeastatMost__psubset__iff_3, cls_le__inf__iff_1, cls_image__vimage__subset_0, cls_less__supI1_0, cls_minus__diff__eq_0, cls_Int__Un__distrib2_0, cls_compl__eq__compl__iff_0, cls_inf1E_1, cls_Diff__triv_0, cls_insert__iff_1, cls_insert__subset_0, cls_triples__valid__Suc_1, cls_sup__inf__distrib2_0, clsarity_fun__Lattices_Oupper__semilattice, cls_less__minus__iff_0, cls_inf__sup__distrib1_0, cls_order__less__trans_0, cls_neg__less__iff__less_1, cls_Int__absorb1_0, cls_le__sup__iff_0, cls_ComplD_0, cls_Diff__insert_0, cls_set__rev__mp_0, cls_insert__Diff__if_1, cls_inf__left__commute_0, cls_pred__equals__eq_0, cls_inf__commute_0, cls_Un__left__commute_0, cls_INF__leI_0, cls_vimage__compose_0, cls_atMost__subset__iff_1, cls_diff__eq_0, cls_INT__absorb_0, cls_disjoint__eq__subset__Compl_0, cls_vimage__Compl_0, cls_subset__insert__iff_2, cls_set__mp_0, cls_ivl__disj__un_I13_J_0, clsarity_bool__HOL_Oord, cls_Int__empty__right_0, cls_Compl__atMost_0, cls_UN__extend__simps_I1_J_0, cls_psubset__insert__iff_8, cls_atLeast__iff_0, cls_Un__Int__distrib2_0, cls_not__psubset__empty_0, cls_vimage__insert_0, cls_Un__empty_2, cls_le__iff__sup_1, cls_INT__subset__iff_0, cls_order__less__asym_0, cls_inf__fun__eq_0, cls_linorder__not__less_0, cls_Inf__singleton_0, cls_atLeastLessThan__empty__iff2_0, cls_le__supI_0, cls_inf__eq__neg__sup_0, cls_Un__subset__iff_1, cls_Inf__binary_0, cls_ivl__disj__int_I11_J_0, cls_neg__sup__eq__inf_0, cls_subsetI_0, cls_order__le__less_0, cls_order__less__asym_H_0, cls_rev__image__eqI_0, cls_linorder__antisym__conv1_0, cls_SUP1__I_0, cls_le__supE_1, cls_UN__iff_2, cls_linorder__antisym__conv2_0, cls_le__iff__sup_0, cls_empty__is__image_0, cls_psubset__eq_1, cls_UN__extend__simps_I3_J_0, cls_order__eq__refl_0, cls_UN__absorb_0, clsarity_fun__Orderings_Obot, cls_atLeast__subset__iff_1, cls_minus__less__iff_1, cls_vimageI_0, cls_sup__eq__neg__inf_0, cls_lessThan__subset__iff_1, cls_triple__valid__Suc_0, cls_psubset__insert__iff_5, cls_id__apply_0, cls_atLeastatMost__subset__iff_3, cls_psubset__trans_0, cls_inf__sup__aci_I8_J_0, cls_Un__empty__right_0, cls_insert__ident_0, cls_weak__coinduct_0, cls_image__id_0, cls_greaterThan__subset__iff_1, cls_Un__absorb2_0, clsarity_bool__Orderings_Oorder, cls_bot__least_0, cls_less__le__not__le_2, cls_Compl__lessThan_0, cls_vimage__id_0, cls_xt1_I10_J_0, cls_le__minus__iff_0, cls_sup__eq__bot__eq2_0, cls_UnCI_0, cls_Un__upper2_0, cls_Compl__disjoint2_0, cls_not__less__iff__gr__or__eq_0, cls_UN__Un_0, cls_Sup__singleton_0, cls_Int__insert__right_1, cls_atLeastatMost__psubset__iff_0, cls_lessThan__eq__iff_0, cls_subset__iff_0, cls_insert__code_2, cls_lessThan__iff_0, cls_Diff__idemp_0, cls_subset__empty_0, cls_rev__predicate1D_0, cls_greaterThan__iff_0, cls_subset__Compl__self__eq_1, cls_singleton__iff_1, cls_atLeastatMost__empty__iff_1, clsarity_fun__HOL_Oord, cls_Compl__Un_0, cls_insert__Diff__single_0, cls_predicate1I_1, cls_image__insert_0, cls_UN__subset__iff_0, cls_vimage__Un_0, cls_diff__single__insert_0, cls_inf__absorb2_0, cls_atLeastatMost__empty__iff2_0, clsarity_bool__Lattices_Oupper__semilattice, cls_le__minus__iff_1, cls_Compl__disjoint_0, cls_Sup__binary_0, cls_doubleton__eq__iff_2, cls_SUP1__iff_2, cls_ivl__disj__un_I1_J_0, cls_Un__insert__left_0, cls_inf__sup__ord_I2_J_0, cls_vimage__singleton__eq_1, cls_subset__insert__iff_3, cls_Inf__insert_0, clsarity_nat__Orderings_Obot, cls_greaterThan__subset__iff_0, clsarity_nat__Lattices_Olower__semilattice, cls_xt1_I8_J_0, cls_id__fcomp_0, cls_ivl__disj__int_I4_J_0, cls_inf__sup__aci_I3_J_0, cls_set__eq__subset_2, cls_Un__mono_0, cls_less__infI1_0, cls_Int__insert__left_1, cls_insert__subset_1, cls_Int__empty__left_0, cls_psubset__insert__iff_4, cls_INT__iff_0, cls_INT__extend__simps_I2_J_0, cls_ex__in__conv_0, cls_sup__commute_0, cls_Compl__anti__mono_0, cls_le__inf__iff_0, cls_Int__subset__iff_1, cls_subset__iff__psubset__eq_0, cls_neg__inf__eq__sup_0, cls_compl__inf__bot_0, cls_atMost__subset__iff_0, cls_Un__subset__iff_2, cls_ivl__disj__int_I8_J_0, clsarity_fun__Lattices_Olattice, cls_INT__lower_0, cls_linorder__linear_0, cls_Un__empty_0, cls_atLeastLessThan__empty__iff_1, cls_not__leE_0, cls_Int__assoc_0, cls_order__antisym_0, cls_order__trans_0, cls_atMost__eq__iff_0, cls_psubset__insert__iff_9, cls_atLeast__iff_1, cls_sup__Un__eq_0, cls_inf__le2_0, cls_Compl__eq__Compl__iff_0, cls_insert__is__Un_0, cls_image__empty_0, cls_Compl__subset__Compl__iff_0, clsarity_bool__HOL_Ouminus, cls_subset__trans_0, cls_atLeastAtMost__singleton_0, cls_double__diff_0, cls_atLeastatMost__psubset__iff_4, cls_insertI1_0, cls_DiffI_0, cls_linorder__antisym__conv1_1, cls_psubset__insert__iff_6, cls_le__supE_0, cls_atLeast__eq__iff_0, cls_subset__Compl__self__eq_0, cls_inf__compl__bot_0, cls_sup__assoc_0, cls_insert__Diff1_0, cls_lessThan__subset__iff_0, cls_Diff__Int__distrib2_0, cls_le__sup__iff_1, clsarity_bool__Orderings_Obot, cls_mem__def_0, cls_inf__sup__aci_I7_J_0, cls_Un__Int__crazy_0, clsarity_bool__Orderings_Opreorder, cls_INF1__iff_0, cls_empty__not__insert_0, cls_empty__subsetI_0, cls_atLeastatMost__subset__iff_0, cls_Un__absorb1_0, cls_Diff__insert2_0, cls_Int__commute_0, cls_minus__less__iff_0, cls_sup__least_0, cls_subset__refl_0, cls_ivl__disj__un_I2_J_0, cls_linorder__not__le_1, cls_doubleton__eq__iff_0, cls_inf__sup__aci_I1_J_0, cls_sup1E_0, cls_distrib__inf__le_0, cls_Sup__upper_0, cls_atMost__iff_0, cls_singletonE_0, clsarity_nat__Orderings_Opreorder, cls_image__diff__subset_0, clsarity_nat__Lattices_Olattice, cls_DiffE_0, cls_Int__Diff_0, cls_sup1CI_1, cls_image__iff_2, cls_less__minus__iff_1, cls_psubset__eq_0, clsarity_fun__Lattices_Oboolean__algebra, cls_image__Int__subset_0, cls_pred__subset__eq_1, cls_vimage__Int_0, cls_Un__Diff__cancel_0, cls_image__Un_0, cls_insert__Diff_0, cls_not__less__iff__gr__or__eq_1, cls_subset__iff_2, cls_insertCI_0, cls_order__le__neq__trans_0, cls_le__infE_0, cls_le__inf__iff_2, cls_subsetI_1, cls_le__funI_0, cls_order__eq__iff_2, cls_le__infI1_0, cls_weaken_0, cls_Int__absorb_0, cls_inf__assoc_0, cls_insert__mono_0, cls_le__supI2_0, cls_less__le__not__le_1, cls_Un__Diff__cancel2_0, cls_INT__extend__simps_I1_J_0, cls_bex__empty_0, cls_bot1E_0, cls_linorder__antisym__conv3_0, cls_linorder__neqE__ordered__idom_0, cls_ivl__disj__un_I10_J_0, cls_ivl__diff_0, cls_Int__lower2_0, cls_o__eq__dest_0, cls_Un__assoc_0, cls_Diff__disjoint_0, cls_inf__sup__ord_I4_J_0, cls_psubset__insert__iff_0, cls_fcomp__id_0, cls_o__eq__dest__lhs_0, cls_atLeastatMost__empty__iff_0, cls_Diff__Int__distrib_0, cls_psubset__insert__iff_1, cls_nat_Oinject_0, cls_UnE_0, cls_subset__insertI2_0, cls_vimage__mono_0, cls_Int__left__absorb_0, cls_order__neq__le__trans_0, cls_Compl__Int_0, cls_id__def_0, cls_doubleton__eq__iff_3, cls_Diff__mono_0, cls_order__le__less_1, cls_linorder__neq__iff_1, cls_psubset__subset__trans_0, cls_Un__absorb_0, cls_order__antisym__conv_0, cls_psubsetD_0, cls_Int__lower1_0, clsarity_bool__Lattices_Olattice, cls_le__imp__neg__le_0, cls_psubset__insert__iff_3, cls_ivl__disj__int_I7_J_0, cls_Compl__atLeast_0, cls_vimage__eq_1, cls_order__less__le_2, cls_Un__Int__distrib_0, clsarity_bool__Lattices_Obounded__lattice, cls_inf__sup__ord_I1_J_0, cls_le__infI_0, cls_subset__insert__iff_4, cls_Int__subset__iff_0, cls_linorder__less__linear_0, cls_hoare__valids__def_1, cls_ivl__disj__int_I15_J_0, cls_bot__empty__eq_0, cls_eq__eqI_0, cls_insert__subset_2, cls_le__supI1_0, cls_le__eqI_0, cls_sup__left__idem_0, cls_o__id_0, cls_thin_0, cls_subsetD_0, cls_insert__not__empty_0, cls_xt1_I11_J_0, cls_inf__idem_0, clsarity_fun__Lattices_Obounded__lattice, cls_ivl__disj__un_I14_J_0, cls_vimageE_0, cls_inf__bot__left_0, cls_inf1I_0, cls_Int__left__commute_0, cls_le__sup__iff_2, cls_o__def_0, clsarity_fun__Complete__Lattice_Ocomplete__lattice, cls_insert__absorb2_0, cls_sup__fun__eq_0, cls_UNION__empty__conv_I1_J_0, cls_inf__sup__aci_I4_J_0, cls_atLeastatMost__psubset__iff_5, cls_sup__inf__absorb_0, cls_double__compl_0, cls_subset__singletonD_0, cls_Int__iff_2, cls_Un__Int__assoc__eq_1, cls_doubleton__eq__iff_1, cls_UN__extend__simps_I2_J_0, cls_fun__diff__def_0, cls_inf__Int__eq_0, cls_Sup__insert_0, cls_vimage__singleton__eq_0, cls_xt1_I6_J_0, cls_subset__insert__iff_0, cls_vimage__code_1, cls_UN__I_0, cls_ComplI_0, cls_minus__le__iff_1, cls_atLeastLessThan__empty__iff2_1, cls_greaterThan__eq__iff_0, cls_subset__psubset__trans_0, clsarity_bool__Complete__Lattice_Ocomplete__lattice, cls_Diff__empty_0, cls_atLeastatMost__subset__iff_1, cls_INF1__E_0, cls_IntI_0, cls_atLeastatMost__psubset__iff_6, cls_inf__greatest_0, cls_Sup__empty_0, cls_Un__left__absorb_0, cls_linorder__not__le_0, cls_order__less__irrefl_0, cls_inf__sup__ord_I3_J_0, cls_less__infI2_0, cls_inf__sup__aci_I5_J_0, cls_Diff__Int_0, cls_less__supI2_0, cls_neg__le__iff__le_0, cls_less__fun__def_2, cls_atLeastLessThan__empty_0, cls_Un__empty_1, cls_comp__cong_0, cls_le__iff__inf_0, clsarity_bool__Lattices_Oboolean__algebra, cls_subset__insert_0, cls_sup__idem_0, clsarity_nat__Lattices_Oupper__semilattice, cls_emptyE_0, cls_eq__eqI_1, cls_Diff__Compl_0, cls_INT__insert_0, cls_sup__eq__bot__eq1_0, cls_comm__monoid__add_Ononempty__iff_2, cls_singleton__inject_0, cls_less__eqI_0, cls_vimageI2_0, cls_sup__ge2_0, cls_UN__upper_0, cls_Un__least_0, cls_double__complement_0, cls_sup1CI_0, cls_Int__greatest_0, cls_INT__Un_0, clsarity_fun__Orderings_Opreorder, cls_atLeastatMost__empty__iff2_1, cls_n__not__Suc__n_0, cls_IntE_1, cls_IntE_0, cls_atLeastLessThan__subset__iff_0, cls_subset__Un__eq_1, cls_sup__left__commute_0, clsarity_bool__Lattices_Odistrib__lattice, cls_le__infE_1, cls_greaterThan__iff_1, cls_image__eqI_0, cls_pred__subset__eq_0, cls_fcomp__apply_0, cls_image__subset__iff_0, cls_inf__le1_0, cls_insertCI_1, cls_inf__left__idem_0, cls_doubleton__eq__iff_4, cls_atLeastLessThan__empty__iff_0, cls_compl__inf_0, cls_Diff__subset__conv_1, cls_atMost__iff_1, cls_insert__code_0, cls_le__eqI_1, cls_vimageD_0, cls_ivl__disj__un_I6_J_0, cls_Diff__Int2_0, cls_DiffE_1, cls_Un__Diff__Int_0, cls_subset__insertI_0, cls_order__less__imp__le_0, cls_fcomp__def_0, cls_Diff__insert__absorb_0, cls_Diff__partition_0, cls_sup__bot__left_0, cls_psubset__insert__iff_2, cls_sup__inf__distrib1_0, cls_fcomp__assoc_0, cls_vimage__empty_0, cls_Un__Int__assoc__eq_0, cls_gfp__upperbound_0, cls_insert__commute_0, cls_INT__E_0, cls_insert__iff_2, cls_le__infI2_0, cls_UNION__empty__conv_I2_J_0, cls_hoare__valids__def_0, cls_insert__image_0, cls_disjoint__iff__not__equal_0, cls_INF1__D_0, clsarity_nat__Orderings_Oorder, cls_xt1_I7_J_0, cls_image__compose_0, cls_Compl__greaterThan_0, cls_linorder__not__less_1, cls_UN__insert_0, cls_Un__insert__right_0, cls_psubset__insert__iff_7, cls_equalityE_0, cls_inf__sup__distrib2_0, cls_cut_0, cls_ivl__disj__int_I2_J_0, cls_weak__coinduct__image_0, cls_less__eqI_1, cls_order__less__le_1, cls_less__fun__def_0, clsarity_fun__HOL_Ouminus, cls_image__is__empty_0, cls_ivl__disj__un_I17_J_0, cls_imageI_0, clsarity_fun__Lattices_Odistrib__lattice, cls_atLeast__subset__iff_0, clsarity_fun__HOL_Ominus, cls_disjoint__eq__subset__Compl_1, cls_o__apply_0, cls_inf__bot__right_0, cls_sup__absorb1_0, cls_ball__empty_0, cls_Int__insert__right_0, cls_psubset__eq_2, cls_atLeastatMost__empty_0, cls_empty__Diff_0, clsarity_nat__HOL_Ominus, cls_o__assoc_0, cls_lessThan__iff_1, cls_subset__insert__iff_1, cls_neg__less__iff__less_0, cls_triples__valid__Suc_0, cls_single__Diff__lessThan_0, cls_Diff__subset_0, cls_predicate1D_0, cls_inf1E_0
% 25.96/7.25 % No. of inferences in proof: 1159
% 25.96/7.25 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 6594 ms resp. 5514 ms w/o parsing
% 28.58/7.80 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 28.58/7.81 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------