%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWW350+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n020.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 09:09:59 AM UTC 2026
% Result : Theorem 25.96s 13.23s
% Output : Refutation 27.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 290
% Syntax : Number of formulae : 582 ( 158 unt; 0 typ; 0 def)
% Number of atoms : 1557 ( 373 equ; 0 cnn)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 10356 ( 205 ~; 69 |; 203 &;9176 @)
% ( 76 <=>; 627 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 11 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 94 ( 92 usr; 16 con; 0-7 aty)
% Number of variables : 2125 ( 0 ^;2048 !; 77 ?;2125 :)
% Comments :
%------------------------------------------------------------------------------
thf(hBOOL_decl,type,
hBOOL: $i > $o ).
thf(hAPP_decl,type,
hAPP: $i > $i > $i ).
thf(c_Natural_Oevalc_decl,type,
c_Natural_Oevalc: $i > $i ).
thf(v_c_decl,type,
v_c: $i ).
thf(v_Z_decl,type,
v_Z: $i ).
thf(v_s_H_decl,type,
v_s_H: $i ).
thf(c_Orderings_Oord__class_Oless_decl,type,
c_Orderings_Oord__class_Oless: $i > $i ).
thf(tc_Nat_Onat_decl,type,
tc_Nat_Onat: $i ).
thf(c_Groups_Oplus__class_Oplus_decl,type,
c_Groups_Oplus__class_Oplus: $i > $i ).
thf(c_Orderings_Oord__class_Oless__eq_decl,type,
c_Orderings_Oord__class_Oless__eq: $i > $i ).
thf(c_Groups_Ozero__class_Ozero_decl,type,
c_Groups_Ozero__class_Ozero: $i > $i ).
thf(c_Divides_Odiv__class_Odiv_decl,type,
c_Divides_Odiv__class_Odiv: $i > $i > $i ).
thf(c_Divides_Odiv__class_Omod_decl,type,
c_Divides_Odiv__class_Omod: $i > $i > $i > $i ).
thf(c_member_decl,type,
c_member: $i > $i ).
thf(c_Set_Oimage_decl,type,
c_Set_Oimage: $i > $i > $i > $i ).
thf(c_Finite__Set_Ofinite_decl,type,
c_Finite__Set_Ofinite: $i > $i ).
thf(c_SetInterval_Oord__class_OatLeastLessThan_decl,type,
c_SetInterval_Oord__class_OatLeastLessThan: $i > $i > $i ).
thf(c_Divides_Odivmod__nat__rel_decl,type,
c_Divides_Odivmod__nat__rel: $i > $i > $i ).
thf(c_Product__Type_OPair_decl,type,
c_Product__Type_OPair: $i > $i > $i ).
thf(c_SetInterval_Oord__class_OatLeastAtMost_decl,type,
c_SetInterval_Oord__class_OatLeastAtMost: $i > $i > $i > $i ).
thf(c_Finite__Set_Ofolding__image__simple_decl,type,
c_Finite__Set_Ofolding__image__simple: $i > $i > $i > $i > $i > $i > $o ).
thf(c_Finite__Set_Ofold__image_decl,type,
c_Finite__Set_Ofold__image: $i > $i > $i > $i ).
thf(c_Finite__Set_Ofold__graph_decl,type,
c_Finite__Set_Ofold__graph: $i > $i > $i > $i > $i > $i ).
thf(c_SetInterval_Oord__class_OlessThan_decl,type,
c_SetInterval_Oord__class_OlessThan: $i > $i ).
thf(c_Divides_Odivmod__nat_decl,type,
c_Divides_Odivmod__nat: $i > $i > $i ).
thf(c_Set_Oinsert_decl,type,
c_Set_Oinsert: $i > $i ).
thf(c_SetInterval_Oord__class_OatMost_decl,type,
c_SetInterval_Oord__class_OatMost: $i > $i ).
thf(c_Sum__Type_Osum_Osum__case_decl,type,
c_Sum__Type_Osum_Osum__case: $i > $i > $i > $i > $i > $i ).
thf(c_Com_Ocom_OWhile_decl,type,
c_Com_Ocom_OWhile: $i > $i > $i ).
thf(c_Com_Ocom_OSemi_decl,type,
c_Com_Ocom_OSemi: $i > $i > $i ).
thf(c_Natural_Oevaln_decl,type,
c_Natural_Oevaln: $i ).
thf(c_Com_Ocom_OCond_decl,type,
c_Com_Ocom_OCond: $i > $i > $i > $i ).
thf(c_Hilbert__Choice_OLeastM_decl,type,
c_Hilbert__Choice_OLeastM: $i > $i > $i > $i > $i ).
thf(c_Set_Ovimage_decl,type,
c_Set_Ovimage: $i > $i > $i > $i ).
thf(c_Com_Ocom_OAss_decl,type,
c_Com_Ocom_OAss: $i > $i > $i ).
thf(c_Natural_Oupdate_decl,type,
c_Natural_Oupdate: $i ).
thf(c_Hoare__Mirabelle_Otriple__valid_decl,type,
c_Hoare__Mirabelle_Otriple__valid: $i > $i > $i > $o ).
thf(c_Hoare__Mirabelle_Otriple_Otriple_decl,type,
c_Hoare__Mirabelle_Otriple_Otriple: $i > $i ).
thf(class_Orderings_Owellorder_decl,type,
class_Orderings_Owellorder: $i > $o ).
thf(c_Com_Ocom_OSKIP_decl,type,
c_Com_Ocom_OSKIP: $i ).
thf(c_Typedef_Otype__definition_decl,type,
c_Typedef_Otype__definition: $i > $i > $i > $i > $i > $o ).
thf(c_Wellfounded_OwfP_decl,type,
c_Wellfounded_OwfP: $i > $i > $o ).
thf(c_Wellfounded_Oaccp_decl,type,
c_Wellfounded_Oaccp: $i > $i > $i ).
thf(c_Finite__Set_Ofolding__one__idem_decl,type,
c_Finite__Set_Ofolding__one__idem: $i > $i > $i > $o ).
thf(c_Finite__Set_Ofold_decl,type,
c_Finite__Set_Ofold: $i > $i > $i > $i ).
thf(c_SetInterval_Oord__class_OgreaterThanAtMost_decl,type,
c_SetInterval_Oord__class_OgreaterThanAtMost: $i > $i > $i > $i ).
thf(c_Nitpick_Opair__box_OPairBox_decl,type,
c_Nitpick_Opair__box_OPairBox: $i > $i > $i > $i > $i ).
thf(c_Equiv__Relations_Oequivp_decl,type,
c_Equiv__Relations_Oequivp: $i > $i > $o ).
thf(c_fequal_decl,type,
c_fequal: $i ).
thf(c_Orderings_Oord__class_OLeast_decl,type,
c_Orderings_Oord__class_OLeast: $i > $i > $i ).
thf(c_SetInterval_Oord__class_OgreaterThanLessThan_decl,type,
c_SetInterval_Oord__class_OgreaterThanLessThan: $i > $i > $i > $i ).
thf(c_Com_Ovname_OGlb_decl,type,
c_Com_Ovname_OGlb: $i > $i ).
thf(c_Finite__Set_Ofolding__one_decl,type,
c_Finite__Set_Ofolding__one: $i > $i > $i > $o ).
thf(c_Finite__Set_Ofold1_decl,type,
c_Finite__Set_Ofold1: $i > $i > $i ).
thf(c_Hilbert__Choice_OEps_decl,type,
c_Hilbert__Choice_OEps: $i > $i > $i ).
thf(c_Big__Operators_Ocomm__monoid__big_decl,type,
c_Big__Operators_Ocomm__monoid__big: $i > $i > $i > $i > $i > $o ).
thf(class_Enum_Oenum_decl,type,
class_Enum_Oenum: $i > $o ).
thf(c_Enum_Oenum__class_Oenum__all_decl,type,
c_Enum_Oenum__class_Oenum__all: $i > $i ).
thf(c_Enum_Oenum__class_Oenum__ex_decl,type,
c_Enum_Oenum__class_Oenum__ex: $i > $i ).
thf(c_Nitpick_Opair__box_Opair__box__rec_decl,type,
c_Nitpick_Opair__box_Opair__box__rec: $i > $i > $i > $i > $i > $i ).
thf(c_Hoare__Mirabelle_Otriple_Otriple__rec_decl,type,
c_Hoare__Mirabelle_Otriple_Otriple__rec: $i > $i > $i > $i > $i ).
thf(c_SetInterval_Oord_OgreaterThan_decl,type,
c_SetInterval_Oord_OgreaterThan: $i > $i > $i > $i ).
thf(c_fimplies_decl,type,
c_fimplies: $i ).
thf(c_fNot_decl,type,
c_fNot: $i ).
thf(c_FunDef_Oreduction__pair_decl,type,
c_FunDef_Oreduction__pair: $i > $i > $o ).
thf(c_FunDef_Orp__inv__image_decl,type,
c_FunDef_Orp__inv__image: $i > $i > $i ).
thf(c_Predicate_OPowp_decl,type,
c_Predicate_OPowp: $i > $i > $i ).
thf(c_Big__Operators_Osemilattice__big_decl,type,
c_Big__Operators_Osemilattice__big: $i > $i > $i > $o ).
thf(c_Predicate_Opred__comp_decl,type,
c_Predicate_Opred__comp: $i > $i > $i > $i > $i > $i > $i > $o ).
thf(c_fdisj_decl,type,
c_fdisj: $i ).
thf(c_Predicate_ORangeP_decl,type,
c_Predicate_ORangeP: $i > $i > $i > $i ).
thf(c_fTrue_decl,type,
c_fTrue: $i ).
thf(c_SetInterval_Oord_OatLeastLessThan_decl,type,
c_SetInterval_Oord_OatLeastLessThan: $i > $i > $i > $i > $i > $i ).
thf(c_fconj_decl,type,
c_fconj: $i ).
thf(c_Hoare__Mirabelle_Opeek__and_decl,type,
c_Hoare__Mirabelle_Opeek__and: $i > $i > $i > $i ).
thf(c_SetInterval_Oord_OatLeast_decl,type,
c_SetInterval_Oord_OatLeast: $i > $i > $i > $i ).
thf(c_fFalse_decl,type,
c_fFalse: $i ).
thf(c_SetInterval_Oord_OgreaterThanLessThan_decl,type,
c_SetInterval_Oord_OgreaterThanLessThan: $i > $i > $i > $i > $i ).
thf(c_SetInterval_Oord_OgreaterThanAtMost_decl,type,
c_SetInterval_Oord_OgreaterThanAtMost: $i > $i > $i > $i > $i > $i ).
thf(c_SetInterval_Oord_OatMost_decl,type,
c_SetInterval_Oord_OatMost: $i > $i > $i > $i ).
thf(c_SetInterval_Oord_OlessThan_decl,type,
c_SetInterval_Oord_OlessThan: $i > $i > $i > $i ).
thf(c_New__Random__Sequence_Opos__not__random__dseq_decl,type,
c_New__Random__Sequence_Opos__not__random__dseq: $i > $i > $i > $i > $i ).
thf(c_New__DSequence_Opos__not__seq_decl,type,
c_New__DSequence_Opos__not__seq: $i > $i ).
thf(c_Nitpick_Opair__box_Opair__box__case_decl,type,
c_Nitpick_Opair__box_Opair__box__case: $i > $i > $i > $i > $i > $i ).
thf(c_Com_Ovname_Ovname__rec_decl,type,
c_Com_Ovname_Ovname__rec: $i > $i > $i > $i > $i ).
thf(c_Int_ORep__Integ_decl,type,
c_Int_ORep__Integ: $i ).
thf(c_Predicate_ODomainP_decl,type,
c_Predicate_ODomainP: $i > $i > $i > $i ).
thf(c_Com_Ovname_Ovname__case_decl,type,
c_Com_Ovname_Ovname__case: $i > $i > $i > $i > $i ).
thf(v_Sledgehammer_058s__2_decl,type,
v_Sledgehammer_058s__2: $i > $i > $i ).
thf(c_Predicate_Oreflp_decl,type,
c_Predicate_Oreflp: $i > $i > $o ).
thf(c_Product__Type_Oprod_Oprod__rec_decl,type,
c_Product__Type_Oprod_Oprod__rec: $i > $i > $i > $i > $i > $i ).
thf(c_SetInterval_Oord_OatLeastAtMost_decl,type,
c_SetInterval_Oord_OatLeastAtMost: $i > $i > $i > $i > $i ).
thf(138,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ hAPP ) @ hBOOL )
=> ( ! [E: $i] :
( ( E @ ( D @ hAPP ) @ hBOOL )
=> ( E @ ( A @ hAPP ) @ ( D @ ( A @ ( tc_Nat_Onat @ ( B @ c_Hilbert__Choice_OLeastM ) ) ) @ ( A @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( D @ ( A @ ( tc_Nat_Onat @ ( B @ c_Hilbert__Choice_OLeastM ) ) ) @ ( D @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_LeastM__nat__lemma) ).
thf(892,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ hAPP ) @ hBOOL )
=> ( ! [E: $i] :
( ( E @ ( D @ hAPP ) @ hBOOL )
=> ( E @ ( A @ hAPP ) @ ( D @ ( A @ ( tc_Nat_Onat @ ( B @ c_Hilbert__Choice_OLeastM ) ) ) @ ( A @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( D @ ( A @ ( tc_Nat_Onat @ ( B @ c_Hilbert__Choice_OLeastM ) ) ) @ ( D @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(87,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( D @ ( E @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( G @ c_Divides_Odivmod__nat__rel ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( C @ c_Divides_Odivmod__nat__rel ) @ hAPP ) @ hBOOL )
=> ( ( F @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( F @ ( A @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( F @ ( A @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv ) @ hAPP ) @ ( B @ ( E @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( C @ ( G @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odivmod__nat__rel ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__nat__rel__add1__eq) ).
thf(629,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( D @ ( E @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( G @ c_Divides_Odivmod__nat__rel ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( C @ c_Divides_Odivmod__nat__rel ) @ hAPP ) @ hBOOL )
=> ( ( F @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( F @ ( A @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( F @ ( A @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv ) @ hAPP ) @ ( B @ ( E @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( F @ ( C @ ( G @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ c_Divides_Odivmod__nat__rel ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(167,axiom,
! [A: $i,B: $i] :
( ( ( B @ c_Com_Ovname_OGlb )
= ( A @ c_Com_Ovname_OGlb ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vname_Osimps_I1_J) ).
thf(1024,plain,
! [A: $i,B: $i] :
( ( ( B = A )
=> ( ( B @ c_Com_Ovname_OGlb )
= ( A @ c_Com_Ovname_OGlb ) ) )
& ( ( ( B @ c_Com_Ovname_OGlb )
= ( A @ c_Com_Ovname_OGlb ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(283,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Predicate_Oreflp ) )
=> ( A @ ( A @ ( B @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_reflpE) ).
thf(1559,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Predicate_Oreflp ) )
=> ( A @ ( A @ ( B @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(16,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
<=> ( C = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__right__cancel) ).
thf(347,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C = A )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) )
& ( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
=> ( C = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(230,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_SetInterval_Oord_OatLeast ) ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( C @ ( A @ ( B @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord_OatLeast__iff) ).
thf(1315,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( A @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ c_SetInterval_Oord_OatLeast ) ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( D @ c_SetInterval_Oord_OatLeast ) ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( B @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(153,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insertI2) ).
thf(962,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(149,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( c_Com_Ocom_OSKIP @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evaln__elim__cases_I1_J) ).
thf(941,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( c_Com_Ocom_OSKIP @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(71,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_Divides_Odivmod__nat ) )
= ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__nat__base) ).
thf(555,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ c_Divides_Odivmod__nat ) )
= ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(98,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( C @ ( D @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( C @ ( B @ ( D @ c_Com_Ocom_OWhile ) @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evaln_OWhileFalse) ).
thf(666,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( C @ ( D @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( C @ ( B @ ( D @ c_Com_Ocom_OWhile ) @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(225,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( D @ ( F @ c_SetInterval_Oord_OatLeastLessThan ) ) ) ) @ ( E @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( A @ ( E @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
& ( E @ ( B @ ( D @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord_OatLeastLessThan__iff) ).
thf(1295,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ( A @ ( E @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
& ( E @ ( B @ ( D @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( C @ ( D @ ( F @ c_SetInterval_Oord_OatLeastLessThan ) ) ) ) @ ( E @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ ( D @ ( F @ c_SetInterval_Oord_OatLeastLessThan ) ) ) ) @ ( E @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( E @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
& ( E @ ( B @ ( D @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(162,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( E @ c_Com_Ocom_OAss ) )
!= ( A @ ( B @ ( C @ c_Com_Ocom_OCond ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I26_J) ).
thf(1005,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( E @ c_Com_Ocom_OAss ) )
!= ( A @ ( B @ ( C @ c_Com_Ocom_OCond ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(273,axiom,
! [A: $i,B: $i] :
( ( A @ hBOOL )
| ~ ( B @ hBOOL )
| ~ ( A @ ( B @ ( c_fimplies @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fimplies__3) ).
thf(1522,plain,
! [A: $i,B: $i] :
( ( A @ hBOOL )
| ~ ( B @ hBOOL )
| ~ ( A @ ( B @ ( c_fimplies @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(208,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_Big__Operators_Osemilattice__big ) ) )
=> ( ( A @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ hAPP ) )
= ( A @ ( C @ ( D @ c_Finite__Set_Ofold1 ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_semilattice__big_OF__eq) ).
thf(1205,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_Big__Operators_Osemilattice__big ) ) )
=> ( ( A @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ hAPP ) )
= ( A @ ( C @ ( D @ c_Finite__Set_Ofold1 ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(218,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( E @ ( A @ ( B @ c_Predicate_ORangeP ) ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_RangeP_Ointros) ).
thf(1269,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( E @ ( A @ ( B @ c_Predicate_ORangeP ) ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(78,axiom,
! [A: $i] :
~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less0) ).
thf(597,plain,
! [A: $i] :
~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(137,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( D @ c_Com_Ocom_OWhile ) )
= ( A @ ( B @ c_Com_Ocom_OWhile ) ) )
<=> ( ( C = A )
& ( D = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I5_J) ).
thf(878,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( C = A )
& ( D = B ) )
=> ( ( C @ ( D @ c_Com_Ocom_OWhile ) )
= ( A @ ( B @ c_Com_Ocom_OWhile ) ) ) )
& ( ( ( C @ ( D @ c_Com_Ocom_OWhile ) )
= ( A @ ( B @ c_Com_Ocom_OWhile ) ) )
=> ( ( C = A )
& ( D = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(94,axiom,
! [A: $i,B: $i] : ( A @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( tc_Nat_Onat @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__atLeastAtMost) ).
thf(655,plain,
! [A: $i,B: $i] : ( A @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( tc_Nat_Onat @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(26,axiom,
! [A: $i,B: $i] : ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add2) ).
thf(384,plain,
! [A: $i,B: $i] : ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(122,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( C @ ( D @ ( E @ ( F @ ( G @ ( H @ c_Finite__Set_Ofolding__image__simple ) ) ) ) ) )
=> ( ( B @ ( G @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ~ ( B @ ( A @ ( G @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( G @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ hAPP ) )
= ( B @ ( C @ hAPP ) @ ( A @ ( D @ hAPP ) @ ( F @ hAPP ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__image__simple_Oinsert) ).
thf(797,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( C @ ( D @ ( E @ ( F @ ( G @ ( H @ c_Finite__Set_Ofolding__image__simple ) ) ) ) ) )
=> ( ( B @ ( G @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ~ ( B @ ( A @ ( G @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( G @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ hAPP ) )
= ( B @ ( C @ hAPP ) @ ( A @ ( D @ hAPP ) @ ( F @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I3_J) ).
thf(340,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(237,axiom,
! [A: $i] : ( A @ ( A @ ( c_Com_Ocom_OSKIP @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evalc_OSkip) ).
thf(1354,plain,
! [A: $i] : ( A @ ( A @ ( c_Com_Ocom_OSKIP @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(270,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ hAPP ) @ hBOOL )
=> ( D @ ( A @ ( tc_Nat_Onat @ ( B @ c_Hilbert__Choice_OLeastM ) ) ) @ ( D @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_LeastM__natI) ).
thf(1507,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ hAPP ) @ hBOOL )
=> ( D @ ( A @ ( tc_Nat_Onat @ ( B @ c_Hilbert__Choice_OLeastM ) ) ) @ ( D @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(100,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( C @ ( D @ hAPP ) @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( D @ ( E @ ( A @ c_Set_Ovimage ) ) @ hAPP ) @ ( C @ ( A @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimageI2) ).
thf(670,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( C @ ( D @ hAPP ) @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( D @ ( E @ ( A @ c_Set_Ovimage ) ) @ hAPP ) @ ( C @ ( A @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(38,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( E @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C
= ( E @ ( B @ hAPP ) ) )
=> ( D @ ( B @ ( A @ ( F @ c_Set_Oimage ) ) @ hAPP ) @ ( C @ ( A @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__image__eqI) ).
thf(417,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( E @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C
= ( E @ ( B @ hAPP ) ) )
=> ( D @ ( B @ ( A @ ( F @ c_Set_Oimage ) ) @ hAPP ) @ ( C @ ( A @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(42,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__antisym) ).
thf(436,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(272,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( B @ ( C @ ( D @ ( E @ ( F @ c_Typedef_Otype__definition ) ) ) ) )
=> ( ( A @ ( D @ hAPP ) @ ( C @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_type__definition_ORep__inverse) ).
thf(1518,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( B @ ( C @ ( D @ ( E @ ( F @ c_Typedef_Otype__definition ) ) ) ) )
=> ( ( A @ ( D @ hAPP ) @ ( C @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(28,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__mono1) ).
thf(389,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(15,axiom,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat_Oadd__0__right) ).
thf(344,plain,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(229,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( c_fimplies @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( B @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fimplies__2) ).
thf(1313,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( c_fimplies @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( B @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(68,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__less) ).
thf(542,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(290,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ hAPP ) @ hBOOL )
=> ( C @ ( A @ c_Hilbert__Choice_OEps ) @ ( C @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_someI) ).
thf(1577,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ hAPP ) @ hBOOL )
=> ( C @ ( A @ c_Hilbert__Choice_OEps ) @ ( C @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(256,axiom,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] : ( D @ ( C @ hAPP ) @ hBOOL )
<=> ! [D: $i,E: $i] : ( E @ ( D @ ( A @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__paired__All) ).
thf(1455,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i,E: $i] : ( E @ ( D @ ( A @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hBOOL )
=> ! [D: $i] : ( D @ ( C @ hAPP ) @ hBOOL ) )
& ( ! [D: $i] : ( D @ ( C @ hAPP ) @ hBOOL )
=> ! [D: $i,E: $i] : ( E @ ( D @ ( A @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(18,axiom,
! [A: $i,B: $i] : ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add1) ).
thf(357,plain,
! [A: $i,B: $i] : ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(204,axiom,
! [A: $i] :
( ( A @ ( c_fNot @ hAPP ) @ hBOOL )
| ~ ~ ( A @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fNot__2) ).
thf(1191,plain,
! [A: $i] :
( ( A @ ( c_fNot @ hAPP ) @ hBOOL )
| ( A @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(140,axiom,
! [A: $i] : ( c_fequal @ ( A @ c_Equiv__Relations_Oequivp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_identity__equivp) ).
thf(902,plain,
! [A: $i] : ( c_fequal @ ( A @ c_Equiv__Relations_Oequivp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(91,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( C @ ( D @ ( E @ ( F @ ( G @ c_Sum__Type_Osum_Osum__case ) ) ) ) )
= ( A @ ( B @ ( E @ ( F @ ( G @ c_Sum__Type_Osum_Osum__case ) ) ) ) ) )
=> ~ ( ( D = B )
=> ( C != A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sum__case__inject) ).
thf(638,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( C @ ( D @ ( E @ ( F @ ( G @ c_Sum__Type_Osum_Osum__case ) ) ) ) )
= ( A @ ( B @ ( E @ ( F @ ( G @ c_Sum__Type_Osum_Osum__case ) ) ) ) ) )
=> ~ ( ( D = B )
=> ( C != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(39,axiom,
! [A: $i,B: $i] :
( ( B != A )
<=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__neq__iff) ).
thf(421,plain,
! [A: $i,B: $i] :
( ( ( ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( B != A ) )
& ( ( B != A )
=> ( ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(263,axiom,
! [A: $i,B: $i] :
( ( A @ hBOOL )
| ( B @ hBOOL )
| ~ ( A @ ( B @ ( c_fdisj @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fdisj__3) ).
thf(1479,plain,
! [A: $i,B: $i] :
( ( A @ hBOOL )
| ( B @ hBOOL )
| ~ ( A @ ( B @ ( c_fdisj @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(156,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Owellorder )
=> ( ( A @ ( B @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_OLeast ) @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Least__le) ).
thf(969,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Owellorder )
=> ( ( A @ ( B @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_Orderings_Oord__class_OLeast ) @ ( C @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(236,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( D @ ( F @ c_SetInterval_Oord_OgreaterThanAtMost ) ) ) ) @ ( E @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( A @ ( E @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
& ( E @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord_OgreaterThanAtMost__iff) ).
thf(1347,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ( A @ ( E @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
& ( E @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( C @ ( D @ ( F @ c_SetInterval_Oord_OgreaterThanAtMost ) ) ) ) @ ( E @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ ( D @ ( F @ c_SetInterval_Oord_OgreaterThanAtMost ) ) ) ) @ ( E @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( E @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
& ( E @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(44,axiom,
! [A: $i,B: $i] : ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_Divides_Odivmod__nat__rel ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__nat__rel) ).
thf(448,plain,
! [A: $i,B: $i] : ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( A @ ( B @ c_Divides_Odivmod__nat__rel ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(266,axiom,
! [A: $i,B: $i] :
( ( B @ class_Enum_Oenum )
=> ( ? [C: $i] : ( C @ ( A @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ c_Enum_Oenum__class_Oenum__ex @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_exists__code) ).
thf(1494,plain,
! [A: $i,B: $i] :
( ( B @ class_Enum_Oenum )
=> ( ( ( A @ ( B @ c_Enum_Oenum__class_Oenum__ex @ hAPP ) @ hBOOL )
=> ? [C: $i] : ( C @ ( A @ hAPP ) @ hBOOL ) )
& ( ? [C: $i] : ( C @ ( A @ hAPP ) @ hBOOL )
=> ( A @ ( B @ c_Enum_Oenum__class_Oenum__ex @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(119,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite_OinsertI) ).
thf(789,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(242,axiom,
! [A: $i] : ( A @ ( A @ ( c_Com_Ocom_OSKIP @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evalc_Oequations_I1_J) ).
thf(1373,plain,
! [A: $i] : ( A @ ( A @ ( c_Com_Ocom_OSKIP @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(184,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Com_Ocom_OWhile ) )
!= ( A @ ( B @ c_Com_Ocom_OAss ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I29_J) ).
thf(1109,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Com_Ocom_OWhile ) )
!= ( A @ ( B @ c_Com_Ocom_OAss ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(24,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__less__add1) ).
thf(376,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(85,axiom,
! [A: $i] :
( ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gr0I) ).
thf(623,plain,
! [A: $i] :
( ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(130,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ c_Com_Ocom_OCond ) ) @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( C @ ( F @ hAPP ) @ hBOOL )
=> ~ ( A @ ( B @ ( C @ ( E @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ~ ( ~ ( C @ ( F @ hAPP ) @ hBOOL )
=> ~ ( A @ ( B @ ( C @ ( D @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evaln__elim__cases_I5_J) ).
thf(834,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ c_Com_Ocom_OCond ) ) @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( C @ ( F @ hAPP ) @ hBOOL )
=> ~ ( A @ ( B @ ( C @ ( E @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ~ ( ~ ( C @ ( F @ hAPP ) @ hBOOL )
=> ~ ( A @ ( B @ ( C @ ( D @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(75,axiom,
! [A: $i,B: $i] :
( ( ( B = A )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__or__eq__imp__le) ).
thf(574,plain,
! [A: $i,B: $i] :
( ( ( B = A )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(155,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C != B )
=> ( A @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insertE) ).
thf(966,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C != B )
=> ( A @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(202,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( c_fimplies @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fimplies__1) ).
thf(1183,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( c_fimplies @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(56,axiom,
! [A: $i,B: $i] : ( B @ ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__le__dividend) ).
thf(492,plain,
! [A: $i,B: $i] : ( B @ ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(258,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com__det) ).
thf(1465,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(226,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( B @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ ( B @ ( E @ c_Com_Ocom_OSemi ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evalc_OSemi) ).
thf(1302,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( B @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ ( B @ ( E @ c_Com_Ocom_OSemi ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(114,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ~ ( E @ ( F @ ( G @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( E @ ( B @ ( C @ ( D @ ( G @ c_Finite__Set_Ofold__graph ) ) ) ) @ hAPP ) @ hBOOL )
=> ( A @ ( F @ ( C @ hAPP ) @ hAPP ) @ ( E @ ( F @ ( G @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ ( G @ c_Finite__Set_Ofold__graph ) ) ) ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold__graph_OinsertI) ).
thf(756,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ~ ( E @ ( F @ ( G @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( E @ ( B @ ( C @ ( D @ ( G @ c_Finite__Set_Ofold__graph ) ) ) ) @ hAPP ) @ hBOOL )
=> ( A @ ( F @ ( C @ hAPP ) @ hAPP ) @ ( E @ ( F @ ( G @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ ( G @ c_Finite__Set_Ofold__graph ) ) ) ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(196,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( C @ ( D @ ( E @ ( F @ ( G @ c_Typedef_Otype__definition ) ) ) ) )
=> ( ( ( B @ ( E @ hAPP ) )
= ( A @ ( E @ hAPP ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_type__definition_ORep__inject) ).
thf(1151,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( C @ ( D @ ( E @ ( F @ ( G @ c_Typedef_Otype__definition ) ) ) ) )
=> ( ( ( B = A )
=> ( ( B @ ( E @ hAPP ) )
= ( A @ ( E @ hAPP ) ) ) )
& ( ( ( B @ ( E @ hAPP ) )
= ( A @ ( E @ hAPP ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(147,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( D @ ( E @ ( F @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ ( C @ ( B @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ ( E @ ( B @ ( F @ c_Com_Ocom_OSemi ) @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evaln_OSemi) ).
thf(937,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( D @ ( E @ ( F @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ ( C @ ( B @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ ( E @ ( B @ ( F @ c_Com_Ocom_OSemi ) @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(136,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( D @ ( E @ ( F @ ( G @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( G @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) ) )
<=> ( ( D = A )
& ( E = B )
& ( F = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_triple_Oinject) ).
thf(866,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( ( D = A )
& ( E = B )
& ( F = C ) )
=> ( ( D @ ( E @ ( F @ ( G @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( G @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) ) ) )
& ( ( ( D @ ( E @ ( F @ ( G @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( G @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) ) )
=> ( ( D = A )
& ( E = B )
& ( F = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(31,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__commute) ).
thf(396,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(96,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( E @ c_Com_Ocom_OSemi ) )
!= ( A @ ( B @ ( C @ c_Com_Ocom_OCond ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I44_J) ).
thf(660,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( E @ c_Com_Ocom_OSemi ) )
!= ( A @ ( B @ ( C @ c_Com_Ocom_OCond ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(134,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__commute) ).
thf(849,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(285,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ ( F @ c_Product__Type_Oprod_Oprod__rec ) ) ) ) )
= ( A @ ( B @ ( C @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_prod_Orecs) ).
thf(1564,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ ( F @ c_Product__Type_Oprod_Oprod__rec ) ) ) ) )
= ( A @ ( B @ ( C @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(255,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( D @ ( A @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( C @ ( A @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eqset__imp__iff) ).
thf(1447,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( ( C @ ( A @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( A @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( D @ ( A @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(3,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__cancel__less) ).
thf(293,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(177,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( E @ ( F @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ ( E @ ( D @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ ( E @ ( A @ ( D @ ( F @ c_Com_Ocom_OCond ) ) @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evaln_OIfTrue) ).
thf(1072,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( E @ ( F @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ ( E @ ( D @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ ( E @ ( A @ ( D @ ( F @ c_Com_Ocom_OCond ) ) @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(46,axiom,
! [A: $i] :
~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__zeroE) ).
thf(453,plain,
! [A: $i] :
~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ? [C: $i] :
( A
= ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__iff__add) ).
thf(307,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( A
= ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ? [C: $i] :
( A
= ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(178,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_Com_Ocom_OWhile ) @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( ? [F: $i] :
( ( A @ ( B @ ( F @ ( D @ ( E @ c_Com_Ocom_OWhile ) @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
& ( F @ ( B @ ( C @ ( D @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( C @ ( E @ hAPP ) @ hBOOL ) )
| ( ~ ( C @ ( E @ hAPP ) @ hBOOL )
& ( A = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evaln_Oequations_I8_J) ).
thf(1074,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( ( ? [F: $i] :
( ( A @ ( B @ ( F @ ( D @ ( E @ c_Com_Ocom_OWhile ) @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
& ( F @ ( B @ ( C @ ( D @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( C @ ( E @ hAPP ) @ hBOOL ) )
| ( ~ ( C @ ( E @ hAPP ) @ hBOOL )
& ( A = C ) ) )
=> ( A @ ( B @ ( C @ ( D @ ( E @ c_Com_Ocom_OWhile ) @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ ( D @ ( E @ c_Com_Ocom_OWhile ) @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ? [F: $i] :
( ( A @ ( B @ ( F @ ( D @ ( E @ c_Com_Ocom_OWhile ) @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
& ( F @ ( B @ ( C @ ( D @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( C @ ( E @ hAPP ) @ hBOOL ) )
| ( ~ ( C @ ( E @ hAPP ) @ hBOOL )
& ( A = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(1,conjecture,
v_s_H @ ( v_Z @ ( v_c @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_3) ).
thf(2,negated_conjecture,
~ ( v_s_H @ ( v_Z @ ( v_c @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(292,plain,
~ ( v_s_H @ ( v_Z @ ( v_c @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(228,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_Hoare__Mirabelle_Opeek__and ) ) @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( A @ ( C @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( D @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_peek__and__def) ).
thf(1306,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( ( A @ ( C @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( D @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( C @ ( D @ ( E @ c_Hoare__Mirabelle_Opeek__and ) ) @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ ( D @ ( E @ c_Hoare__Mirabelle_Opeek__and ) ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ hAPP ) @ hBOOL )
& ( A @ ( B @ ( D @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(260,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( E @ ( F @ c_Nitpick_Opair__box_OPairBox ) ) ) @ ( C @ ( D @ ( E @ ( F @ c_Nitpick_Opair__box_Opair__box__case ) ) ) ) )
= ( A @ ( B @ ( C @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pair__box_Osimps_I2_J) ).
thf(1470,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( E @ ( F @ c_Nitpick_Opair__box_OPairBox ) ) ) @ ( C @ ( D @ ( E @ ( F @ c_Nitpick_Opair__box_Opair__box__case ) ) ) ) )
= ( A @ ( B @ ( C @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(22,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__le__add2) ).
thf(366,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(63,axiom,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) )
= ( A @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OlessThan @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeast0LessThan) ).
thf(512,plain,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) )
= ( A @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OlessThan @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(43,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ hAPP ) @ hBOOL ) )
<=> ! [C: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_all__nat__less__eq) ).
thf(439,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ hAPP ) @ hBOOL ) )
=> ! [C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ hAPP ) @ hBOOL ) ) )
& ( ! [C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ hAPP ) @ hBOOL ) )
=> ! [C: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(221,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ c_Hilbert__Choice_OEps ) @ ( B @ hAPP ) @ hBOOL )
<=> ? [C: $i] : ( C @ ( B @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_some__eq__ex) ).
thf(1274,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] : ( C @ ( B @ hAPP ) @ hBOOL )
=> ( B @ ( A @ c_Hilbert__Choice_OEps ) @ ( B @ hAPP ) @ hBOOL ) )
& ( ( B @ ( A @ c_Hilbert__Choice_OEps ) @ ( B @ hAPP ) @ hBOOL )
=> ? [C: $i] : ( C @ ( B @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(180,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( C @ ( D @ ( E @ ( F @ ( G @ c_Big__Operators_Ocomm__monoid__big ) ) ) ) )
=> ( ( ~ ( B @ ( F @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ hAPP ) @ hAPP ) )
= D ) )
& ( ( B @ ( F @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ hAPP ) @ hAPP ) )
= ( B @ ( D @ ( A @ ( E @ ( F @ ( G @ c_Finite__Set_Ofold__image ) ) @ hAPP ) @ hAPP ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__monoid__big_OF__eq) ).
thf(1091,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( C @ ( D @ ( E @ ( F @ ( G @ c_Big__Operators_Ocomm__monoid__big ) ) ) ) )
=> ( ( ~ ( B @ ( F @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ hAPP ) @ hAPP ) )
= D ) )
& ( ( B @ ( F @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ hAPP ) @ hAPP ) )
= ( B @ ( D @ ( A @ ( E @ ( F @ ( G @ c_Finite__Set_Ofold__image ) ) @ hAPP ) @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(171,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_Finite__Set_Ofolding__one ) ) )
=> ( ( A @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ hAPP ) )
= ( A @ ( C @ ( D @ c_Finite__Set_Ofold1 ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__one_Oeq__fold) ).
thf(1042,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_Finite__Set_Ofolding__one ) ) )
=> ( ( A @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ hAPP ) )
= ( A @ ( C @ ( D @ c_Finite__Set_Ofold1 ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I4_J) ).
thf(302,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(35,axiom,
! [A: $i,B: $i] :
~ ( A @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__add__less2) ).
thf(407,plain,
! [A: $i,B: $i] :
~ ( A @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(127,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ c_Com_Ocom_OCond ) ) @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( ( A @ ( B @ ( C @ ( D @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
& ~ ( C @ ( F @ hAPP ) @ hBOOL ) )
| ( ( A @ ( B @ ( C @ ( E @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
& ( C @ ( F @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evaln_Oequations_I6_J) ).
thf(815,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ( ( A @ ( B @ ( C @ ( D @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
& ~ ( C @ ( F @ hAPP ) @ hBOOL ) )
| ( ( A @ ( B @ ( C @ ( E @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
& ( C @ ( F @ hAPP ) @ hBOOL ) ) )
=> ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ c_Com_Ocom_OCond ) ) @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ c_Com_Ocom_OCond ) ) @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( A @ ( B @ ( C @ ( D @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
& ~ ( C @ ( F @ hAPP ) @ hBOOL ) )
| ( ( A @ ( B @ ( C @ ( E @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
& ( C @ ( F @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(287,axiom,
! [A: $i,B: $i] :
( ( A @ hBOOL )
| ~ ( A @ ( B @ ( c_fconj @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fconj__3) ).
thf(1570,plain,
! [A: $i,B: $i] :
( ( A @ hBOOL )
| ~ ( A @ ( B @ ( c_fconj @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(200,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( F @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ c_Hoare__Mirabelle_Otriple_Otriple__rec ) ) ) )
= ( A @ ( B @ ( C @ ( D @ hAPP ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_triple_Orecs) ).
thf(1174,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( F @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ c_Hoare__Mirabelle_Otriple_Otriple__rec ) ) ) )
= ( A @ ( B @ ( C @ ( D @ hAPP ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(51,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ hAPP ) @ hBOOL ) )
<=> ! [C: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( C @ ( tc_Nat_Onat @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_all__nat__less) ).
thf(467,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( C @ ( tc_Nat_Onat @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ hAPP ) @ hBOOL ) )
=> ! [C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ hAPP ) @ hBOOL ) ) )
& ( ! [C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ hAPP ) @ hBOOL ) )
=> ! [C: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( C @ ( tc_Nat_Onat @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(133,axiom,
! [A: $i,B: $i] : ( A @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OgreaterThanAtMost ) ) @ ( tc_Nat_Onat @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__greaterThanAtMost) ).
thf(847,plain,
! [A: $i,B: $i] : ( A @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OgreaterThanAtMost ) ) @ ( tc_Nat_Onat @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(129,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Com_Ocom_OAss ) )
!= ( A @ ( B @ c_Com_Ocom_OSemi ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I24_J) ).
thf(830,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Com_Ocom_OAss ) )
!= ( A @ ( B @ c_Com_Ocom_OSemi ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(206,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_FunDef_Oreduction__pair ) )
=> ( A @ ( C @ ( B @ ( D @ c_FunDef_Orp__inv__image ) @ hAPP ) @ hAPP ) @ ( B @ c_FunDef_Oreduction__pair ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rp__inv__image__rp) ).
thf(1195,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_FunDef_Oreduction__pair ) )
=> ( A @ ( C @ ( B @ ( D @ c_FunDef_Orp__inv__image ) @ hAPP ) @ hAPP ) @ ( B @ c_FunDef_Oreduction__pair ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(190,axiom,
! [A: $i,B: $i] :
( ( B = A )
| ~ ( A @ ( B @ ( c_fequal @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fequal__1) ).
thf(1128,plain,
! [A: $i,B: $i] :
( ( B = A )
| ~ ( A @ ( B @ ( c_fequal @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(47,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__imp__le__nat) ).
thf(456,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(288,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( E @ ( A @ ( B @ c_Predicate_ODomainP ) ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DomainP_Ointros) ).
thf(1573,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( E @ ( A @ ( B @ c_Predicate_ODomainP ) ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(135,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( C @ ( D @ ( E @ ( F @ c_Nitpick_Opair__box_OPairBox ) ) ) )
= ( A @ ( B @ ( E @ ( F @ c_Nitpick_Opair__box_OPairBox ) ) ) ) )
<=> ( ( C = A )
& ( D = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pair__box_Oinject) ).
thf(852,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ( C = A )
& ( D = B ) )
=> ( ( C @ ( D @ ( E @ ( F @ c_Nitpick_Opair__box_OPairBox ) ) ) )
= ( A @ ( B @ ( E @ ( F @ c_Nitpick_Opair__box_OPairBox ) ) ) ) ) )
& ( ( ( C @ ( D @ ( E @ ( F @ c_Nitpick_Opair__box_OPairBox ) ) ) )
= ( A @ ( B @ ( E @ ( F @ c_Nitpick_Opair__box_OPairBox ) ) ) ) )
=> ( ( C = A )
& ( D = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(281,axiom,
! [A: $i,B: $i,C: $i] : ( A @ ( B @ hAPP ) @ ( C @ ( A @ ( c_Natural_Oupdate @ hAPP ) @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( C @ c_Com_Ocom_OAss ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evalc_Oequations_I2_J) ).
thf(1555,plain,
! [A: $i,B: $i,C: $i] : ( A @ ( B @ hAPP ) @ ( C @ ( A @ ( c_Natural_Oupdate @ hAPP ) @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( C @ c_Com_Ocom_OAss ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(197,axiom,
! [A: $i,B: $i] : ( A @ ( B @ c_Divides_Odivmod__nat ) @ ( A @ ( B @ c_Divides_Odivmod__nat__rel ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__nat__rel__divmod__nat) ).
thf(1159,plain,
! [A: $i,B: $i] : ( A @ ( B @ c_Divides_Odivmod__nat ) @ ( A @ ( B @ c_Divides_Odivmod__nat__rel ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(49,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__not__refl3) ).
thf(461,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(65,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( ( C = B )
=> ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( ( C @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__less__cases) ).
thf(519,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( ( C = B )
=> ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( ( ( C @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( C @ ( B @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(276,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Predicate_ODomainP ) ) @ hAPP ) @ hBOOL )
<=> ? [E: $i] : ( E @ ( A @ ( B @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DomainP_Oequations) ).
thf(1534,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ? [E: $i] : ( E @ ( A @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ ( D @ c_Predicate_ODomainP ) ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ ( D @ c_Predicate_ODomainP ) ) @ hAPP ) @ hBOOL )
=> ? [E: $i] : ( E @ ( A @ ( B @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(82,axiom,
! [A: $i] : ( A @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__refl) ).
thf(615,plain,
! [A: $i] : ( A @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(213,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Equiv__Relations_Oequivp ) )
<=> ! [C: $i,D: $i] :
( ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( C @ ( A @ hAPP ) )
= ( D @ ( A @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equivp__def) ).
thf(1227,plain,
! [A: $i,B: $i] :
( ( ! [C: $i,D: $i] :
( ( ( ( C @ ( A @ hAPP ) )
= ( D @ ( A @ hAPP ) ) )
=> ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ hAPP ) )
= ( D @ ( A @ hAPP ) ) ) ) )
=> ( A @ ( B @ c_Equiv__Relations_Oequivp ) ) )
& ( ( A @ ( B @ c_Equiv__Relations_Oequivp ) )
=> ! [C: $i,D: $i] :
( ( ( ( C @ ( A @ hAPP ) )
= ( D @ ( A @ hAPP ) ) )
=> ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( D @ ( C @ ( A @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ hAPP ) )
= ( D @ ( A @ hAPP ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(277,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( A @ ( D @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( C @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eqelem__imp__iff) ).
thf(1540,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( ( A @ ( C @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( D @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(193,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( B @ ( A @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mem__def) ).
thf(1138,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(187,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Finite__Set_Ofolding__one__idem ) ) )
=> ( ( B @ ( E @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ hAPP ) @ ( A @ ( D @ hAPP ) @ hAPP ) )
= ( B @ ( C @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__one__idem_Oin__idem) ).
thf(1118,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Finite__Set_Ofolding__one__idem ) ) )
=> ( ( B @ ( E @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ hAPP ) @ ( A @ ( D @ hAPP ) @ hAPP ) )
= ( B @ ( C @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(246,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( F @ ( G @ ( H @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( F @ ( E @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( G @ ( E @ ( H @ ( A @ ( B @ ( C @ c_Predicate_Opred__comp ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pred__comp_Ointros) ).
thf(1397,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( F @ ( G @ ( H @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( D @ ( F @ ( E @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( G @ ( E @ ( H @ ( A @ ( B @ ( C @ c_Predicate_Opred__comp ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(243,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( ( D @ ( A @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( C @ ( A @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ~ ( ~ ( D @ ( A @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equalityCE) ).
thf(1375,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( ( D @ ( A @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( C @ ( A @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ~ ( ~ ( D @ ( A @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(188,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( E @ c_Equiv__Relations_Oequivp ) )
=> ( ( B @ ( C @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equivp__transp) ).
thf(1121,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( E @ c_Equiv__Relations_Oequivp ) )
=> ( ( B @ ( C @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( D @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(33,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I2_J) ).
thf(403,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(267,axiom,
! [A: $i] :
( ~ ( A @ hBOOL )
| ~ ( A @ ( c_fNot @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fNot__1) ).
thf(1498,plain,
! [A: $i] :
( ~ ( A @ hBOOL )
| ~ ( A @ ( c_fNot @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(286,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( C @ ( B @ hAPP ) )
= ( C @ ( A @ hAPP ) ) )
=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ext) ).
thf(1567,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( C @ ( B @ hAPP ) )
= ( C @ ( A @ hAPP ) ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(240,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_SetInterval_Oord_OatMost ) ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( C @ ( B @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord_OatMost__iff) ).
thf(1361,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ ( C @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ c_SetInterval_Oord_OatMost ) ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( D @ c_SetInterval_Oord_OatMost ) ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( B @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(224,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Divides_Odivmod__nat__rel ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ c_Divides_Odivmod__nat ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__nat__eq) ).
thf(1292,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Divides_Odivmod__nat__rel ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ c_Divides_Odivmod__nat ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(257,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( A @ ( C @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__mem__trans) ).
thf(1461,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( A @ ( C @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(52,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__le__linear) ).
thf(476,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(55,axiom,
! [A: $i] :
~ ( A @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__irrefl__nat) ).
thf(489,plain,
! [A: $i] :
~ ( A @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(210,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ ( G @ c_Predicate_Opred__comp ) ) ) ) ) ) )
<=> ? [H: $i] :
( ( A @ ( H @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
& ( H @ ( B @ ( D @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pred__comp_Oequations) ).
thf(1214,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ? [H: $i] :
( ( A @ ( H @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
& ( H @ ( B @ ( D @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ ( G @ c_Predicate_Opred__comp ) ) ) ) ) ) ) )
& ( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ ( G @ c_Predicate_Opred__comp ) ) ) ) ) ) )
=> ? [H: $i] :
( ( A @ ( H @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
& ( H @ ( B @ ( D @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(164,axiom,
! [A: $i,B: $i] : ( A @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OgreaterThanLessThan ) ) @ ( tc_Nat_Onat @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__greaterThanLessThan) ).
thf(1016,plain,
! [A: $i,B: $i] : ( A @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OgreaterThanLessThan ) ) @ ( tc_Nat_Onat @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(170,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_Com_Ocom_OAss ) @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A
= ( C @ ( D @ hAPP ) @ ( E @ ( C @ ( c_Natural_Oupdate @ hAPP ) @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evaln__elim__cases_I2_J) ).
thf(1039,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_Com_Ocom_OAss ) @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A
= ( C @ ( D @ hAPP ) @ ( E @ ( C @ ( c_Natural_Oupdate @ hAPP ) @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(70,axiom,
! [A: $i] :
( ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
<=> ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neq0__conv) ).
thf(547,plain,
! [A: $i] :
( ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(106,axiom,
tc_Nat_Onat @ class_Orderings_Owellorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Owellorder) ).
thf(706,plain,
tc_Nat_Onat @ class_Orderings_Owellorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(217,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Predicate_ORangeP ) ) @ hAPP ) @ hBOOL )
<=> ? [E: $i] : ( A @ ( E @ ( B @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_RangeP_Oequations) ).
thf(1263,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ? [E: $i] : ( A @ ( E @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ ( D @ c_Predicate_ORangeP ) ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ ( D @ c_Predicate_ORangeP ) ) @ hAPP ) @ hBOOL )
=> ? [E: $i] : ( A @ ( E @ ( B @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(159,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_Com_Ocom_OSemi ) @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
<=> ? [F: $i] :
( ( A @ ( B @ ( F @ ( D @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
& ( F @ ( B @ ( C @ ( E @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evaln_Oequations_I4_J) ).
thf(985,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ? [F: $i] :
( ( A @ ( B @ ( F @ ( D @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
& ( F @ ( B @ ( C @ ( E @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( C @ ( D @ ( E @ c_Com_Ocom_OSemi ) @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ ( D @ ( E @ c_Com_Ocom_OSemi ) @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ? [F: $i] :
( ( A @ ( B @ ( F @ ( D @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
& ( F @ ( B @ ( C @ ( E @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(64,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__not__refl2) ).
thf(515,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(112,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( D @ c_Com_Ocom_OAss ) )
= ( A @ ( B @ c_Com_Ocom_OAss ) ) )
<=> ( ( C = A )
& ( D = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I1_J) ).
thf(738,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( C = A )
& ( D = B ) )
=> ( ( C @ ( D @ c_Com_Ocom_OAss ) )
= ( A @ ( B @ c_Com_Ocom_OAss ) ) ) )
& ( ( ( C @ ( D @ c_Com_Ocom_OAss ) )
= ( A @ ( B @ c_Com_Ocom_OAss ) ) )
=> ( ( C = A )
& ( D = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(191,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Com_Ocom_OAss ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A
= ( B @ ( C @ hAPP ) @ ( D @ ( B @ ( c_Natural_Oupdate @ hAPP ) @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evalc__elim__cases_I2_J) ).
thf(1131,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Com_Ocom_OAss ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A
= ( B @ ( C @ hAPP ) @ ( D @ ( B @ ( c_Natural_Oupdate @ hAPP ) @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(161,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( B @ ( E @ c_Set_Oimage ) ) @ hAPP ) @ ( D @ ( A @ hAPP ) @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
= ( C @ ( A @ ( B @ ( E @ c_Set_Oimage ) ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__image) ).
thf(1002,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( B @ ( E @ c_Set_Oimage ) ) @ hAPP ) @ ( D @ ( A @ hAPP ) @ ( B @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
= ( C @ ( A @ ( B @ ( E @ c_Set_Oimage ) ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(214,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_Com_Ocom_OCond ) ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( ( A @ ( B @ ( C @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
& ~ ( B @ ( E @ hAPP ) @ hBOOL ) )
| ( ( A @ ( B @ ( D @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
& ( B @ ( E @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evalc_Oequations_I5_J) ).
thf(1246,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( ( ( A @ ( B @ ( C @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
& ~ ( B @ ( E @ hAPP ) @ hBOOL ) )
| ( ( A @ ( B @ ( D @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
& ( B @ ( E @ hAPP ) @ hBOOL ) ) )
=> ( A @ ( B @ ( C @ ( D @ ( E @ c_Com_Ocom_OCond ) ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ ( D @ ( E @ c_Com_Ocom_OCond ) ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( A @ ( B @ ( C @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
& ~ ( B @ ( E @ hAPP ) @ hBOOL ) )
| ( ( A @ ( B @ ( D @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
& ( B @ ( E @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(60,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gr__implies__not0) ).
thf(503,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A
!= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(81,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( B != A )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__less__le) ).
thf(605,plain,
! [A: $i,B: $i] :
( ( ( ( B != A )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B != A )
& ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(233,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( E @ c_SetInterval_Oord_OgreaterThanLessThan ) ) ) @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( A @ ( D @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
& ( D @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord_OgreaterThanLessThan__iff) ).
thf(1333,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( ( A @ ( D @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
& ( D @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( C @ ( E @ c_SetInterval_Oord_OgreaterThanLessThan ) ) ) @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ ( E @ c_SetInterval_Oord_OgreaterThanLessThan ) ) ) @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
& ( D @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(89,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv ) @ hAPP ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__le__mono) ).
thf(633,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv ) @ hAPP ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(61,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ c_Finite__Set_Ofold__graph ) ) ) ) @ hAPP ) @ hBOOL )
=> ( B @ ( F @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold__graph__imp__finite) ).
thf(508,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ c_Finite__Set_Ofold__graph ) ) ) ) @ hAPP ) @ hBOOL )
=> ( B @ ( F @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(95,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Divides_Odivmod__nat__rel ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( D @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv ) @ hAPP ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__eq) ).
thf(657,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Divides_Odivmod__nat__rel ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( D @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv ) @ hAPP ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(173,axiom,
! [A: $i,B: $i] :
( c_Com_Ocom_OSKIP
!= ( A @ ( B @ c_Com_Ocom_OAss ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I8_J) ).
thf(1054,plain,
! [A: $i,B: $i] :
( c_Com_Ocom_OSKIP
!= ( A @ ( B @ c_Com_Ocom_OAss ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(72,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( B = A )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__eq__less__or__eq) ).
thf(558,plain,
! [A: $i,B: $i] :
( ( ( ( B = A )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B = A )
| ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(102,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ c_Com_Ocom_OCond ) ) @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( ( A @ ( B @ ( C @ ( D @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
& ~ ( C @ ( F @ hAPP ) @ hBOOL ) )
| ( ( A @ ( B @ ( C @ ( E @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
& ( C @ ( F @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evaln_Oequations_I5_J) ).
thf(674,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ( ( A @ ( B @ ( C @ ( D @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
& ~ ( C @ ( F @ hAPP ) @ hBOOL ) )
| ( ( A @ ( B @ ( C @ ( E @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
& ( C @ ( F @ hAPP ) @ hBOOL ) ) )
=> ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ c_Com_Ocom_OCond ) ) @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ c_Com_Ocom_OCond ) ) @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( A @ ( B @ ( C @ ( D @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
& ~ ( C @ ( F @ hAPP ) @ hBOOL ) )
| ( ( A @ ( B @ ( C @ ( E @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
& ( C @ ( F @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(66,axiom,
! [A: $i,B: $i] :
( ? [C: $i] :
( ( C @ ( A @ hAPP ) @ hBOOL )
& ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
<=> ? [C: $i] :
( ( C @ ( A @ hAPP ) @ hBOOL )
& ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( C @ ( tc_Nat_Onat @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ex__nat__less) ).
thf(530,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( ( C @ ( A @ hAPP ) @ hBOOL )
& ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( C @ ( tc_Nat_Onat @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ? [C: $i] :
( ( C @ ( A @ hAPP ) @ hBOOL )
& ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) )
& ( ? [C: $i] :
( ( C @ ( A @ hAPP ) @ hBOOL )
& ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ? [C: $i] :
( ( C @ ( A @ hAPP ) @ hBOOL )
& ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastAtMost ) ) @ ( C @ ( tc_Nat_Onat @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(203,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_Com_Ocom_OCond ) ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( B @ ( E @ hAPP ) @ hBOOL )
=> ~ ( A @ ( B @ ( D @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ~ ( ~ ( B @ ( E @ hAPP ) @ hBOOL )
=> ~ ( A @ ( B @ ( C @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evalc__elim__cases_I5_J) ).
thf(1185,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_Com_Ocom_OCond ) ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( B @ ( E @ hAPP ) @ hBOOL )
=> ~ ( A @ ( B @ ( D @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ~ ( ~ ( B @ ( E @ hAPP ) @ hBOOL )
=> ~ ( A @ ( B @ ( C @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(182,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Com_Ocom_OWhile ) )
!= c_Com_Ocom_OSKIP ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I17_J) ).
thf(1103,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Com_Ocom_OWhile ) )
!= c_Com_Ocom_OSKIP ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(265,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Com_Ocom_OWhile ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( A = B )
=> ( B @ ( D @ hAPP ) @ hBOOL ) )
=> ~ ( ( B @ ( D @ hAPP ) @ hBOOL )
=> ! [E: $i] :
( ( E @ ( B @ ( C @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( A @ ( E @ ( C @ ( D @ c_Com_Ocom_OWhile ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evalc__WHILE__case) ).
thf(1483,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Com_Ocom_OWhile ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( A = B )
=> ( B @ ( D @ hAPP ) @ hBOOL ) )
=> ~ ( ( B @ ( D @ hAPP ) @ hBOOL )
=> ! [E: $i] :
( ( E @ ( B @ ( C @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( A @ ( E @ ( C @ ( D @ c_Com_Ocom_OWhile ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(220,axiom,
c_fTrue @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fTrue__1) ).
thf(1273,plain,
c_fTrue @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(278,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ c_Com_Ovname_OGlb @ ( B @ ( C @ ( D @ c_Com_Ovname_Ovname__case ) ) ) )
= ( A @ ( C @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vname_Osimps_I5_J) ).
thf(1548,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ c_Com_Ovname_OGlb @ ( B @ ( C @ ( D @ c_Com_Ovname_Ovname__case ) ) ) )
= ( A @ ( C @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(141,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Com_Ocom_OSemi ) )
!= ( A @ ( B @ c_Com_Ocom_OWhile ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I46_J) ).
thf(904,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Com_Ocom_OSemi ) )
!= ( A @ ( B @ c_Com_Ocom_OWhile ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(244,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_SetInterval_Oord_OlessThan ) ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( C @ ( B @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord_OlessThan__iff) ).
thf(1389,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ ( C @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ c_SetInterval_Oord_OlessThan ) ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( D @ c_SetInterval_Oord_OlessThan ) ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( B @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(132,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Com_Ocom_OSemi ) )
!= ( A @ ( B @ c_Com_Ocom_OAss ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I25_J) ).
thf(843,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Com_Ocom_OSemi ) )
!= ( A @ ( B @ c_Com_Ocom_OAss ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(116,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( B @ ( C @ ( D @ ( E @ ( F @ c_Typedef_Otype__definition ) ) ) ) )
=> ( ( B @ ( A @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ hAPP ) @ ( D @ hAPP ) )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_type__definition_OAbs__inverse) ).
thf(772,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( B @ ( C @ ( D @ ( E @ ( F @ c_Typedef_Otype__definition ) ) ) ) )
=> ( ( B @ ( A @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ hAPP ) @ ( D @ hAPP ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(152,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Com_Ocom_OCond ) ) )
!= ( A @ ( B @ c_Com_Ocom_OAss ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I27_J) ).
thf(958,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Com_Ocom_OCond ) ) )
!= ( A @ ( B @ c_Com_Ocom_OAss ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(189,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_Finite__Set_Ofolding__one__idem ) ) )
=> ( ( A @ ( A @ ( C @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__one__idem_Oidem) ).
thf(1124,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_Finite__Set_Ofolding__one__idem ) ) )
=> ( ( A @ ( A @ ( C @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(69,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( B @ ( A @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__less__divisor) ).
thf(545,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( B @ ( A @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(37,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__leE) ).
thf(413,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(128,axiom,
! [A: $i,B: $i] :
( c_Com_Ocom_OSKIP
!= ( A @ ( B @ c_Com_Ocom_OSemi ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I12_J) ).
thf(826,plain,
! [A: $i,B: $i] :
( c_Com_Ocom_OSKIP
!= ( A @ ( B @ c_Com_Ocom_OSemi ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(108,axiom,
! [A: $i,B: $i] : ( A @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( tc_Nat_Onat @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__atLeastLessThan) ).
thf(711,plain,
! [A: $i,B: $i] : ( A @ ( B @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( tc_Nat_Onat @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(251,axiom,
! [A: $i,B: $i,C: $i] :
( ? [D: $i] : ( D @ ( C @ hAPP ) @ hBOOL )
=> ( ( B
= ( C @ ( A @ c_Hilbert__Choice_OEps ) ) )
=> ( B @ ( C @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_exE__some) ).
thf(1428,plain,
! [A: $i,B: $i,C: $i] :
( ? [D: $i] : ( D @ ( C @ hAPP ) @ hBOOL )
=> ( ( B
= ( C @ ( A @ c_Hilbert__Choice_OEps ) ) )
=> ( B @ ( C @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(74,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__trans) ).
thf(572,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(219,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( E @ hAPP ) @ hBOOL )
=> ( ( B @ ( D @ ( C @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( C @ ( E @ c_Com_Ocom_OWhile ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ ( C @ ( E @ c_Com_Ocom_OWhile ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evalc_OWhileTrue) ).
thf(1271,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( E @ hAPP ) @ hBOOL )
=> ( ( B @ ( D @ ( C @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( C @ ( E @ c_Com_Ocom_OWhile ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ ( C @ ( E @ c_Com_Ocom_OWhile ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(109,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Com_Ocom_OCond ) ) )
!= ( A @ ( B @ c_Com_Ocom_OWhile ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I52_J) ).
thf(713,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Com_Ocom_OCond ) ) )
!= ( A @ ( B @ c_Com_Ocom_OWhile ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(124,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Finite__Set_Ofolding__one__idem ) ) )
=> ( ( B @ ( E @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ hAPP ) )
= ( B @ ( A @ ( D @ ( E @ ( E @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__one__idem_Oeq__fold__idem_H) ).
thf(804,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Finite__Set_Ofolding__one__idem ) ) )
=> ( ( B @ ( E @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ hAPP ) )
= ( B @ ( A @ ( D @ ( E @ ( E @ c_Finite__Set_Ofold ) ) @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(238,axiom,
! [A: $i,B: $i] :
( ? [C: $i] : ( C @ ( B @ hAPP ) @ hBOOL )
=> ( B @ ( A @ c_Hilbert__Choice_OEps ) @ ( B @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_tfl__some) ).
thf(1356,plain,
! [A: $i,B: $i] :
( ? [C: $i] : ( C @ ( B @ hAPP ) @ hBOOL )
=> ( B @ ( A @ c_Hilbert__Choice_OEps ) @ ( B @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(101,axiom,
! [A: $i,B: $i,C: $i,D: $i] : ( B @ ( C @ hAPP ) @ ( D @ ( B @ ( c_Natural_Oupdate @ hAPP ) @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( C @ ( D @ c_Com_Ocom_OAss ) @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evaln_Oequations_I2_J) ).
thf(672,plain,
! [A: $i,B: $i,C: $i,D: $i] : ( B @ ( C @ hAPP ) @ ( D @ ( B @ ( c_Natural_Oupdate @ hAPP ) @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( C @ ( D @ c_Com_Ocom_OAss ) @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(29,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__leD2) ).
thf(391,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(269,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( E @ ( F @ ( G @ ( H @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( C @ ( D @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ? [I: $i] :
( ( A @ ( I @ ( C @ ( D @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
& ( E @ ( I @ ( G @ ( H @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evaln__max2) ).
thf(1503,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( E @ ( F @ ( G @ ( H @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( C @ ( D @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ? [I: $i] :
( ( A @ ( I @ ( C @ ( D @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
& ( E @ ( I @ ( G @ ( H @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(174,axiom,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
<=> ? [B: $i] :
! [C: $i] :
( ( A @ ( C @ ( tc_Nat_Onat @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__nat__set__iff__bounded__le) ).
thf(1058,plain,
! [A: $i] :
( ( ? [B: $i] :
! [C: $i] :
( ( A @ ( C @ ( tc_Nat_Onat @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( tc_Nat_Onat @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) )
& ( ( A @ ( tc_Nat_Onat @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ? [B: $i] :
! [C: $i] :
( ( A @ ( C @ ( tc_Nat_Onat @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(183,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( E @ ( F @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ ( E @ ( D @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ ( E @ ( D @ ( A @ ( F @ c_Com_Ocom_OCond ) ) @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evaln_OIfFalse) ).
thf(1107,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( E @ ( F @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ ( E @ ( D @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ ( E @ ( D @ ( A @ ( F @ c_Com_Ocom_OCond ) ) @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(158,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Wellfounded_OwfP ) )
<=> ! [C: $i] : ( C @ ( A @ ( B @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wfP__accp__iff) ).
thf(979,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] : ( C @ ( A @ ( B @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ c_Wellfounded_OwfP ) ) )
& ( ( A @ ( B @ c_Wellfounded_OwfP ) )
=> ! [C: $i] : ( C @ ( A @ ( B @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(274,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( c_Int_ORep__Integ @ hAPP ) )
= ( A @ ( c_Int_ORep__Integ @ hAPP ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Rep__Integ__inject) ).
thf(1524,plain,
! [A: $i,B: $i] :
( ( ( B = A )
=> ( ( B @ ( c_Int_ORep__Integ @ hAPP ) )
= ( A @ ( c_Int_ORep__Integ @ hAPP ) ) ) )
& ( ( ( B @ ( c_Int_ORep__Integ @ hAPP ) )
= ( A @ ( c_Int_ORep__Integ @ hAPP ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(20,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__mono) ).
thf(362,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(194,axiom,
! [A: $i,B: $i] :
( ( B @ class_Enum_Oenum )
=> ( ( A @ ( B @ c_Enum_Oenum__class_Oenum__ex @ hAPP ) @ hBOOL )
<=> ? [C: $i] : ( C @ ( A @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_enum__ex) ).
thf(1144,plain,
! [A: $i,B: $i] :
( ( B @ class_Enum_Oenum )
=> ( ( ? [C: $i] : ( C @ ( A @ hAPP ) @ hBOOL )
=> ( A @ ( B @ c_Enum_Oenum__class_Oenum__ex @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ c_Enum_Oenum__class_Oenum__ex @ hAPP ) @ hBOOL )
=> ? [C: $i] : ( C @ ( A @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__gr__0) ).
thf(318,plain,
! [A: $i,B: $i] :
( ( ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
| ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(253,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
<=> ? [D: $i] : ( A @ ( D @ ( B @ ( C @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eval__eq) ).
thf(1439,plain,
! [A: $i,B: $i,C: $i] :
( ( ? [D: $i] : ( A @ ( D @ ( B @ ( C @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
=> ? [D: $i] : ( A @ ( D @ ( B @ ( C @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(92,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Com_Ocom_OWhile ) )
!= ( A @ ( B @ c_Com_Ocom_OSemi ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I47_J) ).
thf(649,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Com_Ocom_OWhile ) )
!= ( A @ ( B @ c_Com_Ocom_OSemi ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(41,axiom,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( B @ ( A @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__le__divisor) ).
thf(434,plain,
! [A: $i,B: $i] :
( ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( B @ ( A @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(126,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Com_Ocom_OAss ) )
!= ( A @ ( B @ c_Com_Ocom_OWhile ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I28_J) ).
thf(811,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Com_Ocom_OAss ) )
!= ( A @ ( B @ c_Com_Ocom_OWhile ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(57,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( B @ ( C @ ( D @ ( E @ ( F @ ( G @ c_Finite__Set_Ofolding__image__simple ) ) ) ) ) )
=> ( ( A @ ( F @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ hAPP ) )
= ( A @ ( D @ ( C @ ( E @ ( F @ ( G @ c_Finite__Set_Ofold__image ) ) @ hAPP ) @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__image__simple_Oeq__fold__g) ).
thf(494,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( B @ ( C @ ( D @ ( E @ ( F @ ( G @ c_Finite__Set_Ofolding__image__simple ) ) ) ) ) )
=> ( ( A @ ( F @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ hAPP ) )
= ( A @ ( D @ ( C @ ( E @ ( F @ ( G @ c_Finite__Set_Ofold__image ) ) @ hAPP ) @ hAPP ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(88,axiom,
! [A: $i] : ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__nat_Osimps_I1_J) ).
thf(631,plain,
! [A: $i] : ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(115,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( D @ c_Com_Ocom_OSemi ) )
= ( A @ ( B @ c_Com_Ocom_OSemi ) ) )
<=> ( ( C = A )
& ( D = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I3_J) ).
thf(758,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( C = A )
& ( D = B ) )
=> ( ( C @ ( D @ c_Com_Ocom_OSemi ) )
= ( A @ ( B @ c_Com_Ocom_OSemi ) ) ) )
& ( ( ( C @ ( D @ c_Com_Ocom_OSemi ) )
= ( A @ ( B @ c_Com_Ocom_OSemi ) ) )
=> ( ( C = A )
& ( D = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(282,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
=> ? [D: $i] : ( A @ ( D @ ( B @ ( C @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evalc__evaln) ).
thf(1557,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
=> ? [D: $i] : ( A @ ( D @ ( B @ ( C @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(154,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( E @ ( F @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ ( E @ ( D @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( B @ ( D @ ( F @ c_Com_Ocom_OWhile ) @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( E @ ( D @ ( F @ c_Com_Ocom_OWhile ) @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evaln_OWhileTrue) ).
thf(964,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( E @ ( F @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ ( E @ ( D @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( B @ ( D @ ( F @ c_Com_Ocom_OWhile ) @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( E @ ( D @ ( F @ c_Com_Ocom_OWhile ) @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(86,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Divides_Odivmod__nat ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__nat__div__mod) ).
thf(626,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Divides_Odivmod__nat ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv ) @ hAPP ) @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(235,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( c_Com_Ocom_OSKIP @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evalc__elim__cases_I1_J) ).
thf(1344,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( c_Com_Ocom_OSKIP @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(166,axiom,
! [A: $i,B: $i,C: $i,D: $i] : ( B @ ( C @ hAPP ) @ ( D @ ( B @ ( c_Natural_Oupdate @ hAPP ) @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( C @ ( D @ c_Com_Ocom_OAss ) @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evaln_OAssign) ).
thf(1022,plain,
! [A: $i,B: $i,C: $i,D: $i] : ( B @ ( C @ hAPP ) @ ( D @ ( B @ ( c_Natural_Oupdate @ hAPP ) @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( C @ ( D @ c_Com_Ocom_OAss ) @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(99,axiom,
! [A: $i,B: $i,C: $i] : ( A @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insertI1) ).
thf(668,plain,
! [A: $i,B: $i,C: $i] : ( A @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(201,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_SetInterval_Oord_OgreaterThan ) ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( C @ ( A @ ( B @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord_OgreaterThan__iff) ).
thf(1177,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( A @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( D @ c_SetInterval_Oord_OgreaterThan ) ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( D @ c_SetInterval_Oord_OgreaterThan ) ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( B @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(32,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= B )
=> ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__eq__self__zero) ).
thf(399,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= B )
=> ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(104,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( E @ c_Com_Ocom_OWhile ) )
!= ( A @ ( B @ ( C @ c_Com_Ocom_OCond ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I53_J) ).
thf(695,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( E @ c_Com_Ocom_OWhile ) )
!= ( A @ ( B @ ( C @ c_Com_Ocom_OCond ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(30,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__le__add1) ).
thf(394,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(185,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Divides_Odivmod__nat__rel ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( D @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__eq) ).
thf(1113,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_Divides_Odivmod__nat__rel ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( D @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__assoc) ).
thf(299,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(93,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( C @ ( D @ ( E @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ ( E @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evaln__nonstrict) ).
thf(653,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( C @ ( D @ ( E @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( D @ ( E @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(284,axiom,
! [A: $i,B: $i] :
( ? [C: $i] : ( C @ ( B @ hAPP ) @ hBOOL )
=> ( B @ ( A @ c_Hilbert__Choice_OEps ) @ ( B @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_someI__ex) ).
thf(1562,plain,
! [A: $i,B: $i] :
( ? [C: $i] : ( C @ ( B @ hAPP ) @ hBOOL )
=> ( B @ ( A @ c_Hilbert__Choice_OEps ) @ ( B @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(143,axiom,
! [A: $i] : ( A @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatMost @ hAPP ) @ ( tc_Nat_Onat @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__atMost) ).
thf(912,plain,
! [A: $i] : ( A @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatMost @ hAPP ) @ ( tc_Nat_Onat @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(103,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( E @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_Hoare__Mirabelle_Otriple__valid ) ) )
<=> ! [F: $i,G: $i] :
( ( G @ ( F @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [H: $i] :
( ( H @ ( D @ ( G @ ( B @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( H @ ( F @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_triple__valid__def2) ).
thf(685,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ! [F: $i,G: $i] :
( ( G @ ( F @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [H: $i] :
( ( H @ ( D @ ( G @ ( B @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( H @ ( F @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ) )
=> ( A @ ( B @ ( C @ ( E @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_Hoare__Mirabelle_Otriple__valid ) ) ) )
& ( ( A @ ( B @ ( C @ ( E @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_Hoare__Mirabelle_Otriple__valid ) ) )
=> ! [F: $i,G: $i] :
( ( G @ ( F @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [H: $i] :
( ( H @ ( D @ ( G @ ( B @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( H @ ( F @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(175,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Com_Ocom_OSemi ) )
!= c_Com_Ocom_OSKIP ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I13_J) ).
thf(1066,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Com_Ocom_OSemi ) )
!= c_Com_Ocom_OSKIP ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(254,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Owellorder )
=> ( ( A @ ( B @ hAPP ) @ hBOOL )
=> ( B @ ( C @ c_Orderings_Oord__class_OLeast ) @ ( B @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_LeastI) ).
thf(1445,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Owellorder )
=> ( ( A @ ( B @ hAPP ) @ hBOOL )
=> ( B @ ( C @ c_Orderings_Oord__class_OLeast ) @ ( B @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(248,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_New__Random__Sequence_Opos__not__random__dseq ) ) ) )
= ( A @ ( B @ ( C @ ( D @ hAPP ) @ hAPP ) @ hAPP ) @ c_New__DSequence_Opos__not__seq ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__not__random__dseq__def) ).
thf(1413,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_New__Random__Sequence_Opos__not__random__dseq ) ) ) )
= ( A @ ( B @ ( C @ ( D @ hAPP ) @ hAPP ) @ hAPP ) @ c_New__DSequence_Opos__not__seq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(168,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( B @ ( C @ ( D @ ( E @ ( F @ c_Typedef_Otype__definition ) ) ) ) )
=> ( B @ ( A @ ( D @ hAPP ) @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_type__definition_ORep) ).
thf(1034,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( B @ ( C @ ( D @ ( E @ ( F @ c_Typedef_Otype__definition ) ) ) ) )
=> ( B @ ( A @ ( D @ hAPP ) @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(227,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( c_fconj @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ hBOOL )
| ~ ( B @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fconj__1) ).
thf(1304,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( c_fconj @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( A @ hBOOL )
| ~ ( B @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(209,axiom,
! [A: $i] :
( ! [B: $i] :
( ( B @ ( v_Z @ ( v_c @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A = B ) )
=> ( A = v_s_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
thf(1208,plain,
! [A: $i] :
( ! [B: $i] :
( ( B @ ( v_Z @ ( v_c @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A = B ) )
=> ( A = v_s_H ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(150,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
<=> ( A @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__insert) ).
thf(944,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( A @ ( C @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(121,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Wellfounded_OwfP ) )
=> ( A @ ( B @ ( C @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_accp__wfPD) ).
thf(795,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Wellfounded_OwfP ) )
=> ( A @ ( B @ ( C @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(250,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL )
<=> ! [D: $i] :
( ( A @ ( D @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( B @ ( C @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_accp_Osimps) ).
thf(1420,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( A @ ( D @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( B @ ( C @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( C @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL )
=> ! [D: $i] :
( ( A @ ( D @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( B @ ( C @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(271,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( A @ ( B @ ( C @ c_Com_Ocom_OWhile ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( A @ ( C @ hAPP ) @ hBOOL )
=> ? [D: $i] :
( ( A @ ( D @ ( B @ ( C @ c_Com_Ocom_OWhile ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
& ( D @ ( A @ ( B @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evalc_Oequations_I7_J) ).
thf(1509,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( A @ ( C @ hAPP ) @ hBOOL )
=> ? [D: $i] :
( ( A @ ( D @ ( B @ ( C @ c_Com_Ocom_OWhile ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
& ( D @ ( A @ ( B @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL ) ) )
=> ( A @ ( A @ ( B @ ( C @ c_Com_Ocom_OWhile ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( A @ ( B @ ( C @ c_Com_Ocom_OWhile ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ hAPP ) @ hBOOL )
=> ? [D: $i] :
( ( A @ ( D @ ( B @ ( C @ c_Com_Ocom_OWhile ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
& ( D @ ( A @ ( B @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(83,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) @ hAPP ) )
= ( A @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) @ hAPP ) @ ( B @ ( C @ hAPP ) @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__insert) ).
thf(617,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( E @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) @ hAPP ) )
= ( A @ ( C @ ( D @ ( E @ c_Set_Oimage ) ) @ hAPP ) @ ( B @ ( C @ hAPP ) @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(14,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__mono) ).
thf(342,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(165,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Com_Ocom_OCond ) ) )
!= c_Com_Ocom_OSKIP ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I15_J) ).
thf(1018,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Com_Ocom_OCond ) ) )
!= c_Com_Ocom_OSKIP ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(17,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__leD1) ).
thf(355,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(48,axiom,
! [A: $i,B: $i] :
( ( B != A )
=> ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__neqE__nat) ).
thf(458,plain,
! [A: $i,B: $i] :
( ( B != A )
=> ( ~ ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(279,axiom,
? [A: $i] : ( A @ ( v_s_H @ ( v_Z @ v_Sledgehammer_058s__2 ) @ ( v_c @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_2) ).
thf(1551,plain,
? [A: $i] : ( A @ ( v_s_H @ ( v_Z @ v_Sledgehammer_058s__2 ) @ ( v_c @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(192,axiom,
! [A: $i,B: $i] :
( ( B @ class_Enum_Oenum )
=> ( ( A @ ( B @ c_Enum_Oenum__class_Oenum__all @ hAPP ) @ hBOOL )
<=> ! [C: $i] : ( C @ ( A @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_enum__all) ).
thf(1134,plain,
! [A: $i,B: $i] :
( ( B @ class_Enum_Oenum )
=> ( ( ! [C: $i] : ( C @ ( A @ hAPP ) @ hBOOL )
=> ( A @ ( B @ c_Enum_Oenum__class_Oenum__all @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ c_Enum_Oenum__class_Oenum__all @ hAPP ) @ hBOOL )
=> ! [C: $i] : ( C @ ( A @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(54,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( B @ ( E @ c_Set_Oimage ) ) @ hAPP ) @ ( D @ ( A @ hAPP ) @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_imageI) ).
thf(487,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( B @ ( E @ c_Set_Oimage ) ) @ hAPP ) @ ( D @ ( A @ hAPP ) @ ( B @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(148,axiom,
! [A: $i,B: $i] : ( B @ ( A @ ( B @ ( c_Com_Ocom_OSKIP @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evaln_Oequations_I1_J) ).
thf(939,plain,
! [A: $i,B: $i] : ( B @ ( A @ ( B @ ( c_Com_Ocom_OSKIP @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(234,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( c_fequal @ hAPP ) @ hAPP ) @ hBOOL )
| ( B != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fequal__2) ).
thf(1340,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( c_fequal @ hAPP ) @ hAPP ) @ hBOOL )
| ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(117,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( A @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
| ( C = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__iff) ).
thf(776,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( A @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
| ( C = B ) )
=> ( A @ ( B @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
| ( C = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(76,axiom,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__0__eq) ).
thf(580,plain,
! [A: $i] :
( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(176,axiom,
! [A: $i,B: $i] : ( B @ ( A @ ( B @ ( c_Com_Ocom_OSKIP @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evaln_OSkip) ).
thf(1070,plain,
! [A: $i,B: $i] : ( B @ ( A @ ( B @ ( c_Com_Ocom_OSKIP @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(157,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( C @ ( D @ ( E @ ( F @ ( G @ c_Typedef_Otype__definition ) ) ) ) )
=> ( ( C @ ( B @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( B @ ( D @ hAPP ) )
= ( A @ ( D @ hAPP ) ) )
<=> ( B = A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_type__definition_OAbs__inject) ).
thf(971,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( C @ ( D @ ( E @ ( F @ ( G @ c_Typedef_Otype__definition ) ) ) ) )
=> ( ( C @ ( B @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( C @ ( A @ ( F @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( B = A )
=> ( ( B @ ( D @ hAPP ) )
= ( A @ ( D @ hAPP ) ) ) )
& ( ( ( B @ ( D @ hAPP ) )
= ( A @ ( D @ hAPP ) ) )
=> ( B = A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(212,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( c_fdisj @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( B @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fdisj__2) ).
thf(1225,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( c_fdisj @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( B @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(107,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Com_Ocom_OAss ) )
!= c_Com_Ocom_OSKIP ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I9_J) ).
thf(707,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Com_Ocom_OAss ) )
!= c_Com_Ocom_OSKIP ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(252,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Com_Ocom_OSemi ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
<=> ? [E: $i] :
( ( A @ ( E @ ( C @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
& ( E @ ( B @ ( D @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evalc_Oequations_I4_J) ).
thf(1432,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ? [E: $i] :
( ( A @ ( E @ ( C @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
& ( E @ ( B @ ( D @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( C @ ( D @ c_Com_Ocom_OSemi ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ ( D @ c_Com_Ocom_OSemi ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
=> ? [E: $i] :
( ( A @ ( E @ ( C @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
& ( E @ ( B @ ( D @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(120,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Com_Ocom_OCond ) ) )
!= ( A @ ( B @ c_Com_Ocom_OSemi ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I45_J) ).
thf(791,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Com_Ocom_OCond ) ) )
!= ( A @ ( B @ c_Com_Ocom_OSemi ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(110,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__absorb) ).
thf(717,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(131,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( E @ c_Set_Ovimage ) ) @ hAPP ) @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ ( B @ hAPP ) @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimageD) ).
thf(840,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( E @ c_Set_Ovimage ) ) @ hAPP ) @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ ( B @ hAPP ) @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(12,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__less__add2) ).
thf(338,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(19,axiom,
! [A: $i,B: $i] :
~ ( B @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__add__less1) ).
thf(359,plain,
! [A: $i,B: $i] :
~ ( B @ ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(291,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( E @ c_SetInterval_Oord_OatLeastAtMost ) ) ) @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( A @ ( D @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
& ( D @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord_OatLeastAtMost__iff) ).
thf(1579,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( ( A @ ( D @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
& ( D @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( C @ ( E @ c_SetInterval_Oord_OatLeastAtMost ) ) ) @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ ( E @ c_SetInterval_Oord_OatLeastAtMost ) ) ) @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( D @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
& ( D @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(239,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Equiv__Relations_Oequivp ) )
=> ( ( A @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equivp__symp) ).
thf(1358,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Equiv__Relations_Oequivp ) )
=> ( ( A @ ( B @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( A @ ( C @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(11,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I1_J) ).
thf(336,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(215,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( G = F )
=> ( ( G @ ( A @ ( B @ ( C @ ( D @ ( E @ c_Sum__Type_Osum_Osum__case ) ) ) ) @ hAPP ) )
= ( F @ ( A @ ( B @ ( C @ ( D @ ( E @ c_Sum__Type_Osum_Osum__case ) ) ) ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sum__case__weak__cong) ).
thf(1257,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( G = F )
=> ( ( G @ ( A @ ( B @ ( C @ ( D @ ( E @ c_Sum__Type_Osum_Osum__case ) ) ) ) @ hAPP ) )
= ( F @ ( A @ ( B @ ( C @ ( D @ ( E @ c_Sum__Type_Osum_Osum__case ) ) ) ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(79,axiom,
! [A: $i] :
~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__nat__zero__code) ).
thf(600,plain,
! [A: $i] :
~ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(27,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv ) @ hAPP ) )
= ( A @ ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv ) @ hAPP ) @ ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv ) @ hAPP ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__add1__eq) ).
thf(386,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv ) @ hAPP ) )
= ( A @ ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv ) @ hAPP ) @ ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv ) @ hAPP ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(58,axiom,
! [A: $i,B: $i] :
( ( B = A )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__imp__le) ).
thf(497,plain,
! [A: $i,B: $i] :
( ( B = A )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(211,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Com_Ocom_OSemi ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ! [E: $i] :
( ( E @ ( B @ ( D @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( A @ ( E @ ( C @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evalc__elim__cases_I4_J) ).
thf(1221,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Com_Ocom_OSemi ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ! [E: $i] :
( ( E @ ( B @ ( D @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( A @ ( E @ ( C @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(223,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL )
<=> ! [D: $i] :
( ( A @ ( D @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( B @ ( C @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_accp_Oequations) ).
thf(1284,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( A @ ( D @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( B @ ( C @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( C @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL )
=> ! [D: $i] :
( ( A @ ( D @ ( B @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( B @ ( C @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(50,axiom,
! [A: $i] : ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le0) ).
thf(465,plain,
! [A: $i] : ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(45,axiom,
! [A: $i] :
~ ( A @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__not__refl) ).
thf(450,plain,
! [A: $i] :
~ ( A @ ( A @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(67,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__less) ).
thf(539,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(280,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( c_fdisj @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( B @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fdisj__1) ).
thf(1553,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( c_fdisj @ hAPP ) @ hAPP ) @ hBOOL )
| ~ ( B @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(231,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( A @ ( B @ hAPP ) @ hBOOL )
| ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__code) ).
thf(1321,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( A @ ( B @ hAPP ) @ hBOOL )
| ( C = A ) )
=> ( A @ ( B @ ( C @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( B @ hAPP ) @ hBOOL )
| ( C = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(289,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( B @ ( C @ hAPP ) @ hBOOL )
=> ( B @ ( B @ ( A @ ( C @ c_Com_Ocom_OWhile ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evalc_OWhileFalse) ).
thf(1575,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( B @ ( C @ hAPP ) @ hBOOL )
=> ( B @ ( B @ ( A @ ( C @ c_Com_Ocom_OWhile ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(23,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__cancel) ).
thf(368,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B = A )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ) )
& ( ( ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(262,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ c_Com_Ovname_OGlb @ ( B @ ( C @ ( D @ c_Com_Ovname_Ovname__rec ) ) ) )
= ( A @ ( C @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vname_Orecs_I1_J) ).
thf(1476,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ c_Com_Ovname_OGlb @ ( B @ ( C @ ( D @ c_Com_Ovname_Ovname__rec ) ) ) )
= ( A @ ( C @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(139,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C = A ) )
=> ( B @ ( A @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insertCI) ).
thf(896,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C = A ) )
=> ( B @ ( A @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__commute) ).
thf(304,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(264,axiom,
! [A: $i,B: $i] :
( ( B @ hBOOL )
| ~ ( A @ ( B @ ( c_fconj @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fconj__2) ).
thf(1481,plain,
! [A: $i,B: $i] :
( ( B @ hBOOL )
| ~ ( A @ ( B @ ( c_fconj @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(118,axiom,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ c_Divides_Odivmod__nat ) )
= ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__nat__zero) ).
thf(786,plain,
! [A: $i] :
( ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( A @ c_Divides_Odivmod__nat ) )
= ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ ( tc_Nat_Onat @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(77,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( E @ ( C @ c_Set_Oimage ) ) @ hAPP ) @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ? [F: $i] :
( ( D
= ( F @ ( B @ hAPP ) ) )
& ( A @ ( F @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__iff) ).
thf(588,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ? [F: $i] :
( ( D
= ( F @ ( B @ hAPP ) ) )
& ( A @ ( F @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( E @ ( C @ c_Set_Oimage ) ) @ hAPP ) @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( E @ ( C @ c_Set_Oimage ) ) @ hAPP ) @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ? [F: $i] :
( ( D
= ( F @ ( B @ hAPP ) ) )
& ( A @ ( F @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(105,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( C @ ( D @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) )
=> ~ ( ( D = B )
=> ( C != A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pair__inject) ).
thf(699,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( C @ ( D @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) )
=> ~ ( ( D = B )
=> ( C != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(73,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F
= ( D @ ( E @ hAPP ) ) )
=> ( ( B @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( E @ ( A @ ( C @ c_Set_Oimage ) ) @ hAPP ) @ ( F @ ( A @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__eqI) ).
thf(568,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F
= ( D @ ( E @ hAPP ) ) )
=> ( ( B @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( E @ ( A @ ( C @ c_Set_Oimage ) ) @ hAPP ) @ ( F @ ( A @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(62,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv ) @ hAPP ) @ ( B @ ( A @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__le__mono2) ).
thf(510,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv ) @ hAPP ) @ ( B @ ( A @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Odiv ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(146,axiom,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
<=> ? [B: $i] :
! [C: $i] :
( ( A @ ( C @ ( tc_Nat_Onat @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__nat__set__iff__bounded) ).
thf(929,plain,
! [A: $i] :
( ( ? [B: $i] :
! [C: $i] :
( ( A @ ( C @ ( tc_Nat_Onat @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ( A @ ( tc_Nat_Onat @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) )
& ( ( A @ ( tc_Nat_Onat @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ? [B: $i] :
! [C: $i] :
( ( A @ ( C @ ( tc_Nat_Onat @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(205,axiom,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Owellorder )
=> ( ? [C: $i] : ( C @ ( A @ hAPP ) @ hBOOL )
=> ( A @ ( B @ c_Orderings_Oord__class_OLeast ) @ ( A @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_LeastI__ex) ).
thf(1193,plain,
! [A: $i,B: $i] :
( ( B @ class_Orderings_Owellorder )
=> ( ? [C: $i] : ( C @ ( A @ hAPP ) @ hBOOL )
=> ( A @ ( B @ c_Orderings_Oord__class_OLeast ) @ ( A @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(53,axiom,
! [A: $i,B: $i] :
( ? [C: $i] :
( ( C @ ( A @ hAPP ) @ hBOOL )
& ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
<=> ? [C: $i] :
( ( C @ ( A @ hAPP ) @ hBOOL )
& ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ex__nat__less__eq) ).
thf(478,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( ( C @ ( A @ hAPP ) @ hBOOL )
& ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ? [C: $i] :
( ( C @ ( A @ hAPP ) @ hBOOL )
& ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) )
& ( ? [C: $i] :
( ( C @ ( A @ hAPP ) @ hBOOL )
& ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) )
=> ? [C: $i] :
( ( C @ ( A @ hAPP ) @ hBOOL )
& ( B @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastLessThan ) @ hAPP ) @ ( C @ ( tc_Nat_Onat @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(172,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ ( B @ ( C @ ( D @ c_Com_Ocom_OWhile ) @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( B @ ( D @ hAPP ) @ hBOOL )
=> ? [E: $i] :
( ( B @ ( A @ ( E @ ( C @ ( D @ c_Com_Ocom_OWhile ) @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
& ( E @ ( A @ ( B @ ( C @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evaln_Oequations_I7_J) ).
thf(1045,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( B @ ( D @ hAPP ) @ hBOOL )
=> ? [E: $i] :
( ( B @ ( A @ ( E @ ( C @ ( D @ c_Com_Ocom_OWhile ) @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
& ( E @ ( A @ ( B @ ( C @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ) )
=> ( B @ ( A @ ( B @ ( C @ ( D @ c_Com_Ocom_OWhile ) @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( B @ ( A @ ( B @ ( C @ ( D @ c_Com_Ocom_OWhile ) @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( D @ hAPP ) @ hBOOL )
=> ? [E: $i] :
( ( B @ ( A @ ( E @ ( C @ ( D @ c_Com_Ocom_OWhile ) @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
& ( E @ ( A @ ( B @ ( C @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(198,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_Com_Ocom_OCond ) ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( ( A @ ( B @ ( C @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
& ~ ( B @ ( E @ hAPP ) @ hBOOL ) )
| ( ( A @ ( B @ ( D @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
& ( B @ ( E @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evalc_Oequations_I6_J) ).
thf(1161,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( ( ( A @ ( B @ ( C @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
& ~ ( B @ ( E @ hAPP ) @ hBOOL ) )
| ( ( A @ ( B @ ( D @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
& ( B @ ( E @ hAPP ) @ hBOOL ) ) )
=> ( A @ ( B @ ( C @ ( D @ ( E @ c_Com_Ocom_OCond ) ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ ( D @ ( E @ c_Com_Ocom_OCond ) ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( A @ ( B @ ( C @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
& ~ ( B @ ( E @ hAPP ) @ hBOOL ) )
| ( ( A @ ( B @ ( D @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
& ( B @ ( E @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(144,axiom,
! [A: $i,B: $i] :
( c_Com_Ocom_OSKIP
!= ( A @ ( B @ c_Com_Ocom_OWhile ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I16_J) ).
thf(914,plain,
! [A: $i,B: $i] :
( c_Com_Ocom_OSKIP
!= ( A @ ( B @ c_Com_Ocom_OWhile ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(25,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__cancel__le) ).
thf(378,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(186,axiom,
! [A: $i] : ( A @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OlessThan @ hAPP ) @ ( tc_Nat_Onat @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__lessThan) ).
thf(1116,plain,
! [A: $i] : ( A @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OlessThan @ hAPP ) @ ( tc_Nat_Onat @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(84,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B != A )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__neq__implies__less) ).
thf(620,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( B != A )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(113,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( E @ ( F @ hAPP ) )
= D )
=> ( ( B @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( F @ ( C @ ( A @ c_Set_Ovimage ) ) @ hAPP ) @ ( E @ ( A @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimageI) ).
thf(752,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( E @ ( F @ hAPP ) )
= D )
=> ( ( B @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( F @ ( C @ ( A @ c_Set_Ovimage ) ) @ hAPP ) @ ( E @ ( A @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(40,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( B @ ( D @ c_Set_Oimage ) ) @ hAPP ) @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__imageI) ).
thf(432,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( B @ ( D @ c_Set_Oimage ) ) @ hAPP ) @ ( B @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(36,axiom,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_plus__nat_Oadd__0) ).
thf(410,plain,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(245,axiom,
! [A: $i,B: $i,C: $i] : ( A @ ( B @ hAPP ) @ ( C @ ( A @ ( c_Natural_Oupdate @ hAPP ) @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( C @ c_Com_Ocom_OAss ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evalc_OAssign) ).
thf(1395,plain,
! [A: $i,B: $i,C: $i] : ( A @ ( B @ hAPP ) @ ( C @ ( A @ ( c_Natural_Oupdate @ hAPP ) @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( C @ c_Com_Ocom_OAss ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(34,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__lessD1) ).
thf(405,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(195,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( E @ ( F @ c_Nitpick_Opair__box_OPairBox ) ) ) @ ( C @ ( D @ ( E @ ( F @ c_Nitpick_Opair__box_Opair__box__rec ) ) ) ) )
= ( A @ ( B @ ( C @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pair__box_Orecs) ).
thf(1148,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( E @ ( F @ c_Nitpick_Opair__box_OPairBox ) ) ) @ ( C @ ( D @ ( E @ ( F @ c_Nitpick_Opair__box_Opair__box__rec ) ) ) ) )
= ( A @ ( B @ ( C @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(80,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I5_J) ).
thf(603,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(8,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__eq__less) ).
thf(315,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( C @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( A @ ( D @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) ) )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(222,axiom,
! [A: $i,B: $i] :
( ( B @ class_Enum_Oenum )
=> ( ! [C: $i] : ( C @ ( A @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ c_Enum_Oenum__class_Oenum__all @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_all__code) ).
thf(1280,plain,
! [A: $i,B: $i] :
( ( B @ class_Enum_Oenum )
=> ( ( ( A @ ( B @ c_Enum_Oenum__class_Oenum__all @ hAPP ) @ hBOOL )
=> ! [C: $i] : ( C @ ( A @ hAPP ) @ hBOOL ) )
& ( ! [C: $i] : ( C @ ( A @ hAPP ) @ hBOOL )
=> ( A @ ( B @ c_Enum_Oenum__class_Oenum__all @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(151,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( c_fequal @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__mem) ).
thf(950,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B = A )
=> ( A @ ( c_fequal @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( c_fequal @ hAPP ) @ ( B @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(181,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( E @ c_Set_Ovimage ) ) @ hAPP ) @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( D @ ( B @ hAPP ) @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimage__eq) ).
thf(1097,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( A @ ( D @ ( B @ hAPP ) @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ ( E @ c_Set_Ovimage ) ) @ hAPP ) @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ ( E @ c_Set_Ovimage ) ) @ hAPP ) @ ( D @ ( E @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( D @ ( B @ hAPP ) @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
<=> ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__is__0) ).
thf(326,plain,
! [A: $i,B: $i] :
( ( ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
=> ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) )
& ( ( ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) )
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
=> ( ( A
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) )
& ( B
= ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(125,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_Com_Ocom_OSemi ) @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ! [F: $i] :
( ( F @ ( B @ ( C @ ( E @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( A @ ( B @ ( F @ ( D @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evaln__elim__cases_I4_J) ).
thf(807,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_Com_Ocom_OSemi ) @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ! [F: $i] :
( ( F @ ( B @ ( C @ ( E @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( A @ ( B @ ( F @ ( D @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(199,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( E @ hAPP ) @ hBOOL )
=> ( ( B @ ( D @ ( C @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( D @ ( A @ ( C @ ( E @ c_Com_Ocom_OCond ) ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evalc_OIfTrue) ).
thf(1172,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( E @ hAPP ) @ hBOOL )
=> ( ( B @ ( D @ ( C @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( D @ ( A @ ( C @ ( E @ c_Com_Ocom_OCond ) ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(97,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ hAPP ) @ hBOOL )
=> ( C @ ( B @ hAPP ) @ ( D @ ( B @ ( tc_Nat_Onat @ ( A @ c_Hilbert__Choice_OLeastM ) ) ) @ ( B @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_LeastM__nat__le) ).
thf(664,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ hAPP ) @ hBOOL )
=> ( C @ ( B @ hAPP ) @ ( D @ ( B @ ( tc_Nat_Onat @ ( A @ c_Hilbert__Choice_OLeastM ) ) ) @ ( B @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(207,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Predicate_OPowp ) @ hAPP ) @ hBOOL )
<=> ! [D: $i] :
( ( A @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( B @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Powp__def) ).
thf(1197,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( A @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( B @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( C @ c_Predicate_OPowp ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ c_Predicate_OPowp ) @ hAPP ) @ hBOOL )
=> ! [D: $i] :
( ( A @ ( D @ ( C @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( D @ ( B @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(111,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( E @ ( F @ c_Com_Ocom_OCond ) ) )
= ( A @ ( B @ ( C @ c_Com_Ocom_OCond ) ) ) )
<=> ( ( D = A )
& ( E = B )
& ( F = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I4_J) ).
thf(720,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ( D = A )
& ( E = B )
& ( F = C ) )
=> ( ( D @ ( E @ ( F @ c_Com_Ocom_OCond ) ) )
= ( A @ ( B @ ( C @ c_Com_Ocom_OCond ) ) ) ) )
& ( ( ( D @ ( E @ ( F @ c_Com_Ocom_OCond ) ) )
= ( A @ ( B @ ( C @ c_Com_Ocom_OCond ) ) ) )
=> ( ( D = A )
& ( E = B )
& ( F = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(145,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_Com_Ocom_OWhile ) @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( A = C )
=> ( C @ ( E @ hAPP ) @ hBOOL ) )
=> ~ ( ( C @ ( E @ hAPP ) @ hBOOL )
=> ! [F: $i] :
( ( F @ ( B @ ( C @ ( D @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( A @ ( B @ ( F @ ( D @ ( E @ c_Com_Ocom_OWhile ) @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evaln__WHILE__case) ).
thf(918,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_Com_Ocom_OWhile ) @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( A = C )
=> ( C @ ( E @ hAPP ) @ hBOOL ) )
=> ~ ( ( C @ ( E @ hAPP ) @ hBOOL )
=> ! [F: $i] :
( ( F @ ( B @ ( C @ ( D @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( A @ ( B @ ( F @ ( D @ ( E @ c_Com_Ocom_OWhile ) @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(123,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__absorb2) ).
thf(801,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(90,axiom,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastAtMost ) ) )
= ( A @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatMost @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeast0AtMost) ).
thf(635,plain,
! [A: $i] :
( ( A @ ( tc_Nat_Onat @ c_Groups_Ozero__class_Ozero @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatLeastAtMost ) ) )
= ( A @ ( tc_Nat_Onat @ c_SetInterval_Oord__class_OatMost @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(261,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Equiv__Relations_Oequivp ) )
=> ( A @ ( A @ ( B @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equivp__reflp) ).
thf(1473,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Equiv__Relations_Oequivp ) )
=> ( A @ ( A @ ( B @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(216,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ~ ( D @ ( E @ hAPP ) @ hBOOL )
=> ( ( B @ ( D @ ( C @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( D @ ( C @ ( A @ ( E @ c_Com_Ocom_OCond ) ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evalc_OIfFalse) ).
thf(1261,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ~ ( D @ ( E @ hAPP ) @ hBOOL )
=> ( ( B @ ( D @ ( C @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
=> ( B @ ( D @ ( C @ ( A @ ( E @ c_Com_Ocom_OCond ) ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(275,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_accp__downward) ).
thf(1532,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Wellfounded_Oaccp ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(268,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_Divides_Odivmod__nat__rel ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ c_Divides_Odivmod__nat__rel ) @ hAPP ) @ hBOOL )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__nat__rel__unique) ).
thf(1500,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_Divides_Odivmod__nat__rel ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ c_Divides_Odivmod__nat__rel ) @ hAPP ) @ hBOOL )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(247,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Com_Ocom_OWhile ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( ( ? [E: $i] :
( ( A @ ( E @ ( C @ ( D @ c_Com_Ocom_OWhile ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
& ( E @ ( B @ ( C @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( B @ ( D @ hAPP ) @ hBOOL ) )
| ( ~ ( B @ ( D @ hAPP ) @ hBOOL )
& ( A = B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evalc_Oequations_I8_J) ).
thf(1399,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( ? [E: $i] :
( ( A @ ( E @ ( C @ ( D @ c_Com_Ocom_OWhile ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
& ( E @ ( B @ ( C @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( B @ ( D @ hAPP ) @ hBOOL ) )
| ( ~ ( B @ ( D @ hAPP ) @ hBOOL )
& ( A = B ) ) )
=> ( A @ ( B @ ( C @ ( D @ c_Com_Ocom_OWhile ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ ( D @ c_Com_Ocom_OWhile ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ? [E: $i] :
( ( A @ ( E @ ( C @ ( D @ c_Com_Ocom_OWhile ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
& ( E @ ( B @ ( C @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( B @ ( D @ hAPP ) @ hBOOL ) )
| ( ~ ( B @ ( D @ hAPP ) @ hBOOL )
& ( A = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(59,axiom,
! [A: $i,B: $i] : ( B @ ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__less__eq__dividend) ).
thf(501,plain,
! [A: $i,B: $i] : ( B @ ( A @ ( B @ ( tc_Nat_Onat @ c_Divides_Odiv__class_Omod ) ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(142,axiom,
! [A: $i,B: $i,C: $i] :
( c_Com_Ocom_OSKIP
!= ( A @ ( B @ ( C @ c_Com_Ocom_OCond ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I14_J) ).
thf(908,plain,
! [A: $i,B: $i,C: $i] :
( c_Com_Ocom_OSKIP
!= ( A @ ( B @ ( C @ c_Com_Ocom_OCond ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(160,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( C @ ( D @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) )
<=> ( ( C = A )
& ( D = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pair__eq) ).
thf(992,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ( C = A )
& ( D = B ) )
=> ( ( C @ ( D @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) ) )
& ( ( ( C @ ( D @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) )
=> ( ( C = A )
& ( D = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(232,axiom,
~ ( c_fFalse @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fFalse__1) ).
thf(1331,plain,
~ ( c_fFalse @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(241,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_Set_Ovimage ) ) @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( C @ hAPP ) @ ( B @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimage__code) ).
thf(1367,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( A @ ( C @ hAPP ) @ ( B @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ ( D @ ( E @ c_Set_Ovimage ) ) @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ ( D @ ( E @ c_Set_Ovimage ) ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ hAPP ) @ ( B @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(163,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ~ ( A @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( B @ ( C @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__ident) ).
thf(1009,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( B @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ~ ( A @ ( C @ ( D @ c_member @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( ( B = A )
=> ( ( B @ ( C @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) ) )
& ( ( ( B @ ( C @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Set_Oinsert @ hAPP ) @ hAPP ) ) )
=> ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(169,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Owellorder )
=> ( ( A @ ( C @ c_Orderings_Oord__class_OLeast ) @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( B @ ( A @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less__Least) ).
thf(1037,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ class_Orderings_Owellorder )
=> ( ( A @ ( C @ c_Orderings_Oord__class_OLeast ) @ ( B @ ( C @ c_Orderings_Oord__class_Oless @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ( B @ ( A @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(249,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( C @ ( D @ ( E @ ( F @ ( G @ c_Big__Operators_Ocomm__monoid__big ) ) ) ) )
=> ( ~ ( B @ ( F @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ hAPP ) @ hAPP ) )
= D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__monoid__big_Oinfinite) ).
thf(1416,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( C @ ( D @ ( E @ ( F @ ( G @ c_Big__Operators_Ocomm__monoid__big ) ) ) ) )
=> ( ~ ( B @ ( F @ c_Finite__Set_Ofinite @ hAPP ) @ hBOOL )
=> ( ( B @ ( A @ ( C @ hAPP ) @ hAPP ) )
= D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(179,axiom,
! [A: $i,B: $i] :
( ( A @ ( c_fequal @ hAPP ) @ ( B @ c_Hilbert__Choice_OEps ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_some__sym__eq__trivial) ).
thf(1088,plain,
! [A: $i,B: $i] :
( ( A @ ( c_fequal @ hAPP ) @ ( B @ c_Hilbert__Choice_OEps ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(259,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evaln__evalc) ).
thf(1468,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ ( c_Natural_Oevaln @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( D @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(21,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__mono1) ).
thf(364,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( A @ ( C @ ( tc_Nat_Onat @ c_Groups_Oplus__class_Oplus @ hAPP ) @ hAPP ) @ ( tc_Nat_Onat @ c_Orderings_Oord__class_Oless__eq @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(1754,plain,
$false,
inference(e,[status(thm)],[892,629,1024,1559,347,1315,962,941,555,666,1295,1005,1522,1205,1269,597,878,655,384,797,340,1354,1507,670,417,436,1518,389,344,1313,542,1577,1455,357,1191,902,638,421,1479,969,1347,448,1494,789,1373,1109,376,623,834,574,966,1183,492,1465,1302,756,1151,937,866,396,660,849,1564,1447,293,1072,453,307,1074,292,1306,1470,366,512,439,1274,1091,1042,302,407,815,1570,1174,467,847,830,1195,1128,456,1573,852,1555,1159,461,519,1534,615,1227,1540,1138,1118,1397,1375,1121,403,1498,1567,1361,1292,1461,476,489,1214,1016,1039,547,706,1263,985,515,738,1131,1002,1246,503,605,1333,633,508,657,1054,558,674,530,1185,1103,1483,1273,1548,904,1389,843,772,958,1124,545,413,826,711,1428,572,1271,713,804,1356,672,391,1503,1058,1107,979,1524,362,1144,318,1439,649,434,811,494,631,758,1557,964,626,1344,1022,668,1177,399,695,394,1113,299,653,1562,912,685,1066,1445,1413,1034,1304,1208,944,795,1420,1509,617,342,1018,355,458,1551,1134,487,939,1340,776,580,1070,971,1225,707,1432,791,717,840,338,359,1579,1358,336,1257,600,386,497,1221,1284,465,450,539,1553,1321,1575,368,1476,896,304,1481,786,588,699,568,510,929,1193,478,1045,1161,914,378,1116,620,752,432,410,1395,405,1148,603,315,1280,950,1097,326,807,1172,664,1197,720,918,801,635,1473,1261,1532,1500,1399,501,908,992,1331,1367,1009,1037,1416,1088,1468,364]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW350+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.09 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.14/5.43 % Computer : n020.cluster.edu
% 0.14/5.43 % Model : x86_64 x86_64
% 0.14/5.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/5.43 % Memory : 8046.5625MB
% 0.14/5.43 % OS : Linux 6.8.0-71-generic
% 0.14/5.43 % CPULimit : 300
% 0.14/5.43 % WCLimit : 300
% 0.14/5.43 % DateTime : Sat Sep 26 15:44:09 UTC 2026
% 0.14/5.44 % CPUTime :
% 0.14/5.44 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.20/6.01 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 4.38/7.07 % [INFO] Parsing done (1059ms).
% 4.38/7.09 % [INFO] Running in sequential loop mode.
% 5.18/7.48 % [INFO] eprover registered as external prover.
% 5.18/7.48 % [INFO] Scanning for conjecture ...
% 8.93/8.43 % [INFO] Found a conjecture (or negated_conjecture) and 5228 axioms. Running axiom selection ...
% 11.48/9.57 % [INFO] Axiom selection finished. Selected 289 axioms (removed 4939 axioms).
% 12.21/9.88 % [INFO] Problem is first-order (TPTP FOF).
% 12.55/9.91 % [INFO] Type checking passed.
% 12.55/9.91 % [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 ...
% 25.96/13.23 % External prover 'e' found a proof!
% 25.96/13.23 % [INFO] Killing All external provers ...
% 25.96/13.23 % Time passed: 7651ms (effective reasoning time: 6131ms)
% 25.96/13.23 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 25.96/13.23 % Axioms used in derivation (289): fact_Nat_Oadd__0__right, fact_divmod__nat__zero, fact_divmod__nat__rel__divmod__nat, fact_insertCI, fact_evalc_Oequations_I8_J, fact_com__det, fact_com_Osimps_I8_J, fact_divmod__nat__base, fact_evalc__evaln, fact_accp_Oequations, fact_finite__greaterThanAtMost, fact_nat__add__left__commute, fact_insert__iff, fact_image__insert, fact_evalc_OIfFalse, fact_le__eq__less__or__eq, fact_termination__basic__simps_I5_J, fact_trans__less__add1, fact_com_Osimps_I17_J, fact_evaln__elim__cases_I5_J, fact_nat__less__cases, fact_less__imp__le__nat, fact_sum__case__weak__cong, fact_add__leD1, fact_divmod__nat__eq, fact_prod_Orecs, fact_mod__eq, fact_less__nat__zero__code, fact_equivp__transp, fact_add__less__mono, fact_pair__box_Oinject, fact_evalc__elim__cases_I1_J, fact_insertI1, fact_LeastM__nat__le, fact_comm__monoid__big_Oinfinite, fact_folding__image__simple_Oeq__fold__g, fact_com_Osimps_I24_J, fact_com_Osimps_I46_J, fact_evalc__elim__cases_I4_J, fact_evalc_Oequations_I1_J, fact_nat__add__right__cancel, fact_div__le__dividend, help_c__fconj__3, fact_evaln_OAssign, fact_mod__less, help_c__fequal__2, fact_le__neq__implies__less, fact_divmod__nat__rel__unique, fact_com_Osimps_I27_J, fact_triple__valid__def2, fact_nat__add__left__cancel__less, help_c__fFalse__1, fact_peek__and__def, fact_type__definition_OAbs__inject, fact_split__paired__All, fact_evalc__elim__cases_I2_J, fact_finite__atLeastLessThan, fact_folding__one__idem_Oin__idem, fact_triple_Oinject, fact_vname_Orecs_I1_J, fact_finite__nat__set__iff__bounded__le, fact_fold__graph__imp__finite, fact_gr0I, fact_le__iff__add, fact_less__add__eq__less, fact_com_Osimps_I14_J, fact_less__eq__nat_Osimps_I1_J, fact_someI__ex, fact_com_Osimps_I53_J, fact_termination__basic__simps_I4_J, fact_add__lessD1, fact_add__le__mono1, fact_vname_Osimps_I5_J, fact_com_Osimps_I5_J, fact_folding__one_Oeq__fold, fact_ord_OatMost__iff, fact_folding__one__idem_Oeq__fold__idem_H, fact_not__add__less2, fact_less__or__eq__imp__le, fact_com_Osimps_I3_J, fact_rev__image__eqI, fact_vimage__eq, fact_Rep__Integ__inject, fact_ord_OgreaterThan__iff, fact_com_Osimps_I13_J, fact_evaln_Oequations_I2_J, fact_evalc_OIfTrue, help_c__fconj__2, fact_reflpE, fact_le__add2, fact_less__irrefl__nat, fact_Powp__def, fact_LeastI__ex, fact_not__less0, fact_trans__less__add2, fact_mod__less__divisor, fact_insert__code, help_c__fNot__1, fact_add__leD2, fact_evalc_Oequations_I4_J, fact_vname_Osimps_I1_J, fact_evaln_OWhileFalse, fact_nat__neq__iff, fact_evaln_Oequations_I7_J, fact_type__definition_ORep, fact_less__zeroE, fact_termination__basic__simps_I2_J, fact_com_Osimps_I47_J, fact_insert__image, fact_less__not__refl3, fact_evaln_OSkip, fact_evaln__nonstrict, fact_LeastM__nat__lemma, conj_2, fact_evaln_OSemi, fact_nat__add__left__cancel__le, fact_vimageI2, fact_eq__mem, fact_evaln_OIfTrue, fact_some__eq__ex, fact_finite__insert, fact_equivp__symp, fact_com_Osimps_I12_J, arity_Nat__Onat__Orderings_Owellorder, fact_evalc_OSemi, fact_insertI2, fact_evalc_OSkip, fact_folding__one__idem_Oidem, fact_insert__absorb, fact_div__less, fact_insert__absorb2, fact_eqset__imp__iff, fact_vimageI, fact_com_Osimps_I45_J, fact_com_Osimps_I28_J, fact_wfP__accp__iff, help_c__fdisj__1, help_c__fimplies__1, fact_finite__nat__set__iff__bounded, fact_mod__le__divisor, fact_Least__le, fact_folding__image__simple_Oinsert, help_c__fequal__1, fact_finite__imageI, fact_vimage__code, fact_evalc__WHILE__case, fact_accp__wfPD, fact_div__le__mono2, fact_rp__inv__image__rp, fact_insert__commute, fact_pair__box_Orecs, fact_pred__comp_Ointros, fact_equivp__def, fact_DomainP_Ointros, fact_linorder__neqE__nat, fact_accp__downward, fact_ex__nat__less, help_c__fdisj__2, fact_divmod__nat__div__mod, help_c__fconj__1, fact_ord_OlessThan__iff, fact_com_Osimps_I26_J, fact_Pair__inject, fact_fold__graph_OinsertI, fact_not__add__less1, fact_div__add1__eq, fact_evaln_OIfFalse, fact_ext, help_c__fNot__2, fact_enum__all, fact_semilattice__big_OF__eq, fact_RangeP_Ointros, fact_finite__atLeastAtMost, fact_add__eq__self__zero, fact_evaln__WHILE__case, fact_nat__add__left__cancel, fact_equivp__reflp, fact_someI, fact_nat__le__linear, fact_finite__atMost, fact_evaln_Oequations_I5_J, fact_all__nat__less, fact_evalc_OWhileFalse, fact_add__gr__0, fact_evaln_Oequations_I6_J, fact_insert__ident, fact_div__eq, fact_com_Osimps_I16_J, fact_ex__nat__less__eq, fact_ord_OgreaterThanLessThan__iff, fact_eq__mem__trans, fact_ord_OatLeastLessThan__iff, fact_evaln__elim__cases_I2_J, help_c__fimplies__2, fact_evalc_OWhileTrue, fact_RangeP_Oequations, fact_LeastI, fact_divmod__nat__rel__add1__eq, fact_less__not__refl2, fact_le__add1, fact_evaln__elim__cases_I4_J, fact_trans__le__add2, fact_accp_Osimps, fact_atLeast0LessThan, fact_le__refl, fact_nat__add__assoc, conj_1, fact_com_Osimps_I9_J, fact_pred__comp_Oequations, fact_comm__monoid__big_OF__eq, fact_all__nat__less__eq, fact_tfl__some, fact_add__is__0, fact_termination__basic__simps_I3_J, fact_com_Osimps_I44_J, fact_enum__ex, fact_mod__less__eq__dividend, fact_evaln_OWhileTrue, fact_Pair__eq, fact_evalc_Oequations_I5_J, fact_com_Osimps_I25_J, fact_com_Osimps_I29_J, fact_image__iff, fact_less__not__refl, fact_evalc__elim__cases_I5_J, fact_ord_OgreaterThanAtMost__iff, fact_le0, fact_finite__lessThan, fact_le__trans, fact_all__code, fact_equalityCE, fact_com_Osimps_I1_J, fact_sum__case__inject, fact_gr__implies__not0, fact_finite_OinsertI, fact_LeastM__natI, fact_nat__add__commute, fact_add__leE, help_c__fimplies__3, fact_type__definition_OAbs__inverse, fact_image__eqI, fact_evaln_Oequations_I4_J, fact_eq__imp__le, help_c__fTrue__1, fact_exists__code, fact_plus__nat_Oadd__0, fact_insertE, fact_divmod__nat__rel, fact_finite__greaterThanLessThan, fact_some__sym__eq__trivial, fact_type__definition_ORep__inject, fact_exE__some, fact_div__le__mono, fact_neq0__conv, fact_pos__not__random__dseq__def, fact_le__antisym, fact_eqelem__imp__iff, fact_com_Osimps_I52_J, fact_evalc_Oequations_I2_J, fact_trans__le__add1, fact_DomainP_Oequations, fact_ord_OatLeastAtMost__iff, fact_pair__box_Osimps_I2_J, fact_le__0__eq, fact_termination__basic__simps_I1_J, fact_com_Osimps_I15_J, fact_evaln__max2, fact_evalc_Oequations_I6_J, fact_triple_Orecs, fact_add__le__mono, fact_evaln_Oequations_I8_J, fact_mem__def, fact_vimageD, fact_type__definition_ORep__inverse, fact_add__less__mono1, fact_identity__equivp, fact_evalc_OAssign, fact_com_Osimps_I4_J, fact_nat__less__le, fact_evalc_Oequations_I7_J, fact_atLeast0AtMost, fact_not__less__Least, fact_evaln__elim__cases_I1_J, fact_eval__eq, help_c__fdisj__3, fact_evaln_Oequations_I1_J, fact_evaln__evalc, fact_ord_OatLeast__iff, fact_imageI
% 25.96/13.23 % No. of inferences in proof: 582
% 25.96/13.23 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 7651 ms resp. 6131 ms w/o parsing
% 27.07/13.57 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 27.07/13.57 % [INFO] Killing All external provers ...
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