TSTP Solution File: SWW350+1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SWW350+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n017.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 12:23:36 EDT 2023
% Result : Theorem 16.27s 4.93s
% Output : Refutation 17.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 382
% Syntax : Number of formulae : 674 ( 158 unt; 92 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 : 208 ( 208 >; 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_type,type,
hBOOL: $i > $o ).
thf(hAPP_type,type,
hAPP: $i > $i > $i ).
thf(c_Natural_Oevalc_type,type,
c_Natural_Oevalc: $i > $i ).
thf(v_c_type,type,
v_c: $i ).
thf(v_Z_type,type,
v_Z: $i ).
thf(v_s_H_type,type,
v_s_H: $i ).
thf(c_Orderings_Oord__class_Oless_type,type,
c_Orderings_Oord__class_Oless: $i > $i ).
thf(tc_Nat_Onat_type,type,
tc_Nat_Onat: $i ).
thf(c_Groups_Oplus__class_Oplus_type,type,
c_Groups_Oplus__class_Oplus: $i > $i ).
thf(c_Orderings_Oord__class_Oless__eq_type,type,
c_Orderings_Oord__class_Oless__eq: $i > $i ).
thf(c_Groups_Ozero__class_Ozero_type,type,
c_Groups_Ozero__class_Ozero: $i > $i ).
thf(c_Divides_Odiv__class_Odiv_type,type,
c_Divides_Odiv__class_Odiv: $i > $i > $i ).
thf(c_Divides_Odiv__class_Omod_type,type,
c_Divides_Odiv__class_Omod: $i > $i > $i > $i ).
thf(c_member_type,type,
c_member: $i > $i ).
thf(c_Set_Oimage_type,type,
c_Set_Oimage: $i > $i > $i > $i ).
thf(c_Finite__Set_Ofinite_type,type,
c_Finite__Set_Ofinite: $i > $i ).
thf(c_SetInterval_Oord__class_OatLeastLessThan_type,type,
c_SetInterval_Oord__class_OatLeastLessThan: $i > $i > $i ).
thf(c_Divides_Odivmod__nat__rel_type,type,
c_Divides_Odivmod__nat__rel: $i > $i > $i ).
thf(c_Product__Type_OPair_type,type,
c_Product__Type_OPair: $i > $i > $i ).
thf(c_SetInterval_Oord__class_OatLeastAtMost_type,type,
c_SetInterval_Oord__class_OatLeastAtMost: $i > $i > $i > $i ).
thf(c_Finite__Set_Ofolding__image__simple_type,type,
c_Finite__Set_Ofolding__image__simple: $i > $i > $i > $i > $i > $i > $o ).
thf(c_Finite__Set_Ofold__image_type,type,
c_Finite__Set_Ofold__image: $i > $i > $i > $i ).
thf(c_Finite__Set_Ofold__graph_type,type,
c_Finite__Set_Ofold__graph: $i > $i > $i > $i > $i > $i ).
thf(c_SetInterval_Oord__class_OlessThan_type,type,
c_SetInterval_Oord__class_OlessThan: $i > $i ).
thf(c_Divides_Odivmod__nat_type,type,
c_Divides_Odivmod__nat: $i > $i > $i ).
thf(c_Set_Oinsert_type,type,
c_Set_Oinsert: $i > $i ).
thf(c_SetInterval_Oord__class_OatMost_type,type,
c_SetInterval_Oord__class_OatMost: $i > $i ).
thf(c_Sum__Type_Osum_Osum__case_type,type,
c_Sum__Type_Osum_Osum__case: $i > $i > $i > $i > $i > $i ).
thf(c_Com_Ocom_OWhile_type,type,
c_Com_Ocom_OWhile: $i > $i > $i ).
thf(c_Com_Ocom_OSemi_type,type,
c_Com_Ocom_OSemi: $i > $i > $i ).
thf(c_Natural_Oevaln_type,type,
c_Natural_Oevaln: $i ).
thf(c_Com_Ocom_OCond_type,type,
c_Com_Ocom_OCond: $i > $i > $i > $i ).
thf(c_Hilbert__Choice_OLeastM_type,type,
c_Hilbert__Choice_OLeastM: $i > $i > $i > $i > $i ).
thf(c_Set_Ovimage_type,type,
c_Set_Ovimage: $i > $i > $i > $i ).
thf(c_Com_Ocom_OAss_type,type,
c_Com_Ocom_OAss: $i > $i > $i ).
thf(c_Natural_Oupdate_type,type,
c_Natural_Oupdate: $i ).
thf(c_Hoare__Mirabelle_Otriple__valid_type,type,
c_Hoare__Mirabelle_Otriple__valid: $i > $i > $i > $o ).
thf(c_Hoare__Mirabelle_Otriple_Otriple_type,type,
c_Hoare__Mirabelle_Otriple_Otriple: $i > $i ).
thf(class_Orderings_Owellorder_type,type,
class_Orderings_Owellorder: $i > $o ).
thf(c_Com_Ocom_OSKIP_type,type,
c_Com_Ocom_OSKIP: $i ).
thf(c_Typedef_Otype__definition_type,type,
c_Typedef_Otype__definition: $i > $i > $i > $i > $i > $o ).
thf(c_Wellfounded_OwfP_type,type,
c_Wellfounded_OwfP: $i > $i > $o ).
thf(c_Wellfounded_Oaccp_type,type,
c_Wellfounded_Oaccp: $i > $i > $i ).
thf(c_Finite__Set_Ofolding__one__idem_type,type,
c_Finite__Set_Ofolding__one__idem: $i > $i > $i > $o ).
thf(c_Finite__Set_Ofold_type,type,
c_Finite__Set_Ofold: $i > $i > $i > $i ).
thf(c_SetInterval_Oord__class_OgreaterThanAtMost_type,type,
c_SetInterval_Oord__class_OgreaterThanAtMost: $i > $i > $i > $i ).
thf(c_Nitpick_Opair__box_OPairBox_type,type,
c_Nitpick_Opair__box_OPairBox: $i > $i > $i > $i > $i ).
thf(c_Equiv__Relations_Oequivp_type,type,
c_Equiv__Relations_Oequivp: $i > $i > $o ).
thf(c_fequal_type,type,
c_fequal: $i ).
thf(c_Orderings_Oord__class_OLeast_type,type,
c_Orderings_Oord__class_OLeast: $i > $i > $i ).
thf(c_SetInterval_Oord__class_OgreaterThanLessThan_type,type,
c_SetInterval_Oord__class_OgreaterThanLessThan: $i > $i > $i > $i ).
thf(c_Com_Ovname_OGlb_type,type,
c_Com_Ovname_OGlb: $i > $i ).
thf(c_Finite__Set_Ofolding__one_type,type,
c_Finite__Set_Ofolding__one: $i > $i > $i > $o ).
thf(c_Finite__Set_Ofold1_type,type,
c_Finite__Set_Ofold1: $i > $i > $i ).
thf(c_Hilbert__Choice_OEps_type,type,
c_Hilbert__Choice_OEps: $i > $i > $i ).
thf(c_Big__Operators_Ocomm__monoid__big_type,type,
c_Big__Operators_Ocomm__monoid__big: $i > $i > $i > $i > $i > $o ).
thf(class_Enum_Oenum_type,type,
class_Enum_Oenum: $i > $o ).
thf(c_Enum_Oenum__class_Oenum__all_type,type,
c_Enum_Oenum__class_Oenum__all: $i > $i ).
thf(c_Enum_Oenum__class_Oenum__ex_type,type,
c_Enum_Oenum__class_Oenum__ex: $i > $i ).
thf(c_Nitpick_Opair__box_Opair__box__rec_type,type,
c_Nitpick_Opair__box_Opair__box__rec: $i > $i > $i > $i > $i > $i ).
thf(c_Hoare__Mirabelle_Otriple_Otriple__rec_type,type,
c_Hoare__Mirabelle_Otriple_Otriple__rec: $i > $i > $i > $i > $i ).
thf(c_SetInterval_Oord_OgreaterThan_type,type,
c_SetInterval_Oord_OgreaterThan: $i > $i > $i > $i ).
thf(c_fimplies_type,type,
c_fimplies: $i ).
thf(c_fNot_type,type,
c_fNot: $i ).
thf(c_FunDef_Oreduction__pair_type,type,
c_FunDef_Oreduction__pair: $i > $i > $o ).
thf(c_FunDef_Orp__inv__image_type,type,
c_FunDef_Orp__inv__image: $i > $i > $i ).
thf(c_Predicate_OPowp_type,type,
c_Predicate_OPowp: $i > $i > $i ).
thf(c_Big__Operators_Osemilattice__big_type,type,
c_Big__Operators_Osemilattice__big: $i > $i > $i > $o ).
thf(c_Predicate_Opred__comp_type,type,
c_Predicate_Opred__comp: $i > $i > $i > $i > $i > $i > $i > $o ).
thf(c_fdisj_type,type,
c_fdisj: $i ).
thf(c_Predicate_ORangeP_type,type,
c_Predicate_ORangeP: $i > $i > $i > $i ).
thf(c_fTrue_type,type,
c_fTrue: $i ).
thf(c_SetInterval_Oord_OatLeastLessThan_type,type,
c_SetInterval_Oord_OatLeastLessThan: $i > $i > $i > $i > $i > $i ).
thf(c_fconj_type,type,
c_fconj: $i ).
thf(c_Hoare__Mirabelle_Opeek__and_type,type,
c_Hoare__Mirabelle_Opeek__and: $i > $i > $i > $i ).
thf(c_SetInterval_Oord_OatLeast_type,type,
c_SetInterval_Oord_OatLeast: $i > $i > $i > $i ).
thf(c_fFalse_type,type,
c_fFalse: $i ).
thf(c_SetInterval_Oord_OgreaterThanLessThan_type,type,
c_SetInterval_Oord_OgreaterThanLessThan: $i > $i > $i > $i > $i ).
thf(c_SetInterval_Oord_OgreaterThanAtMost_type,type,
c_SetInterval_Oord_OgreaterThanAtMost: $i > $i > $i > $i > $i > $i ).
thf(c_SetInterval_Oord_OatMost_type,type,
c_SetInterval_Oord_OatMost: $i > $i > $i > $i ).
thf(c_SetInterval_Oord_OlessThan_type,type,
c_SetInterval_Oord_OlessThan: $i > $i > $i > $i ).
thf(c_New__Random__Sequence_Opos__not__random__dseq_type,type,
c_New__Random__Sequence_Opos__not__random__dseq: $i > $i > $i > $i > $i ).
thf(c_New__DSequence_Opos__not__seq_type,type,
c_New__DSequence_Opos__not__seq: $i > $i ).
thf(c_Nitpick_Opair__box_Opair__box__case_type,type,
c_Nitpick_Opair__box_Opair__box__case: $i > $i > $i > $i > $i > $i ).
thf(c_Com_Ovname_Ovname__rec_type,type,
c_Com_Ovname_Ovname__rec: $i > $i > $i > $i > $i ).
thf(c_Int_ORep__Integ_type,type,
c_Int_ORep__Integ: $i ).
thf(c_Predicate_ODomainP_type,type,
c_Predicate_ODomainP: $i > $i > $i > $i ).
thf(c_Com_Ovname_Ovname__case_type,type,
c_Com_Ovname_Ovname__case: $i > $i > $i > $i > $i ).
thf(v_Sledgehammer_058s__2_type,type,
v_Sledgehammer_058s__2: $i > $i > $i ).
thf(c_Predicate_Oreflp_type,type,
c_Predicate_Oreflp: $i > $i > $o ).
thf(c_Product__Type_Oprod_Oprod__rec_type,type,
c_Product__Type_Oprod_Oprod__rec: $i > $i > $i > $i > $i > $i ).
thf(c_SetInterval_Oord_OatLeastAtMost_type,type,
c_SetInterval_Oord_OatLeastAtMost: $i > $i > $i > $i > $i ).
thf(99,axiom,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insertI1) ).
thf(645,plain,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(134,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__commute) ).
thf(809,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(218,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ E @ D ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ B @ A @ E ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_RangeP_Ointros) ).
thf(1190,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ E @ D ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ B @ A @ E ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[218]) ).
thf(122,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( c_Finite__Set_Ofolding__image__simple @ H @ G @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ G ) @ B ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ A ) @ B ) )
=> ( ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ G ) @ A ) @ B ) )
= ( hAPP @ ( hAPP @ F @ ( hAPP @ D @ A ) ) @ ( hAPP @ C @ B ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__image__simple_Oinsert) ).
thf(760,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( c_Finite__Set_Ofolding__image__simple @ H @ G @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ G ) @ B ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ A ) @ B ) )
=> ( ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ G ) @ A ) @ B ) )
= ( hAPP @ ( hAPP @ F @ ( hAPP @ D @ A ) ) @ ( hAPP @ C @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(283,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Predicate_Oreflp @ C @ B )
=> ( hBOOL @ ( hAPP @ ( hAPP @ B @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_reflpE) ).
thf(1454,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Predicate_Oreflp @ C @ B )
=> ( hBOOL @ ( hAPP @ ( hAPP @ B @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[283]) ).
thf(153,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insertI2) ).
thf(909,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(150,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__insert) ).
thf(893,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(196,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( c_Typedef_Otype__definition @ G @ F @ E @ D @ C )
=> ( ( ( hAPP @ E @ B )
= ( hAPP @ E @ A ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_type__definition_ORep__inject) ).
thf(1083,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( c_Typedef_Otype__definition @ G @ F @ E @ D @ C )
=> ( ( ( ( hAPP @ E @ B )
= ( hAPP @ E @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( hAPP @ E @ B )
= ( hAPP @ E @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(215,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( G = F )
=> ( ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ E @ D @ C @ B @ A ) @ G )
= ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ E @ D @ C @ B @ A ) @ F ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sum__case__weak__cong) ).
thf(1179,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( G = F )
=> ( ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ E @ D @ C @ B @ A ) @ G )
= ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ E @ D @ C @ B @ A ) @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[215]) ).
thf(127,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ F @ E @ D ) ) @ C ) @ B ) @ A ) )
<=> ( ( ( hBOOL @ ( hAPP @ F @ C ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ E ) @ C ) @ B ) @ A ) ) )
| ( ~ ( hBOOL @ ( hAPP @ F @ C ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ D ) @ C ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evaln_Oequations_I6_J) ).
thf(777,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ F @ E @ D ) ) @ C ) @ B ) @ A ) )
=> ( ( ( hBOOL @ ( hAPP @ F @ C ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ E ) @ C ) @ B ) @ A ) ) )
| ( ~ ( hBOOL @ ( hAPP @ F @ C ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ D ) @ C ) @ B ) @ A ) ) ) ) )
& ( ( ( ( hBOOL @ ( hAPP @ F @ C ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ E ) @ C ) @ B ) @ A ) ) )
| ( ~ ( hBOOL @ ( hAPP @ F @ C ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ D ) @ C ) @ B ) @ A ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ F @ E @ D ) ) @ C ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(18,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add1) ).
thf(352,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(222,axiom,
! [A: $i,B: $i] :
( ( class_Enum_Oenum @ B )
=> ( ! [C: $i] : ( hBOOL @ ( hAPP @ A @ C ) )
<=> ( hBOOL @ ( hAPP @ ( c_Enum_Oenum__class_Oenum__all @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_all__code) ).
thf(1200,plain,
! [A: $i,B: $i] :
( ( class_Enum_Oenum @ B )
=> ( ( ! [C: $i] : ( hBOOL @ ( hAPP @ A @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Enum_Oenum__class_Oenum__all @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Enum_Oenum__class_Oenum__all @ B ) @ A ) )
=> ! [C: $i] : ( hBOOL @ ( hAPP @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[222]) ).
thf(169,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Owellorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ B ) @ ( c_Orderings_Oord__class_OLeast @ C @ A ) ) )
=> ~ ( hBOOL @ ( hAPP @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less__Least) ).
thf(977,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Owellorder @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ C ) @ B ) @ ( c_Orderings_Oord__class_OLeast @ C @ A ) ) )
=> ~ ( hBOOL @ ( hAPP @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(270,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ D @ C ) )
=> ( hBOOL @ ( hAPP @ D @ ( c_Hilbert__Choice_OLeastM @ B @ tc_Nat_Onat @ A @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_LeastM__natI) ).
thf(1406,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ D @ C ) )
=> ( hBOOL @ ( hAPP @ D @ ( c_Hilbert__Choice_OLeastM @ B @ tc_Nat_Onat @ A @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[270]) ).
thf(278,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Com_Ovname_Ovname__case @ D @ C @ B @ ( c_Com_Ovname_OGlb @ A ) )
= ( hAPP @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vname_Osimps_I5_J) ).
thf(1443,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Com_Ovname_Ovname__case @ D @ C @ B @ ( c_Com_Ovname_OGlb @ A ) )
= ( hAPP @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[278]) ).
thf(274,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ c_Int_ORep__Integ @ B )
= ( hAPP @ c_Int_ORep__Integ @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Rep__Integ__inject) ).
thf(1422,plain,
! [A: $i,B: $i] :
( ( ( ( hAPP @ c_Int_ORep__Integ @ B )
= ( hAPP @ c_Int_ORep__Integ @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( hAPP @ c_Int_ORep__Integ @ B )
= ( hAPP @ c_Int_ORep__Integ @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[274]) ).
thf(27,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ C ) @ A ) ) @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ B ) @ A ) ) ) @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ C @ A ) ) @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A ) ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__add1__eq) ).
thf(379,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ C ) @ A ) ) @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ B ) @ A ) ) ) @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ C @ A ) ) @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A ) ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(45,axiom,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__not__refl) ).
thf(440,plain,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(246,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ H @ G ) @ F ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ E @ F ) @ D ) )
=> ( c_Predicate_Opred__comp @ C @ B @ A @ H @ E @ G @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pred__comp_Ointros) ).
thf(1305,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ H @ G ) @ F ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ E @ F ) @ D ) )
=> ( c_Predicate_Opred__comp @ C @ B @ A @ H @ E @ G @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[246]) ).
thf(83,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ ( hAPP @ C @ B ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__insert) ).
thf(597,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ ( hAPP @ C @ B ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ D @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(29,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__leD2) ).
thf(384,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(70,axiom,
! [A: $i] :
( ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neq0__conv) ).
thf(533,plain,
! [A: $i] :
( ( ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) )
=> ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(63,axiom,
! [A: $i] :
( ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A )
= ( hAPP @ ( c_SetInterval_Oord__class_OlessThan @ tc_Nat_Onat ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeast0LessThan) ).
thf(500,plain,
! [A: $i] :
( ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A )
= ( hAPP @ ( c_SetInterval_Oord__class_OlessThan @ tc_Nat_Onat ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(250,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ C @ B ) @ A ) )
<=> ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ B @ D ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ C @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_accp_Osimps) ).
thf(1327,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ C @ B ) @ A ) )
=> ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ B @ D ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ C @ B ) @ D ) ) ) )
& ( ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ B @ D ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ C @ B ) @ D ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ C @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[250]) ).
thf(236,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ ( c_SetInterval_Oord_OgreaterThanAtMost @ F @ D @ C @ B @ A ) ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ E ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ D @ E ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord_OgreaterThanAtMost__iff) ).
thf(1260,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ ( c_SetInterval_Oord_OgreaterThanAtMost @ F @ D @ C @ B @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ E ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ D @ E ) @ A ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ E ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ D @ E ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ ( c_SetInterval_Oord_OgreaterThanAtMost @ F @ D @ C @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[236]) ).
thf(155,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ A ) ) )
=> ( ( C != B )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insertE) ).
thf(913,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ A ) ) )
=> ( ( C != B )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(161,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ ( hAPP @ A @ D ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ B @ A ) @ C ) )
= ( hAPP @ ( c_Set_Oimage @ E @ B @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__image) ).
thf(945,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ C ) )
=> ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ B ) @ ( hAPP @ A @ D ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ B @ A ) @ C ) )
= ( hAPP @ ( c_Set_Oimage @ E @ B @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(159,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ E @ D ) ) @ C ) @ B ) @ A ) )
<=> ? [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ E ) @ C ) @ B ) @ F ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ D ) @ F ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evaln_Oequations_I4_J) ).
thf(930,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ E @ D ) ) @ C ) @ B ) @ A ) )
=> ? [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ E ) @ C ) @ B ) @ F ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ D ) @ F ) @ B ) @ A ) ) ) )
& ( ? [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ E ) @ C ) @ B ) @ F ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ D ) @ F ) @ B ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ E @ D ) ) @ C ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(104,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Com_Ocom_OWhile @ E @ D )
!= ( c_Com_Ocom_OCond @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I53_J) ).
thf(670,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Com_Ocom_OWhile @ E @ D )
!= ( c_Com_Ocom_OCond @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(190,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fequal @ B ) @ A ) )
| ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fequal__1) ).
thf(1063,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fequal @ B ) @ A ) )
| ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(15,axiom,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Nat_Oadd__0__right) ).
thf(340,plain,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(151,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ c_fequal @ A ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__mem) ).
thf(898,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ c_fequal @ A ) ) )
=> ( B = A ) )
& ( ( B = A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ ( hAPP @ c_fequal @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I4_J) ).
thf(301,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(102,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ F @ E @ D ) ) @ C ) @ B ) @ A ) )
<=> ( ( ( hBOOL @ ( hAPP @ F @ C ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ E ) @ C ) @ B ) @ A ) ) )
| ( ~ ( hBOOL @ ( hAPP @ F @ C ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ D ) @ C ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evaln_Oequations_I5_J) ).
thf(651,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ F @ E @ D ) ) @ C ) @ B ) @ A ) )
=> ( ( ( hBOOL @ ( hAPP @ F @ C ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ E ) @ C ) @ B ) @ A ) ) )
| ( ~ ( hBOOL @ ( hAPP @ F @ C ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ D ) @ C ) @ B ) @ A ) ) ) ) )
& ( ( ( ( hBOOL @ ( hAPP @ F @ C ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ E ) @ C ) @ B ) @ A ) ) )
| ( ~ ( hBOOL @ ( hAPP @ F @ C ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ D ) @ C ) @ B ) @ A ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ F @ E @ D ) ) @ C ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(31,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__commute) ).
thf(389,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(77,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( hAPP @ ( c_Set_Oimage @ C @ E @ B ) @ A ) ) )
<=> ? [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ F ) @ A ) )
& ( D
= ( hAPP @ B @ F ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__iff) ).
thf(570,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( hAPP @ ( c_Set_Oimage @ C @ E @ B ) @ A ) ) )
=> ? [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ F ) @ A ) )
& ( D
= ( hAPP @ B @ F ) ) ) )
& ( ? [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ F ) @ A ) )
& ( D
= ( hAPP @ B @ F ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( hAPP @ ( c_Set_Oimage @ C @ E @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(244,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_SetInterval_Oord_OlessThan @ D @ B @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ B @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord_OlessThan__iff) ).
thf(1298,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_SetInterval_Oord_OlessThan @ D @ B @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ B @ C ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ B @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_SetInterval_Oord_OlessThan @ D @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[244]) ).
thf(113,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hAPP @ F @ E )
= D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ A ) @ E ) @ ( hAPP @ ( c_Set_Ovimage @ A @ C @ F ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimageI) ).
thf(719,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hAPP @ F @ E )
= D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ A ) @ E ) @ ( hAPP @ ( c_Set_Ovimage @ A @ C @ F ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(25,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__cancel__le) ).
thf(372,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(249,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( c_Big__Operators_Ocomm__monoid__big @ G @ F @ E @ D @ C )
=> ( ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ B ) )
=> ( ( hAPP @ ( hAPP @ C @ A ) @ B )
= D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__monoid__big_Oinfinite) ).
thf(1323,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( c_Big__Operators_Ocomm__monoid__big @ G @ F @ E @ D @ C )
=> ( ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ B ) )
=> ( ( hAPP @ ( hAPP @ C @ A ) @ B )
= D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[249]) ).
thf(20,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__mono) ).
thf(357,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(286,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( hAPP @ B @ C )
= ( hAPP @ A @ C ) )
=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ext) ).
thf(1462,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( hAPP @ B @ C )
= ( hAPP @ A @ C ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[286]) ).
thf(189,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Finite__Set_Ofolding__one__idem @ D @ C @ B )
=> ( ( hAPP @ ( hAPP @ C @ A ) @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__one__idem_Oidem) ).
thf(1059,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Finite__Set_Ofolding__one__idem @ D @ C @ B )
=> ( ( hAPP @ ( hAPP @ C @ A ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(208,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Big__Operators_Osemilattice__big @ D @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ A ) )
=> ( ( hAPP @ B @ A )
= ( hAPP @ ( c_Finite__Set_Ofold1 @ D @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_semilattice__big_OF__eq) ).
thf(1132,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Big__Operators_Osemilattice__big @ D @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ A ) )
=> ( ( hAPP @ B @ A )
= ( hAPP @ ( c_Finite__Set_Ofold1 @ D @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(140,axiom,
! [A: $i] : ( c_Equiv__Relations_Oequivp @ A @ c_fequal ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_identity__equivp) ).
thf(853,plain,
! [A: $i] : ( c_Equiv__Relations_Oequivp @ A @ c_fequal ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(233,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( c_SetInterval_Oord_OgreaterThanLessThan @ E @ C @ B @ A ) ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ D ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ C @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord_OgreaterThanLessThan__iff) ).
thf(1247,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( c_SetInterval_Oord_OgreaterThanLessThan @ E @ C @ B @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ D ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ C @ D ) @ A ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ D ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ C @ D ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( c_SetInterval_Oord_OgreaterThanLessThan @ E @ C @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[233]) ).
thf(86,axiom,
! [A: $i,B: $i] :
( ( c_Divides_Odivmod__nat @ B @ A )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ B ) @ A ) ) @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__nat__div__mod) ).
thf(606,plain,
! [A: $i,B: $i] :
( ( c_Divides_Odivmod__nat @ B @ A )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ B ) @ A ) ) @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(125,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ E @ D ) ) @ C ) @ B ) @ A ) )
=> ~ ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ E ) @ C ) @ B ) @ F ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ D ) @ F ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evaln__elim__cases_I4_J) ).
thf(770,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ E @ D ) ) @ C ) @ B ) @ A ) )
=> ~ ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ E ) @ C ) @ B ) @ F ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ D ) @ F ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(267,axiom,
! [A: $i] :
( ~ ( hBOOL @ ( hAPP @ c_fNot @ A ) )
| ~ ( hBOOL @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fNot__1) ).
thf(1398,plain,
! [A: $i] :
( ~ ( hBOOL @ ( hAPP @ c_fNot @ A ) )
| ~ ( hBOOL @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[267]) ).
thf(48,axiom,
! [A: $i,B: $i] :
( ( B != A )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_linorder__neqE__nat) ).
thf(448,plain,
! [A: $i,B: $i] :
( ( B != A )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__gr__0) ).
thf(316,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(54,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ ( hAPP @ A @ D ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ B @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_imageI) ).
thf(475,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ ( hAPP @ A @ D ) ) @ ( hAPP @ ( c_Set_Oimage @ E @ B @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(287,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ B ) @ A ) )
| ( hBOOL @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fconj__3) ).
thf(1465,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ B ) @ A ) )
| ( hBOOL @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[287]) ).
thf(281,axiom,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OAss @ C @ B ) ) @ A ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oupdate @ A ) @ C ) @ ( hAPP @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evalc_Oequations_I2_J) ).
thf(1450,plain,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OAss @ C @ B ) ) @ A ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oupdate @ A ) @ C ) @ ( hAPP @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[281]) ).
thf(46,axiom,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__zeroE) ).
thf(443,plain,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(251,axiom,
! [A: $i,B: $i,C: $i] :
( ? [D: $i] : ( hBOOL @ ( hAPP @ C @ D ) )
=> ( ( B
= ( c_Hilbert__Choice_OEps @ A @ C ) )
=> ( hBOOL @ ( hAPP @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_exE__some) ).
thf(1334,plain,
! [A: $i,B: $i,C: $i] :
( ? [D: $i] : ( hBOOL @ ( hAPP @ C @ D ) )
=> ( ( B
= ( c_Hilbert__Choice_OEps @ A @ C ) )
=> ( hBOOL @ ( hAPP @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[251]) ).
thf(213,axiom,
! [A: $i,B: $i] :
( ( c_Equiv__Relations_Oequivp @ B @ A )
<=> ! [C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ A @ C ) @ D ) )
<=> ( ( hAPP @ A @ C )
= ( hAPP @ A @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equivp__def) ).
thf(1151,plain,
! [A: $i,B: $i] :
( ( ( c_Equiv__Relations_Oequivp @ B @ A )
=> ! [C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ A @ C ) @ D ) )
=> ( ( hAPP @ A @ C )
= ( hAPP @ A @ D ) ) )
& ( ( ( hAPP @ A @ C )
= ( hAPP @ A @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ C ) @ D ) ) ) ) )
& ( ! [C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ A @ C ) @ D ) )
=> ( ( hAPP @ A @ C )
= ( hAPP @ A @ D ) ) )
& ( ( ( hAPP @ A @ C )
= ( hAPP @ A @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ C ) @ D ) ) ) )
=> ( c_Equiv__Relations_Oequivp @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[213]) ).
thf(264,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ B ) @ A ) )
| ( hBOOL @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fconj__2) ).
thf(1383,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ B ) @ A ) )
| ( hBOOL @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[264]) ).
thf(167,axiom,
! [A: $i,B: $i] :
( ( ( c_Com_Ovname_OGlb @ B )
= ( c_Com_Ovname_OGlb @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vname_Osimps_I1_J) ).
thf(966,plain,
! [A: $i,B: $i] :
( ( ( ( c_Com_Ovname_OGlb @ B )
= ( c_Com_Ovname_OGlb @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( c_Com_Ovname_OGlb @ B )
= ( c_Com_Ovname_OGlb @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(186,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ tc_Nat_Onat ) @ ( hAPP @ ( c_SetInterval_Oord__class_OlessThan @ tc_Nat_Onat ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__lessThan) ).
thf(1051,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ tc_Nat_Onat ) @ ( hAPP @ ( c_SetInterval_Oord__class_OlessThan @ tc_Nat_Onat ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(58,axiom,
! [A: $i,B: $i] :
( ( B = A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__imp__le) ).
thf(485,plain,
! [A: $i,B: $i] :
( ( B = A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(137,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_Com_Ocom_OWhile @ D @ C )
= ( c_Com_Ocom_OWhile @ B @ A ) )
<=> ( ( D = B )
& ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I5_J) ).
thf(834,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( c_Com_Ocom_OWhile @ D @ C )
= ( c_Com_Ocom_OWhile @ B @ A ) )
=> ( ( D = B )
& ( C = A ) ) )
& ( ( ( D = B )
& ( C = A ) )
=> ( ( c_Com_Ocom_OWhile @ D @ C )
= ( c_Com_Ocom_OWhile @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(216,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ~ ( hBOOL @ ( hAPP @ E @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ C ) @ D ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ E @ A @ C ) ) @ D ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evalc_OIfFalse) ).
thf(1183,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ~ ( hBOOL @ ( hAPP @ E @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ C ) @ D ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ E @ A @ C ) ) @ D ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[216]) ).
thf(242,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP ) @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evalc_Oequations_I1_J) ).
thf(1283,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[242]) ).
thf(152,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Com_Ocom_OCond @ E @ D @ C )
!= ( c_Com_Ocom_OAss @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I27_J) ).
thf(905,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Com_Ocom_OCond @ E @ D @ C )
!= ( c_Com_Ocom_OAss @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(56,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ B ) @ A ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__le__dividend) ).
thf(480,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ B ) @ A ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(95,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ B ) @ A ) ) )
=> ( ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ D ) @ C )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__eq) ).
thf(634,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ B ) @ A ) ) )
=> ( ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ D ) @ C )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(3,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__cancel__less) ).
thf(293,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(193,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ A ) )
<=> ( hBOOL @ ( hAPP @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mem__def) ).
thf(1072,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ A @ B ) ) )
& ( ( hBOOL @ ( hAPP @ A @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(204,axiom,
! [A: $i] :
( ~ ~ ( hBOOL @ A )
| ( hBOOL @ ( hAPP @ c_fNot @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fNot__2) ).
thf(1119,plain,
! [A: $i] :
( ( hBOOL @ A )
| ( hBOOL @ ( hAPP @ c_fNot @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(33,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I2_J) ).
thf(396,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(255,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ D ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eqset__imp__iff) ).
thf(1351,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ C ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[255]) ).
thf(200,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Hoare__Mirabelle_Otriple_Otriple__rec @ F @ E @ D @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ F ) @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( hAPP @ D @ C ) @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_triple_Orecs) ).
thf(1104,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Hoare__Mirabelle_Otriple_Otriple__rec @ F @ E @ D @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ F ) @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( hAPP @ D @ C ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(65,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) )
=> ( ( ( C = B )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__less__cases) ).
thf(507,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) )
=> ( ( ( C = B )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ B ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(214,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ E @ D @ C ) ) @ B ) @ A ) )
<=> ( ( ( hBOOL @ ( hAPP @ E @ B ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ D ) @ B ) @ A ) ) )
| ( ~ ( hBOOL @ ( hAPP @ E @ B ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ C ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evalc_Oequations_I5_J) ).
thf(1169,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ E @ D @ C ) ) @ B ) @ A ) )
=> ( ( ( hBOOL @ ( hAPP @ E @ B ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ D ) @ B ) @ A ) ) )
| ( ~ ( hBOOL @ ( hAPP @ E @ B ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ C ) @ B ) @ A ) ) ) ) )
& ( ( ( ( hBOOL @ ( hAPP @ E @ B ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ D ) @ B ) @ A ) ) )
| ( ~ ( hBOOL @ ( hAPP @ E @ B ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ C ) @ B ) @ A ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ E @ D @ C ) ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[214]) ).
thf(109,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Com_Ocom_OCond @ E @ D @ C )
!= ( c_Com_Ocom_OWhile @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I52_J) ).
thf(687,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Com_Ocom_OCond @ E @ D @ C )
!= ( c_Com_Ocom_OWhile @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(1,conjecture,
hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ v_c ) @ v_Z ) @ v_s_H ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_3) ).
thf(2,negated_conjecture,
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ v_c ) @ v_Z ) @ v_s_H ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(292,plain,
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ v_c ) @ v_Z ) @ v_s_H ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(103,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Hoare__Mirabelle_Otriple__valid @ E @ D @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ E ) @ C ) @ B ) @ A ) )
<=> ! [F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ C @ F ) @ G ) )
=> ! [H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ B ) @ G ) @ D ) @ H ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ F ) @ H ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_triple__valid__def2) ).
thf(661,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( c_Hoare__Mirabelle_Otriple__valid @ E @ D @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ E ) @ C ) @ B ) @ A ) )
=> ! [F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ C @ F ) @ G ) )
=> ! [H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ B ) @ G ) @ D ) @ H ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ F ) @ H ) ) ) ) )
& ( ! [F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ C @ F ) @ G ) )
=> ! [H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ B ) @ G ) @ D ) @ H ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ F ) @ H ) ) ) )
=> ( c_Hoare__Mirabelle_Otriple__valid @ E @ D @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ E ) @ C ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(158,axiom,
! [A: $i,B: $i] :
( ( c_Wellfounded_OwfP @ B @ A )
<=> ! [C: $i] : ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ B @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_wfP__accp__iff) ).
thf(925,plain,
! [A: $i,B: $i] :
( ( ( c_Wellfounded_OwfP @ B @ A )
=> ! [C: $i] : ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ B @ A ) @ C ) ) )
& ( ! [C: $i] : ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ B @ A ) @ C ) )
=> ( c_Wellfounded_OwfP @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(252,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ D @ C ) ) @ B ) @ A ) )
<=> ? [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ D ) @ B ) @ E ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ C ) @ E ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evalc_Oequations_I4_J) ).
thf(1338,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ D @ C ) ) @ B ) @ A ) )
=> ? [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ D ) @ B ) @ E ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ C ) @ E ) @ A ) ) ) )
& ( ? [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ D ) @ B ) @ E ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ C ) @ E ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ D @ C ) ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[252]) ).
thf(289,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( hBOOL @ ( hAPP @ C @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ C @ A ) ) @ B ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evalc_OWhileFalse) ).
thf(1470,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( hBOOL @ ( hAPP @ C @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ C @ A ) ) @ B ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[289]) ).
thf(12,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__less__add2) ).
thf(334,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(228,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Opeek__and @ E @ D @ C ) @ B ) @ A ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ D @ B ) @ A ) )
& ( hBOOL @ ( hAPP @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_peek__and__def) ).
thf(1223,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Opeek__and @ E @ D @ C ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ D @ B ) @ A ) )
& ( hBOOL @ ( hAPP @ C @ A ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( hAPP @ D @ B ) @ A ) )
& ( hBOOL @ ( hAPP @ C @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Opeek__and @ E @ D @ C ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[228]) ).
thf(206,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_FunDef_Oreduction__pair @ D @ C )
=> ( c_FunDef_Oreduction__pair @ B @ ( hAPP @ ( hAPP @ ( c_FunDef_Orp__inv__image @ D @ B ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rp__inv__image__rp) ).
thf(1123,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_FunDef_Oreduction__pair @ D @ C )
=> ( c_FunDef_Oreduction__pair @ B @ ( hAPP @ ( hAPP @ ( c_FunDef_Orp__inv__image @ D @ B ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(32,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A )
= B )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__eq__self__zero) ).
thf(392,plain,
! [A: $i,B: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A )
= B )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(93,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ E ) @ D ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ E ) @ D ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evaln__nonstrict) ).
thf(630,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ E ) @ D ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ E ) @ D ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(259,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ D ) @ C ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ D ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evaln__evalc) ).
thf(1370,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ D ) @ C ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ D ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[259]) ).
thf(183,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( hBOOL @ ( hAPP @ F @ E ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ D ) @ E ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ F @ A @ D ) ) @ E ) @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evaln_OIfFalse) ).
thf(1042,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( hBOOL @ ( hAPP @ F @ E ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ D ) @ E ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ F @ A @ D ) ) @ E ) @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(163,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) )
=> ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ A ) )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__ident) ).
thf(952,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) )
=> ( ( ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(22,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__le__add2) ).
thf(361,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(146,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ tc_Nat_Onat ) @ A ) )
<=> ? [B: $i] :
! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Nat_Onat ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__nat__set__iff__bounded) ).
thf(879,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ tc_Nat_Onat ) @ A ) )
=> ? [B: $i] :
! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Nat_Onat ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) ) ) )
& ( ? [B: $i] :
! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Nat_Onat ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ tc_Nat_Onat ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(284,axiom,
! [A: $i,B: $i] :
( ? [C: $i] : ( hBOOL @ ( hAPP @ B @ C ) )
=> ( hBOOL @ ( hAPP @ B @ ( c_Hilbert__Choice_OEps @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_someI__ex) ).
thf(1457,plain,
! [A: $i,B: $i] :
( ? [C: $i] : ( hBOOL @ ( hAPP @ B @ C ) )
=> ( hBOOL @ ( hAPP @ B @ ( c_Hilbert__Choice_OEps @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[284]) ).
thf(224,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ C @ B ) @ A ) )
=> ( ( c_Divides_Odivmod__nat @ C @ B )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__nat__eq) ).
thf(1210,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ C @ B ) @ A ) )
=> ( ( c_Divides_Odivmod__nat @ C @ B )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[224]) ).
thf(221,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ B @ ( c_Hilbert__Choice_OEps @ A @ B ) ) )
<=> ? [C: $i] : ( hBOOL @ ( hAPP @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_some__eq__ex) ).
thf(1195,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ B @ ( c_Hilbert__Choice_OEps @ A @ B ) ) )
=> ? [C: $i] : ( hBOOL @ ( hAPP @ B @ C ) ) )
& ( ? [C: $i] : ( hBOOL @ ( hAPP @ B @ C ) )
=> ( hBOOL @ ( hAPP @ B @ ( c_Hilbert__Choice_OEps @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[221]) ).
thf(168,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Typedef_Otype__definition @ F @ E @ D @ C @ B )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ ( hAPP @ D @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_type__definition_ORep) ).
thf(974,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Typedef_Otype__definition @ F @ E @ D @ C @ B )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ ( hAPP @ D @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(178,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ E @ D ) ) @ C ) @ B ) @ A ) )
<=> ( ( ( A = C )
& ~ ( hBOOL @ ( hAPP @ E @ C ) ) )
| ( ( hBOOL @ ( hAPP @ E @ C ) )
& ? [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ D ) @ C ) @ B ) @ F ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ E @ D ) ) @ F ) @ B ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evaln_Oequations_I8_J) ).
thf(1012,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ E @ D ) ) @ C ) @ B ) @ A ) )
=> ( ( ( A = C )
& ~ ( hBOOL @ ( hAPP @ E @ C ) ) )
| ( ( hBOOL @ ( hAPP @ E @ C ) )
& ? [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ D ) @ C ) @ B ) @ F ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ E @ D ) ) @ F ) @ B ) @ A ) ) ) ) ) )
& ( ( ( ( A = C )
& ~ ( hBOOL @ ( hAPP @ E @ C ) ) )
| ( ( hBOOL @ ( hAPP @ E @ C ) )
& ? [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ D ) @ C ) @ B ) @ F ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ E @ D ) ) @ F ) @ B ) @ A ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ E @ D ) ) @ C ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(156,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Owellorder @ C )
=> ( ( hBOOL @ ( hAPP @ B @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C ) @ ( c_Orderings_Oord__class_OLeast @ C @ B ) ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Least__le) ).
thf(916,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Owellorder @ C )
=> ( ( hBOOL @ ( hAPP @ B @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ C ) @ ( c_Orderings_Oord__class_OLeast @ C @ B ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(53,axiom,
! [A: $i,B: $i] :
( ? [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
& ( hBOOL @ ( hAPP @ A @ C ) ) )
<=> ? [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) ) )
& ( hBOOL @ ( hAPP @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ex__nat__less__eq) ).
thf(467,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
& ( hBOOL @ ( hAPP @ A @ C ) ) )
=> ? [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) ) )
& ( hBOOL @ ( hAPP @ A @ C ) ) ) )
& ( ? [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) ) )
& ( hBOOL @ ( hAPP @ A @ C ) ) )
=> ? [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
& ( hBOOL @ ( hAPP @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(78,axiom,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__less0) ).
thf(578,plain,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(239,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Equiv__Relations_Oequivp @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ C @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equivp__symp) ).
thf(1270,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Equiv__Relations_Oequivp @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ C @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[239]) ).
thf(162,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Com_Ocom_OAss @ E @ D )
!= ( c_Com_Ocom_OCond @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I26_J) ).
thf(948,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Com_Ocom_OAss @ E @ D )
!= ( c_Com_Ocom_OCond @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(90,axiom,
! [A: $i] :
( ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
= ( hAPP @ ( c_SetInterval_Oord__class_OatMost @ tc_Nat_Onat ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_atLeast0AtMost) ).
thf(615,plain,
! [A: $i] :
( ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ A )
= ( hAPP @ ( c_SetInterval_Oord__class_OatMost @ tc_Nat_Onat ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(115,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_Com_Ocom_OSemi @ D @ C )
= ( c_Com_Ocom_OSemi @ B @ A ) )
<=> ( ( D = B )
& ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I3_J) ).
thf(725,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( c_Com_Ocom_OSemi @ D @ C )
= ( c_Com_Ocom_OSemi @ B @ A ) )
=> ( ( D = B )
& ( C = A ) ) )
& ( ( ( D = B )
& ( C = A ) )
=> ( ( c_Com_Ocom_OSemi @ D @ C )
= ( c_Com_Ocom_OSemi @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(36,axiom,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_plus__nat_Oadd__0) ).
thf(403,plain,
! [A: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(145,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ E @ D ) ) @ C ) @ B ) @ A ) )
=> ( ( ( A = C )
=> ( hBOOL @ ( hAPP @ E @ C ) ) )
=> ~ ( ( hBOOL @ ( hAPP @ E @ C ) )
=> ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ D ) @ C ) @ B ) @ F ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ E @ D ) ) @ F ) @ B ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evaln__WHILE__case) ).
thf(869,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ E @ D ) ) @ C ) @ B ) @ A ) )
=> ( ( ( A = C )
=> ( hBOOL @ ( hAPP @ E @ C ) ) )
=> ~ ( ( hBOOL @ ( hAPP @ E @ C ) )
=> ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ D ) @ C ) @ B ) @ F ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ E @ D ) ) @ F ) @ B ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(261,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Equiv__Relations_Oequivp @ C @ B )
=> ( hBOOL @ ( hAPP @ ( hAPP @ B @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equivp__reflp) ).
thf(1375,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Equiv__Relations_Oequivp @ C @ B )
=> ( hBOOL @ ( hAPP @ ( hAPP @ B @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[261]) ).
thf(205,axiom,
! [A: $i,B: $i] :
( ( class_Orderings_Owellorder @ B )
=> ( ? [C: $i] : ( hBOOL @ ( hAPP @ A @ C ) )
=> ( hBOOL @ ( hAPP @ A @ ( c_Orderings_Oord__class_OLeast @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_LeastI__ex) ).
thf(1121,plain,
! [A: $i,B: $i] :
( ( class_Orderings_Owellorder @ B )
=> ( ? [C: $i] : ( hBOOL @ ( hAPP @ A @ C ) )
=> ( hBOOL @ ( hAPP @ A @ ( c_Orderings_Oord__class_OLeast @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(180,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( c_Big__Operators_Ocomm__monoid__big @ G @ F @ E @ D @ C )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ B ) )
=> ( ( hAPP @ ( hAPP @ C @ A ) @ B )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ G @ F @ E ) @ A ) @ D ) @ B ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ B ) )
=> ( ( hAPP @ ( hAPP @ C @ A ) @ B )
= D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_comm__monoid__big_OF__eq) ).
thf(1028,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( c_Big__Operators_Ocomm__monoid__big @ G @ F @ E @ D @ C )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ B ) )
=> ( ( hAPP @ ( hAPP @ C @ A ) @ B )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ G @ F @ E ) @ A ) @ D ) @ B ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ B ) )
=> ( ( hAPP @ ( hAPP @ C @ A ) @ B )
= D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(96,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Com_Ocom_OSemi @ E @ D )
!= ( c_Com_Ocom_OCond @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I44_J) ).
thf(637,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Com_Ocom_OSemi @ E @ D )
!= ( c_Com_Ocom_OCond @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(59,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__less__eq__dividend) ).
thf(489,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(279,axiom,
? [A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ v_c ) @ ( v_Sledgehammer_058s__2 @ v_Z @ v_s_H ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_2) ).
thf(1446,plain,
? [A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ v_c ) @ ( v_Sledgehammer_058s__2 @ v_Z @ v_s_H ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[279]) ).
thf(203,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ E @ D @ C ) ) @ B ) @ A ) )
=> ( ( ( hBOOL @ ( hAPP @ E @ B ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ D ) @ B ) @ A ) ) )
=> ~ ( ~ ( hBOOL @ ( hAPP @ E @ B ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ C ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evalc__elim__cases_I5_J) ).
thf(1114,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ E @ D @ C ) ) @ B ) @ A ) )
=> ( ( ( hBOOL @ ( hAPP @ E @ B ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ D ) @ B ) @ A ) ) )
=> ~ ( ~ ( hBOOL @ ( hAPP @ E @ B ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ C ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(172,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ D @ C ) ) @ B ) @ A ) @ B ) )
<=> ( ( hBOOL @ ( hAPP @ D @ B ) )
=> ? [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ C ) @ B ) @ A ) @ E ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ D @ C ) ) @ E ) @ A ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evaln_Oequations_I7_J) ).
thf(985,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ D @ C ) ) @ B ) @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ D @ B ) )
=> ? [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ C ) @ B ) @ A ) @ E ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ D @ C ) ) @ E ) @ A ) @ B ) ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ D @ B ) )
=> ? [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ C ) @ B ) @ A ) @ E ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ D @ C ) ) @ E ) @ A ) @ B ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ D @ C ) ) @ B ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(219,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ E @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ C ) @ D ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ E @ C ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ E @ C ) ) @ D ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evalc_OWhileTrue) ).
thf(1192,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ E @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ C ) @ D ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ E @ C ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ E @ C ) ) @ D ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[219]) ).
thf(51,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ A @ C ) ) )
<=> ! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Nat_Onat ) @ C ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_all__nat__less) ).
thf(457,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ A @ C ) ) )
=> ! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Nat_Onat ) @ C ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ A @ C ) ) ) )
& ( ! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Nat_Onat ) @ C ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ A @ C ) ) )
=> ! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(154,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ F @ E ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ D ) @ E ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ F @ D ) ) @ B ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ F @ D ) ) @ E ) @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evaln_OWhileTrue) ).
thf(911,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ F @ E ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ D ) @ E ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ F @ D ) ) @ B ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ F @ D ) ) @ E ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(275,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ D @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ C @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ D @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_accp__downward) ).
thf(1429,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ D @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ C @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ D @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[275]) ).
thf(64,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__not__refl2) ).
thf(503,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(100,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ ( hAPP @ D @ C ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ A ) @ C ) @ ( hAPP @ ( c_Set_Ovimage @ A @ E @ D ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimageI2) ).
thf(647,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ ( hAPP @ D @ C ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ A ) @ C ) @ ( hAPP @ ( c_Set_Ovimage @ A @ E @ D ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(174,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ tc_Nat_Onat ) @ A ) )
<=> ? [B: $i] :
! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Nat_Onat ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__nat__set__iff__bounded__le) ).
thf(997,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ tc_Nat_Onat ) @ A ) )
=> ? [B: $i] :
! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Nat_Onat ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) ) ) )
& ( ? [B: $i] :
! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Nat_Onat ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ tc_Nat_Onat ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(237,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP ) @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evalc_OSkip) ).
thf(1266,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[237]) ).
thf(230,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_SetInterval_Oord_OatLeast @ D @ B @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ B @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord_OatLeast__iff) ).
thf(1231,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_SetInterval_Oord_OatLeast @ D @ B @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ B @ A ) @ C ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ B @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_SetInterval_Oord_OatLeast @ D @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[230]) ).
thf(16,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ B ) )
<=> ( C = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__right__cancel) ).
thf(343,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ B ) )
=> ( C = A ) )
& ( ( C = A )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(34,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__lessD1) ).
thf(398,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(75,axiom,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
| ( B = A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__or__eq__imp__le) ).
thf(558,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
| ( B = A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(105,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ D ) @ C )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ B ) @ A ) )
=> ~ ( ( D = B )
=> ( C != A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pair__inject) ).
thf(674,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ D ) @ C )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ B ) @ A ) )
=> ~ ( ( D = B )
=> ( C != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(217,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ D @ C @ B ) @ A ) )
<=> ? [E: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ B @ E ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_RangeP_Oequations) ).
thf(1185,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ D @ C @ B ) @ A ) )
=> ? [E: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ B @ E ) @ A ) ) )
& ( ? [E: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ B @ E ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Predicate_ORangeP @ D @ C @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[217]) ).
thf(148,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ c_Com_Ocom_OSKIP ) @ B ) @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evaln_Oequations_I1_J) ).
thf(888,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ c_Com_Ocom_OSKIP ) @ B ) @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(126,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Com_Ocom_OAss @ D @ C )
!= ( c_Com_Ocom_OWhile @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I28_J) ).
thf(773,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Com_Ocom_OAss @ D @ C )
!= ( c_Com_Ocom_OWhile @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(81,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
& ( B != A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__less__le) ).
thf(586,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
& ( B != A ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
& ( B != A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(209,axiom,
! [A: $i] :
( ! [B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ v_c ) @ v_Z ) @ B ) )
=> ( A = B ) )
=> ( A = v_s_H ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
thf(1135,plain,
! [A: $i] :
( ! [B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ v_c ) @ v_Z ) @ B ) )
=> ( A = B ) )
=> ( A = v_s_H ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(91,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( c_Sum__Type_Osum_Osum__case @ G @ F @ E @ D @ C )
= ( c_Sum__Type_Osum_Osum__case @ G @ F @ E @ B @ A ) )
=> ~ ( ( D = B )
=> ( C != A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_sum__case__inject) ).
thf(618,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( c_Sum__Type_Osum_Osum__case @ G @ F @ E @ D @ C )
= ( c_Sum__Type_Osum_Osum__case @ G @ F @ E @ B @ A ) )
=> ~ ( ( D = B )
=> ( C != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(41,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ A @ B ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__le__divisor) ).
thf(425,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ A @ B ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(226,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ E ) @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ B ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ E @ B ) ) @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evalc_OSemi) ).
thf(1219,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ E ) @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ B ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ E @ B ) ) @ D ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[226]) ).
thf(240,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_SetInterval_Oord_OatMost @ D @ B @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ B @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord_OatMost__iff) ).
thf(1273,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_SetInterval_Oord_OatMost @ D @ B @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ B @ C ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ B @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_SetInterval_Oord_OatMost @ D @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[240]) ).
thf(241,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ E @ D @ C ) @ B ) @ A ) )
<=> ( hBOOL @ ( hAPP @ B @ ( hAPP @ C @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimage__code) ).
thf(1278,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ E @ D @ C ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ B @ ( hAPP @ C @ A ) ) ) )
& ( ( hBOOL @ ( hAPP @ B @ ( hAPP @ C @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Set_Ovimage @ E @ D @ C ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[241]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__assoc) ).
thf(298,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) ) @ A )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(211,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ D @ C ) ) @ B ) @ A ) )
=> ~ ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ D ) @ B ) @ E ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ C ) @ E ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evalc__elim__cases_I4_J) ).
thf(1146,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ D @ C ) ) @ B ) @ A ) )
=> ~ ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ D ) @ B ) @ E ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ C ) @ E ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(43,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ A @ C ) ) )
<=> ! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_all__nat__less__eq) ).
thf(430,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ A @ C ) ) )
=> ! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ A @ C ) ) ) )
& ( ! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ A @ C ) ) )
=> ! [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(80,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I5_J) ).
thf(584,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(40,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ ( hAPP @ ( c_Set_Oimage @ D @ B @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__imageI) ).
thf(423,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ B ) @ ( hAPP @ ( c_Set_Oimage @ D @ B @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(111,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( c_Com_Ocom_OCond @ F @ E @ D )
= ( c_Com_Ocom_OCond @ C @ B @ A ) )
<=> ( ( F = C )
& ( E = B )
& ( D = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I4_J) ).
thf(694,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ( c_Com_Ocom_OCond @ F @ E @ D )
= ( c_Com_Ocom_OCond @ C @ B @ A ) )
=> ( ( F = C )
& ( E = B )
& ( D = A ) ) )
& ( ( ( F = C )
& ( E = B )
& ( D = A ) )
=> ( ( c_Com_Ocom_OCond @ F @ E @ D )
= ( c_Com_Ocom_OCond @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(207,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Predicate_OPowp @ C @ B ) @ A ) )
<=> ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ A ) )
=> ( hBOOL @ ( hAPP @ B @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Powp__def) ).
thf(1125,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Predicate_OPowp @ C @ B ) @ A ) )
=> ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ A ) )
=> ( hBOOL @ ( hAPP @ B @ D ) ) ) )
& ( ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ A ) )
=> ( hBOOL @ ( hAPP @ B @ D ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Predicate_OPowp @ C @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(39,axiom,
! [A: $i,B: $i] :
( ( B != A )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__neq__iff) ).
thf(413,plain,
! [A: $i,B: $i] :
( ( ( B != A )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ B ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ B ) ) )
=> ( B != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(164,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ tc_Nat_Onat ) @ ( c_SetInterval_Oord__class_OgreaterThanLessThan @ tc_Nat_Onat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__greaterThanLessThan) ).
thf(958,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ tc_Nat_Onat ) @ ( c_SetInterval_Oord__class_OgreaterThanLessThan @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(269,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ H ) @ G ) @ F ) @ E ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ D ) @ C ) @ B ) @ A ) )
=> ? [I: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ H ) @ G ) @ I ) @ E ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ D ) @ C ) @ I ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evaln__max2) ).
thf(1403,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ H ) @ G ) @ F ) @ E ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ D ) @ C ) @ B ) @ A ) )
=> ? [I: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ H ) @ G ) @ I ) @ E ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ D ) @ C ) @ I ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[269]) ).
thf(97,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ D @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ B @ ( c_Hilbert__Choice_OLeastM @ A @ tc_Nat_Onat @ B @ D ) ) ) @ ( hAPP @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_LeastM__nat__le) ).
thf(641,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ D @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ B @ ( c_Hilbert__Choice_OLeastM @ A @ tc_Nat_Onat @ B @ D ) ) ) @ ( hAPP @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(160,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ D ) @ C )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ B ) @ A ) )
<=> ( ( D = B )
& ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pair__eq) ).
thf(936,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ D ) @ C )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ B ) @ A ) )
=> ( ( D = B )
& ( C = A ) ) )
& ( ( ( D = B )
& ( C = A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ D ) @ C )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(28,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__less__mono1) ).
thf(382,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(8,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ D ) @ C ) )
=> ( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ D ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__add__eq__less) ).
thf(313,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ D ) @ C ) )
=> ( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ C )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ D ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(62,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ A ) @ B ) ) @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__le__mono2) ).
thf(498,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ A ) @ B ) ) @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(201,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_SetInterval_Oord_OgreaterThan @ D @ B @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ B @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord_OgreaterThan__iff) ).
thf(1107,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_SetInterval_Oord_OgreaterThan @ D @ B @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ B @ A ) @ C ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ B @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( c_SetInterval_Oord_OgreaterThan @ D @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(198,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ E @ D @ C ) ) @ B ) @ A ) )
<=> ( ( ( hBOOL @ ( hAPP @ E @ B ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ D ) @ B ) @ A ) ) )
| ( ~ ( hBOOL @ ( hAPP @ E @ B ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ C ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evalc_Oequations_I6_J) ).
thf(1092,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ E @ D @ C ) ) @ B ) @ A ) )
=> ( ( ( hBOOL @ ( hAPP @ E @ B ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ D ) @ B ) @ A ) ) )
| ( ~ ( hBOOL @ ( hAPP @ E @ B ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ C ) @ B ) @ A ) ) ) ) )
& ( ( ( ( hBOOL @ ( hAPP @ E @ B ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ D ) @ B ) @ A ) ) )
| ( ~ ( hBOOL @ ( hAPP @ E @ B ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ C ) @ B ) @ A ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ E @ D @ C ) ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(197,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ B @ A ) @ ( c_Divides_Odivmod__nat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__nat__rel__divmod__nat) ).
thf(1090,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ B @ A ) @ ( c_Divides_Odivmod__nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(17,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__leD1) ).
thf(350,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(71,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( c_Divides_Odivmod__nat @ B @ A )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__nat__base) ).
thf(540,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( c_Divides_Odivmod__nat @ B @ A )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(88,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__eq__nat_Osimps_I1_J) ).
thf(611,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(128,axiom,
! [A: $i,B: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OSemi @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I12_J) ).
thf(787,plain,
! [A: $i,B: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OSemi @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(220,axiom,
hBOOL @ c_fTrue,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fTrue__1) ).
thf(1194,plain,
hBOOL @ c_fTrue,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[220]) ).
thf(37,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) ) @ A ) )
=> ~ ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ A ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__leE) ).
thf(406,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B ) ) @ A ) )
=> ~ ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ A ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(254,axiom,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Owellorder @ C )
=> ( ( hBOOL @ ( hAPP @ B @ A ) )
=> ( hBOOL @ ( hAPP @ B @ ( c_Orderings_Oord__class_OLeast @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_LeastI) ).
thf(1349,plain,
! [A: $i,B: $i,C: $i] :
( ( class_Orderings_Owellorder @ C )
=> ( ( hBOOL @ ( hAPP @ B @ A ) )
=> ( hBOOL @ ( hAPP @ B @ ( c_Orderings_Oord__class_OLeast @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[254]) ).
thf(26,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__add2) ).
thf(377,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(49,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( B != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__not__refl3) ).
thf(451,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(101,axiom,
! [A: $i,B: $i,C: $i,D: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ ( c_Com_Ocom_OAss @ D @ C ) ) @ B ) @ A ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oupdate @ B ) @ D ) @ ( hAPP @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evaln_Oequations_I2_J) ).
thf(649,plain,
! [A: $i,B: $i,C: $i,D: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ ( c_Com_Ocom_OAss @ D @ C ) ) @ B ) @ A ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oupdate @ B ) @ D ) @ ( hAPP @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__commute) ).
thf(303,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(247,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ D @ C ) ) @ B ) @ A ) )
<=> ( ( ( A = B )
& ~ ( hBOOL @ ( hAPP @ D @ B ) ) )
| ( ( hBOOL @ ( hAPP @ D @ B ) )
& ? [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ C ) @ B ) @ E ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ D @ C ) ) @ E ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evalc_Oequations_I8_J) ).
thf(1307,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ D @ C ) ) @ B ) @ A ) )
=> ( ( ( A = B )
& ~ ( hBOOL @ ( hAPP @ D @ B ) ) )
| ( ( hBOOL @ ( hAPP @ D @ B ) )
& ? [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ C ) @ B ) @ E ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ D @ C ) ) @ E ) @ A ) ) ) ) ) )
& ( ( ( ( A = B )
& ~ ( hBOOL @ ( hAPP @ D @ B ) ) )
| ( ( hBOOL @ ( hAPP @ D @ B ) )
& ? [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ C ) @ B ) @ E ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ D @ C ) ) @ E ) @ A ) ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ D @ C ) ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[247]) ).
thf(143,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ tc_Nat_Onat ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatMost @ tc_Nat_Onat ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__atMost) ).
thf(863,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ tc_Nat_Onat ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatMost @ tc_Nat_Onat ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(123,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__absorb2) ).
thf(764,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(170,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ ( c_Com_Ocom_OAss @ E @ D ) ) @ C ) @ B ) @ A ) )
=> ( A
= ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oupdate @ C ) @ E ) @ ( hAPP @ D @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evaln__elim__cases_I2_J) ).
thf(979,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ ( c_Com_Ocom_OAss @ E @ D ) ) @ C ) @ B ) @ A ) )
=> ( A
= ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oupdate @ C ) @ E ) @ ( hAPP @ D @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(107,axiom,
! [A: $i,B: $i] :
( ( c_Com_Ocom_OAss @ B @ A )
!= c_Com_Ocom_OSKIP ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I9_J) ).
thf(681,plain,
! [A: $i,B: $i] :
( ( c_Com_Ocom_OAss @ B @ A )
!= c_Com_Ocom_OSKIP ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(271,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ C @ B ) ) @ A ) @ A ) )
<=> ( ( hBOOL @ ( hAPP @ C @ A ) )
=> ? [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ B ) @ A ) @ D ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ C @ B ) ) @ D ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evalc_Oequations_I7_J) ).
thf(1408,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ C @ B ) ) @ A ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ C @ A ) )
=> ? [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ B ) @ A ) @ D ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ C @ B ) ) @ D ) @ A ) ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ C @ A ) )
=> ? [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ B ) @ A ) @ D ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ C @ B ) ) @ D ) @ A ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ C @ B ) ) @ A ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[271]) ).
thf(185,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ B ) @ A ) ) )
=> ( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ D @ C )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__eq) ).
thf(1048,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ D @ C ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ B ) @ A ) ) )
=> ( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ D @ C )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(116,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Typedef_Otype__definition @ F @ E @ D @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ A ) @ B ) )
=> ( ( hAPP @ D @ ( hAPP @ C @ A ) )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_type__definition_OAbs__inverse) ).
thf(736,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Typedef_Otype__definition @ F @ E @ D @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ A ) @ B ) )
=> ( ( hAPP @ D @ ( hAPP @ C @ A ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(149,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ c_Com_Ocom_OSKIP ) @ C ) @ B ) @ A ) )
=> ( A = C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evaln__elim__cases_I1_J) ).
thf(890,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ c_Com_Ocom_OSKIP ) @ C ) @ B ) @ A ) )
=> ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(55,axiom,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__irrefl__nat) ).
thf(477,plain,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(30,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__le__add1) ).
thf(387,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(195,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Nitpick_Opair__box_Opair__box__rec @ F @ E @ D @ C @ ( c_Nitpick_Opair__box_OPairBox @ F @ E @ B @ A ) )
= ( hAPP @ ( hAPP @ C @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pair__box_Orecs) ).
thf(1080,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Nitpick_Opair__box_Opair__box__rec @ F @ E @ D @ C @ ( c_Nitpick_Opair__box_OPairBox @ F @ E @ B @ A ) )
= ( hAPP @ ( hAPP @ C @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(121,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Wellfounded_OwfP @ C @ B )
=> ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ C @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_accp__wfPD) ).
thf(758,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Wellfounded_OwfP @ C @ B )
=> ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ C @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(73,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F
= ( hAPP @ E @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ A ) @ F ) @ ( hAPP @ ( c_Set_Oimage @ C @ A @ E ) @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_image__eqI) ).
thf(552,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F
= ( hAPP @ E @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ D ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ A ) @ F ) @ ( hAPP @ ( c_Set_Oimage @ C @ A @ E ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(87,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ G @ F ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ E ) @ D ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ C @ F ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ B ) @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ F ) )
=> ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ G ) @ C ) @ F ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ E ) @ B ) ) @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ D ) @ A ) ) @ F ) ) ) @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ D ) @ A ) @ F ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__nat__rel__add1__eq) ).
thf(609,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ G @ F ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ E ) @ D ) ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ C @ F ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ B ) @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ F ) )
=> ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ G ) @ C ) @ F ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ E ) @ B ) ) @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ D ) @ A ) ) @ F ) ) ) @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ D ) @ A ) @ F ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
<=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__is__0) ).
thf(323,plain,
! [A: $i,B: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) )
& ( ( ( B
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
& ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(139,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( C = A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insertCI) ).
thf(848,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ B ) )
=> ( C = A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(92,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Com_Ocom_OWhile @ D @ C )
!= ( c_Com_Ocom_OSemi @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I47_J) ).
thf(626,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Com_Ocom_OWhile @ D @ C )
!= ( c_Com_Ocom_OSemi @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(253,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ C ) @ B ) @ A ) )
<=> ? [D: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ C ) @ B ) @ D ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eval__eq) ).
thf(1344,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ C ) @ B ) @ A ) )
=> ? [D: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ C ) @ B ) @ D ) @ A ) ) )
& ( ? [D: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ C ) @ B ) @ D ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ C ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[253]) ).
thf(263,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ B ) @ A ) )
| ( hBOOL @ B )
| ( hBOOL @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fdisj__3) ).
thf(1381,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ B ) @ A ) )
| ( hBOOL @ B )
| ( hBOOL @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[263]) ).
thf(202,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ B )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fimplies__1) ).
thf(1112,plain,
! [A: $i,B: $i] :
( ( hBOOL @ B )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(212,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ B )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fdisj__2) ).
thf(1149,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ B )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[212]) ).
thf(166,axiom,
! [A: $i,B: $i,C: $i,D: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ ( c_Com_Ocom_OAss @ D @ C ) ) @ B ) @ A ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oupdate @ B ) @ D ) @ ( hAPP @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evaln_OAssign) ).
thf(964,plain,
! [A: $i,B: $i,C: $i,D: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ ( c_Com_Ocom_OAss @ D @ C ) ) @ B ) @ A ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oupdate @ B ) @ D ) @ ( hAPP @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(108,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ tc_Nat_Onat ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__atLeastLessThan) ).
thf(685,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ tc_Nat_Onat ) @ ( hAPP @ ( c_SetInterval_Oord__class_OatLeastLessThan @ tc_Nat_Onat @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(291,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( c_SetInterval_Oord_OatLeastAtMost @ E @ C @ B @ A ) ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ D ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ C @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord_OatLeastAtMost__iff) ).
thf(1474,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( c_SetInterval_Oord_OatLeastAtMost @ E @ C @ B @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ D ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ C @ D ) @ A ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( hAPP @ C @ B ) @ D ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ C @ D ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( c_SetInterval_Oord_OatLeastAtMost @ E @ C @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[291]) ).
thf(225,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ ( c_SetInterval_Oord_OatLeastLessThan @ F @ D @ C @ B @ A ) ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ D @ B ) @ E ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ C @ E ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ord_OatLeastLessThan__iff) ).
thf(1213,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ ( c_SetInterval_Oord_OatLeastLessThan @ F @ D @ C @ B @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ D @ B ) @ E ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ C @ E ) @ A ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( hAPP @ D @ B ) @ E ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ C @ E ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ ( c_SetInterval_Oord_OatLeastLessThan @ F @ D @ C @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[225]) ).
thf(191,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OAss @ D @ C ) ) @ B ) @ A ) )
=> ( A
= ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oupdate @ B ) @ D ) @ ( hAPP @ C @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evalc__elim__cases_I2_J) ).
thf(1066,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OAss @ D @ C ) ) @ B ) @ A ) )
=> ( A
= ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oupdate @ B ) @ D ) @ ( hAPP @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(50,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le0) ).
thf(455,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
<=> ? [C: $i] :
( A
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__iff__add) ).
thf(306,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ? [C: $i] :
( A
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ C ) ) )
& ( ? [C: $i] :
( A
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(76,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
<=> ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__0__eq) ).
thf(563,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
=> ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) )
& ( ( A
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(199,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ E @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ C ) @ D ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ E @ C @ A ) ) @ D ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evalc_OIfTrue) ).
thf(1102,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ E @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ C ) @ D ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ E @ C @ A ) ) @ D ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(44,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ B ) @ A ) ) @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__nat__rel) ).
thf(438,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ B @ A ) @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ B ) @ A ) ) @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(184,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Com_Ocom_OWhile @ D @ C )
!= ( c_Com_Ocom_OAss @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I29_J) ).
thf(1044,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Com_Ocom_OWhile @ D @ C )
!= ( c_Com_Ocom_OAss @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(232,axiom,
~ ( hBOOL @ c_fFalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fFalse__1) ).
thf(1245,plain,
~ ( hBOOL @ c_fFalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[232]) ).
thf(223,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ C @ B ) @ A ) )
<=> ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ B @ D ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ C @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_accp_Oequations) ).
thf(1203,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ C @ B ) @ A ) )
=> ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ B @ D ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ C @ B ) @ D ) ) ) )
& ( ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ B @ D ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ C @ B ) @ D ) ) )
=> ( hBOOL @ ( hAPP @ ( c_Wellfounded_Oaccp @ C @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[223]) ).
thf(69,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ A @ B ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__less__divisor) ).
thf(531,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ A @ B ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(273,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ B ) @ A ) )
| ~ ( hBOOL @ B )
| ( hBOOL @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fimplies__3) ).
thf(1420,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ B ) @ A ) )
| ~ ( hBOOL @ B )
| ( hBOOL @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[273]) ).
thf(135,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( c_Nitpick_Opair__box_OPairBox @ F @ E @ D @ C )
= ( c_Nitpick_Opair__box_OPairBox @ F @ E @ B @ A ) )
<=> ( ( D = B )
& ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pair__box_Oinject) ).
thf(812,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ( c_Nitpick_Opair__box_OPairBox @ F @ E @ D @ C )
= ( c_Nitpick_Opair__box_OPairBox @ F @ E @ B @ A ) )
=> ( ( D = B )
& ( C = A ) ) )
& ( ( ( D = B )
& ( C = A ) )
=> ( ( c_Nitpick_Opair__box_OPairBox @ F @ E @ D @ C )
= ( c_Nitpick_Opair__box_OPairBox @ F @ E @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(118,axiom,
! [A: $i] :
( ( c_Divides_Odivmod__nat @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__nat__zero) ).
thf(749,plain,
! [A: $i] :
( ( c_Divides_Odivmod__nat @ A @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ tc_Nat_Onat @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(290,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ C @ B ) )
=> ( hBOOL @ ( hAPP @ C @ ( c_Hilbert__Choice_OEps @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_someI) ).
thf(1472,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ C @ B ) )
=> ( hBOOL @ ( hAPP @ C @ ( c_Hilbert__Choice_OEps @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[290]) ).
thf(120,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Com_Ocom_OCond @ E @ D @ C )
!= ( c_Com_Ocom_OSemi @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I45_J) ).
thf(754,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Com_Ocom_OCond @ E @ D @ C )
!= ( c_Com_Ocom_OSemi @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(136,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ G ) @ F ) @ E ) @ D )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ G ) @ C ) @ B ) @ A ) )
<=> ( ( F = C )
& ( E = B )
& ( D = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_triple_Oinject) ).
thf(823,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ G ) @ F ) @ E ) @ D )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ G ) @ C ) @ B ) @ A ) )
=> ( ( F = C )
& ( E = B )
& ( D = A ) ) )
& ( ( ( F = C )
& ( E = B )
& ( D = A ) )
=> ( ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ G ) @ F ) @ E ) @ D )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ G ) @ C ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(130,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ F @ E @ D ) ) @ C ) @ B ) @ A ) )
=> ( ( ( hBOOL @ ( hAPP @ F @ C ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ E ) @ C ) @ B ) @ A ) ) )
=> ~ ( ~ ( hBOOL @ ( hAPP @ F @ C ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ D ) @ C ) @ B ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evaln__elim__cases_I5_J) ).
thf(795,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ F @ E @ D ) ) @ C ) @ B ) @ A ) )
=> ( ( ( hBOOL @ ( hAPP @ F @ C ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ E ) @ C ) @ B ) @ A ) ) )
=> ~ ( ~ ( hBOOL @ ( hAPP @ F @ C ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ D ) @ C ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(106,axiom,
class_Orderings_Owellorder @ tc_Nat_Onat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat__Onat__Orderings_Owellorder) ).
thf(680,plain,
class_Orderings_Owellorder @ tc_Nat_Onat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(67,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_mod__less) ).
thf(525,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( c_Divides_Odiv__class_Omod @ tc_Nat_Onat @ B @ A )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(141,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Com_Ocom_OSemi @ D @ C )
!= ( c_Com_Ocom_OWhile @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I46_J) ).
thf(855,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Com_Ocom_OSemi @ D @ C )
!= ( c_Com_Ocom_OWhile @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(179,axiom,
! [A: $i,B: $i] :
( ( c_Hilbert__Choice_OEps @ B @ ( hAPP @ c_fequal @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_some__sym__eq__trivial) ).
thf(1025,plain,
! [A: $i,B: $i] :
( ( c_Hilbert__Choice_OEps @ B @ ( hAPP @ c_fequal @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(268,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ D @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ D @ C ) @ A ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_divmod__nat__rel__unique) ).
thf(1400,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ D @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Divides_Odivmod__nat__rel @ D @ C ) @ A ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[268]) ).
thf(38,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ D ) )
=> ( ( C
= ( hAPP @ B @ E ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ A ) @ C ) @ ( hAPP @ ( c_Set_Oimage @ F @ A @ B ) @ D ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rev__image__eqI) ).
thf(409,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ E ) @ D ) )
=> ( ( C
= ( hAPP @ B @ E ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ A ) @ C ) @ ( hAPP @ ( c_Set_Oimage @ F @ A @ B ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(173,axiom,
! [A: $i,B: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OAss @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I8_J) ).
thf(993,plain,
! [A: $i,B: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OAss @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(187,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Finite__Set_Ofolding__one__idem @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ E ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ A ) @ B ) )
=> ( ( hAPP @ ( hAPP @ D @ A ) @ ( hAPP @ C @ B ) )
= ( hAPP @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__one__idem_Oin__idem) ).
thf(1053,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Finite__Set_Ofolding__one__idem @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ E ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ A ) @ B ) )
=> ( ( hAPP @ ( hAPP @ D @ A ) @ ( hAPP @ C @ B ) )
= ( hAPP @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(282,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ C ) @ B ) @ A ) )
=> ? [D: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ C ) @ B ) @ D ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evalc__evaln) ).
thf(1452,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ C ) @ B ) @ A ) )
=> ? [D: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ C ) @ B ) @ D ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[282]) ).
thf(129,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Com_Ocom_OAss @ D @ C )
!= ( c_Com_Ocom_OSemi @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I24_J) ).
thf(791,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Com_Ocom_OAss @ D @ C )
!= ( c_Com_Ocom_OSemi @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(14,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__mono) ).
thf(338,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ D ) @ B ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(21,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_add__le__mono1) ).
thf(359,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ A ) ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(243,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ D ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ C ) ) )
=> ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equalityCE) ).
thf(1285,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ D ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ C ) ) )
=> ~ ( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[243]) ).
thf(98,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( hBOOL @ ( hAPP @ D @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ D @ B ) ) @ C ) @ A ) @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evaln_OWhileFalse) ).
thf(643,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( hBOOL @ ( hAPP @ D @ C ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ D @ B ) ) @ C ) @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(182,axiom,
! [A: $i,B: $i] :
( ( c_Com_Ocom_OWhile @ B @ A )
!= c_Com_Ocom_OSKIP ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I17_J) ).
thf(1038,plain,
! [A: $i,B: $i] :
( ( c_Com_Ocom_OWhile @ B @ A )
!= c_Com_Ocom_OSKIP ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(24,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_trans__less__add1) ).
thf(370,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(256,axiom,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] : ( hBOOL @ ( hAPP @ C @ D ) )
<=> ! [D: $i,E: $i] : ( hBOOL @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ A ) @ D ) @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__paired__All) ).
thf(1358,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] : ( hBOOL @ ( hAPP @ C @ D ) )
=> ! [D: $i,E: $i] : ( hBOOL @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ A ) @ D ) @ E ) ) ) )
& ( ! [D: $i,E: $i] : ( hBOOL @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ A ) @ D ) @ E ) ) )
=> ! [D: $i] : ( hBOOL @ ( hAPP @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[256]) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I3_J) ).
thf(336,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(235,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP ) @ B ) @ A ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evalc__elim__cases_I1_J) ).
thf(1257,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP ) @ B ) @ A ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[235]) ).
thf(89,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ C ) @ A ) ) @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__le__mono) ).
thf(613,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ C ) @ A ) ) @ ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(227,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ B )
| ~ ( hBOOL @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fconj__1) ).
thf(1221,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ B )
| ~ ( hBOOL @ A )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fconj @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[227]) ).
thf(84,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( B != A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__neq__implies__less) ).
thf(600,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( B != A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(210,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( c_Predicate_Opred__comp @ G @ F @ E @ D @ C @ B @ A )
<=> ? [H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ D @ B ) @ H ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ C @ H ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pred__comp_Oequations) ).
thf(1140,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( c_Predicate_Opred__comp @ G @ F @ E @ D @ C @ B @ A )
=> ? [H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ D @ B ) @ H ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ C @ H ) @ A ) ) ) )
& ( ? [H: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ D @ B ) @ H ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ C @ H ) @ A ) ) )
=> ( c_Predicate_Opred__comp @ G @ F @ E @ D @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(176,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ c_Com_Ocom_OSKIP ) @ B ) @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evaln_OSkip) ).
thf(1008,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ c_Com_Ocom_OSKIP ) @ B ) @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(47,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__imp__le__nat) ).
thf(446,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(142,axiom,
! [A: $i,B: $i,C: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OCond @ C @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I14_J) ).
thf(859,plain,
! [A: $i,B: $i,C: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OCond @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(260,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Nitpick_Opair__box_Opair__box__case @ F @ E @ D @ C @ ( c_Nitpick_Opair__box_OPairBox @ F @ E @ B @ A ) )
= ( hAPP @ ( hAPP @ C @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pair__box_Osimps_I2_J) ).
thf(1372,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Nitpick_Opair__box_Opair__box__case @ F @ E @ D @ C @ ( c_Nitpick_Opair__box_OPairBox @ F @ E @ B @ A ) )
= ( hAPP @ ( hAPP @ C @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[260]) ).
thf(82,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__refl) ).
thf(595,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(138,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ D @ C ) )
=> ( ( hBOOL @ ( hAPP @ D @ ( c_Hilbert__Choice_OLeastM @ B @ tc_Nat_Onat @ A @ D ) ) )
& ! [E: $i] :
( ( hBOOL @ ( hAPP @ D @ E ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ A @ ( c_Hilbert__Choice_OLeastM @ B @ tc_Nat_Onat @ A @ D ) ) ) @ ( hAPP @ A @ E ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_LeastM__nat__lemma) ).
thf(845,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ D @ C ) )
=> ( ( hBOOL @ ( hAPP @ D @ ( c_Hilbert__Choice_OLeastM @ B @ tc_Nat_Onat @ A @ D ) ) )
& ! [E: $i] :
( ( hBOOL @ ( hAPP @ D @ E ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ ( hAPP @ A @ ( c_Hilbert__Choice_OLeastM @ B @ tc_Nat_Onat @ A @ D ) ) ) @ ( hAPP @ A @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(52,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__le__linear) ).
thf(465,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(285,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Product__Type_Oprod_Oprod__rec @ F @ E @ D @ C @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ C @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_prod_Orecs) ).
thf(1459,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Product__Type_Oprod_Oprod__rec @ F @ E @ D @ C @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ C @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[285]) ).
thf(57,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( c_Finite__Set_Ofolding__image__simple @ G @ F @ E @ D @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ A ) )
=> ( ( hAPP @ B @ A )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ G @ F @ E ) @ C ) @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__image__simple_Oeq__fold__g) ).
thf(482,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( c_Finite__Set_Ofolding__image__simple @ G @ F @ E @ D @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ A ) )
=> ( ( hAPP @ B @ A )
= ( hAPP @ ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold__image @ G @ F @ E ) @ C ) @ D ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(79,axiom,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_less__nat__zero__code) ).
thf(581,plain,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ A ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(280,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ B )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fdisj__1) ).
thf(1448,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ B )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fdisj @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[280]) ).
thf(177,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ F @ E ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ D ) @ E ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ F @ D @ A ) ) @ E ) @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evaln_OIfTrue) ).
thf(1010,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ F @ E ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ D ) @ E ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ F @ D @ A ) ) @ E ) @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(23,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat__add__left__cancel) ).
thf(363,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ B )
= ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(74,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__trans) ).
thf(556,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(234,axiom,
! [A: $i,B: $i] :
( ( B != A )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fequal @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fequal__2) ).
thf(1253,plain,
! [A: $i,B: $i] :
( ( B != A )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fequal @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[234]) ).
thf(265,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ D @ C ) ) @ B ) @ A ) )
=> ( ( ( A = B )
=> ( hBOOL @ ( hAPP @ D @ B ) ) )
=> ~ ( ( hBOOL @ ( hAPP @ D @ B ) )
=> ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ C ) @ B ) @ E ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ D @ C ) ) @ E ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evalc__WHILE__case) ).
thf(1385,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ D @ C ) ) @ B ) @ A ) )
=> ( ( ( A = B )
=> ( hBOOL @ ( hAPP @ D @ B ) ) )
=> ~ ( ( hBOOL @ ( hAPP @ D @ B ) )
=> ! [E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ C ) @ B ) @ E ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ D @ C ) ) @ E ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[265]) ).
thf(66,axiom,
! [A: $i,B: $i] :
( ? [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
& ( hBOOL @ ( hAPP @ A @ C ) ) )
<=> ? [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Nat_Onat ) @ C ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B ) ) )
& ( hBOOL @ ( hAPP @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ex__nat__less) ).
thf(517,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
& ( hBOOL @ ( hAPP @ A @ C ) ) )
=> ? [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Nat_Onat ) @ C ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B ) ) )
& ( hBOOL @ ( hAPP @ A @ C ) ) ) )
& ( ? [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ tc_Nat_Onat ) @ C ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Nat_Onat @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) @ B ) ) )
& ( hBOOL @ ( hAPP @ A @ C ) ) )
=> ? [C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ C ) @ B ) )
& ( hBOOL @ ( hAPP @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(94,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ tc_Nat_Onat ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Nat_Onat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__atLeastAtMost) ).
thf(632,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ tc_Nat_Onat ) @ ( c_SetInterval_Oord__class_OatLeastAtMost @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(194,axiom,
! [A: $i,B: $i] :
( ( class_Enum_Oenum @ B )
=> ( ( hBOOL @ ( hAPP @ ( c_Enum_Oenum__class_Oenum__ex @ B ) @ A ) )
<=> ? [C: $i] : ( hBOOL @ ( hAPP @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_enum__ex) ).
thf(1077,plain,
! [A: $i,B: $i] :
( ( class_Enum_Oenum @ B )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Enum_Oenum__class_Oenum__ex @ B ) @ A ) )
=> ? [C: $i] : ( hBOOL @ ( hAPP @ A @ C ) ) )
& ( ? [C: $i] : ( hBOOL @ ( hAPP @ A @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Enum_Oenum__class_Oenum__ex @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(131,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( hAPP @ ( c_Set_Ovimage @ E @ C @ B ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ ( hAPP @ B @ D ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimageD) ).
thf(800,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( hAPP @ ( c_Set_Ovimage @ E @ C @ B ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ ( hAPP @ B @ D ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(119,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite_OinsertI) ).
thf(752,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(229,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ B )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_c__fimplies__2) ).
thf(1229,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ B )
| ( hBOOL @ ( hAPP @ ( hAPP @ c_fimplies @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[229]) ).
thf(266,axiom,
! [A: $i,B: $i] :
( ( class_Enum_Oenum @ B )
=> ( ? [C: $i] : ( hBOOL @ ( hAPP @ A @ C ) )
<=> ( hBOOL @ ( hAPP @ ( c_Enum_Oenum__class_Oenum__ex @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_exists__code) ).
thf(1395,plain,
! [A: $i,B: $i] :
( ( class_Enum_Oenum @ B )
=> ( ( ? [C: $i] : ( hBOOL @ ( hAPP @ A @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Enum_Oenum__class_Oenum__ex @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( c_Enum_Oenum__class_Oenum__ex @ B ) @ A ) )
=> ? [C: $i] : ( hBOOL @ ( hAPP @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[266]) ).
thf(245,axiom,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OAss @ C @ B ) ) @ A ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oupdate @ A ) @ C ) @ ( hAPP @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evalc_OAssign) ).
thf(1303,plain,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OAss @ C @ B ) ) @ A ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oupdate @ A ) @ C ) @ ( hAPP @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[245]) ).
thf(144,axiom,
! [A: $i,B: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OWhile @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I16_J) ).
thf(865,plain,
! [A: $i,B: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OWhile @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(85,axiom,
! [A: $i] :
( ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gr0I) ).
thf(603,plain,
! [A: $i] :
( ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(277,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ D ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eqelem__imp__iff) ).
thf(1436,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ D ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ C ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ D ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[277]) ).
thf(157,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( c_Typedef_Otype__definition @ G @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ A ) @ C ) )
=> ( ( ( hAPP @ D @ B )
= ( hAPP @ D @ A ) )
<=> ( B = A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_type__definition_OAbs__inject) ).
thf(918,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( c_Typedef_Otype__definition @ G @ F @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ F ) @ A ) @ C ) )
=> ( ( ( ( hAPP @ D @ B )
= ( hAPP @ D @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( hAPP @ D @ B )
= ( hAPP @ D @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(257,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eq__mem__trans) ).
thf(1363,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D = C )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ B ) @ D ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[257]) ).
thf(133,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ tc_Nat_Onat ) @ ( c_SetInterval_Oord__class_OgreaterThanAtMost @ tc_Nat_Onat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_finite__greaterThanAtMost) ).
thf(807,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ tc_Nat_Onat ) @ ( c_SetInterval_Oord__class_OgreaterThanAtMost @ tc_Nat_Onat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(124,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Finite__Set_Ofolding__one__idem @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ E ) @ B ) )
=> ( ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ A ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ E @ E @ D ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__one__idem_Oeq__fold__idem_H) ).
thf(767,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Finite__Set_Ofolding__one__idem @ E @ D @ C )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ E ) @ B ) )
=> ( ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ E ) @ A ) @ B ) )
= ( hAPP @ ( hAPP @ ( c_Finite__Set_Ofold @ E @ E @ D ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(188,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Equiv__Relations_Oequivp @ E @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ D @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ D @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ D @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_equivp__transp) ).
thf(1056,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Equiv__Relations_Oequivp @ E @ D )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ D @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ D @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ D @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(165,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Com_Ocom_OCond @ C @ B @ A )
!= c_Com_Ocom_OSKIP ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I15_J) ).
thf(960,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Com_Ocom_OCond @ C @ B @ A )
!= c_Com_Ocom_OSKIP ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(147,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ F ) @ E ) @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ B ) @ C ) @ D ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ F @ B ) ) @ E ) @ D ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evaln_OSemi) ).
thf(886,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ F ) @ E ) @ D ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ B ) @ C ) @ D ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ F @ B ) ) @ E ) @ D ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(181,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( hAPP @ ( c_Set_Ovimage @ E @ C @ B ) @ A ) ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ ( hAPP @ B @ D ) ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vimage__eq) ).
thf(1033,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( hAPP @ ( c_Set_Ovimage @ E @ C @ B ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ ( hAPP @ B @ D ) ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ ( hAPP @ B @ D ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ E ) @ D ) @ ( hAPP @ ( c_Set_Ovimage @ E @ C @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(35,axiom,
! [A: $i,B: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__add__less2) ).
thf(400,plain,
! [A: $i,B: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(117,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ A ) ) )
<=> ( ( C = B )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__iff) ).
thf(740,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ A ) ) )
=> ( ( C = B )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) ) )
& ( ( ( C = B )
| ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ D ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(231,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ B ) @ A ) )
<=> ( ( C = A )
| ( hBOOL @ ( hAPP @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__code) ).
thf(1236,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ B ) @ A ) )
=> ( ( C = A )
| ( hBOOL @ ( hAPP @ B @ A ) ) ) )
& ( ( ( C = A )
| ( hBOOL @ ( hAPP @ B @ A ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ D ) @ C ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[231]) ).
thf(11,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_termination__basic__simps_I1_J) ).
thf(332,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ C ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(238,axiom,
! [A: $i,B: $i] :
( ? [C: $i] : ( hBOOL @ ( hAPP @ B @ C ) )
=> ( hBOOL @ ( hAPP @ B @ ( c_Hilbert__Choice_OEps @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_tfl__some) ).
thf(1268,plain,
! [A: $i,B: $i] :
( ? [C: $i] : ( hBOOL @ ( hAPP @ B @ C ) )
=> ( hBOOL @ ( hAPP @ B @ ( c_Hilbert__Choice_OEps @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[238]) ).
thf(42,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ A ) @ B ) )
=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__antisym) ).
thf(427,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ A ) @ B ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(262,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Com_Ovname_Ovname__rec @ D @ C @ B @ ( c_Com_Ovname_OGlb @ A ) )
= ( hAPP @ C @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vname_Orecs_I1_J) ).
thf(1378,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Com_Ovname_Ovname__rec @ D @ C @ B @ ( c_Com_Ovname_OGlb @ A ) )
= ( hAPP @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[262]) ).
thf(68,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_div__less) ).
thf(528,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( hAPP @ ( c_Divides_Odiv__class_Odiv @ tc_Nat_Onat @ B ) @ A )
= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(114,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ F ) @ E ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ G @ D @ C @ B @ E ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ G @ D @ C @ B @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ G ) @ F ) @ E ) ) @ ( hAPP @ ( hAPP @ C @ F ) @ A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold__graph_OinsertI) ).
thf(723,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ G ) @ F ) @ E ) )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ G @ D @ C @ B @ E ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ G @ D @ C @ B @ ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ G ) @ F ) @ E ) ) @ ( hAPP @ ( hAPP @ C @ F ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(110,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ A )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_insert__absorb) ).
thf(691,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_member @ C ) @ B ) @ A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Set_Oinsert @ C ) @ B ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(171,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Finite__Set_Ofolding__one @ D @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ A ) )
=> ( ( hAPP @ B @ A )
= ( hAPP @ ( c_Finite__Set_Ofold1 @ D @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__one_Oeq__fold) ).
thf(982,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Finite__Set_Ofolding__one @ D @ C @ B )
=> ( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ D ) @ A ) )
=> ( ( hAPP @ B @ A )
= ( hAPP @ ( c_Finite__Set_Ofold1 @ D @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(276,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ D @ C @ B ) @ A ) )
<=> ? [E: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ B @ A ) @ E ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DomainP_Oequations) ).
thf(1431,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ D @ C @ B ) @ A ) )
=> ? [E: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ B @ A ) @ E ) ) )
& ( ? [E: $i] : ( hBOOL @ ( hAPP @ ( hAPP @ B @ A ) @ E ) )
=> ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ D @ C @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[276]) ).
thf(175,axiom,
! [A: $i,B: $i] :
( ( c_Com_Ocom_OSemi @ B @ A )
!= c_Com_Ocom_OSKIP ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I13_J) ).
thf(1004,plain,
! [A: $i,B: $i] :
( ( c_Com_Ocom_OSemi @ B @ A )
!= c_Com_Ocom_OSKIP ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(132,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Com_Ocom_OSemi @ D @ C )
!= ( c_Com_Ocom_OAss @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I25_J) ).
thf(803,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Com_Ocom_OSemi @ D @ C )
!= ( c_Com_Ocom_OAss @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(248,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_New__Random__Sequence_Opos__not__random__dseq @ D @ C @ B @ A )
= ( c_New__DSequence_Opos__not__seq @ ( hAPP @ ( hAPP @ ( hAPP @ D @ C ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__not__random__dseq__def) ).
thf(1320,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_New__Random__Sequence_Opos__not__random__dseq @ D @ C @ B @ A )
= ( c_New__DSequence_Opos__not__seq @ ( hAPP @ ( hAPP @ ( hAPP @ D @ C ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[248]) ).
thf(258,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ D ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ D ) @ C ) @ A ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com__det) ).
thf(1367,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ D ) @ C ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ D ) @ C ) @ A ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[258]) ).
thf(19,axiom,
! [A: $i,B: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_not__add__less1) ).
thf(354,plain,
! [A: $i,B: $i] :
~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ ( hAPP @ ( hAPP @ ( c_Groups_Oplus__class_Oplus @ tc_Nat_Onat ) @ B ) @ A ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(72,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
<=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
| ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_le__eq__less__or__eq) ).
thf(543,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
| ( B = A ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
| ( B = A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless__eq @ tc_Nat_Onat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(272,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Typedef_Otype__definition @ F @ E @ D @ C @ B )
=> ( ( hAPP @ C @ ( hAPP @ D @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_type__definition_ORep__inverse) ).
thf(1416,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Typedef_Otype__definition @ F @ E @ D @ C @ B )
=> ( ( hAPP @ C @ ( hAPP @ D @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[272]) ).
thf(60,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_gr__implies__not0) ).
thf(491,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Orderings_Oord__class_Oless @ tc_Nat_Onat ) @ B ) @ A ) )
=> ( A
!= ( c_Groups_Ozero__class_Ozero @ tc_Nat_Onat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(288,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ E @ D ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ B @ A @ E ) @ D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_DomainP_Ointros) ).
thf(1468,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ E @ D ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Predicate_ODomainP @ B @ A @ E ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[288]) ).
thf(112,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_Com_Ocom_OAss @ D @ C )
= ( c_Com_Ocom_OAss @ B @ A ) )
<=> ( ( D = B )
& ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I1_J) ).
thf(708,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( c_Com_Ocom_OAss @ D @ C )
= ( c_Com_Ocom_OAss @ B @ A ) )
=> ( ( D = B )
& ( C = A ) ) )
& ( ( ( D = B )
& ( C = A ) )
=> ( ( c_Com_Ocom_OAss @ D @ C )
= ( c_Com_Ocom_OAss @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(61,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ F @ E @ D @ C @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_fold__graph__imp__finite) ).
thf(496,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofold__graph @ F @ E @ D @ C @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( c_Finite__Set_Ofinite @ F ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(192,axiom,
! [A: $i,B: $i] :
( ( class_Enum_Oenum @ B )
=> ( ( hBOOL @ ( hAPP @ ( c_Enum_Oenum__class_Oenum__all @ B ) @ A ) )
<=> ! [C: $i] : ( hBOOL @ ( hAPP @ A @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_enum__all) ).
thf(1069,plain,
! [A: $i,B: $i] :
( ( class_Enum_Oenum @ B )
=> ( ( ( hBOOL @ ( hAPP @ ( c_Enum_Oenum__class_Oenum__all @ B ) @ A ) )
=> ! [C: $i] : ( hBOOL @ ( hAPP @ A @ C ) ) )
& ( ! [C: $i] : ( hBOOL @ ( hAPP @ A @ C ) )
=> ( hBOOL @ ( hAPP @ ( c_Enum_Oenum__class_Oenum__all @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(1484,plain,
$false,
inference(e,[status(thm)],[645,809,1190,760,1454,909,893,1083,1179,777,352,1200,977,1406,1443,1422,379,440,1305,597,384,533,500,1327,1260,913,945,930,670,1063,340,898,301,651,389,570,1298,719,372,1323,357,1462,1059,1132,853,1247,606,770,1398,448,316,475,1465,1450,443,1334,1151,1383,966,1051,485,834,1183,1283,905,480,634,293,1072,1119,396,1351,1104,507,1169,687,292,661,925,1338,1470,334,1223,1123,392,630,1370,1042,952,361,879,1457,1210,1195,974,1012,916,467,578,1270,948,615,725,403,869,1375,1121,1028,637,489,1446,1114,985,1192,457,911,1429,503,647,997,1266,1231,343,398,558,674,1185,888,773,586,1135,618,425,1219,1273,1278,298,1146,430,584,423,694,1125,413,958,1403,641,936,382,313,498,1107,1092,1090,350,540,611,787,1194,406,1349,377,451,649,303,1307,863,764,979,681,1408,1048,736,890,477,387,1080,758,552,609,323,848,626,1344,1381,1112,1149,964,685,1474,1213,1066,455,306,563,1102,438,1044,1245,1203,531,1420,812,749,1472,754,823,795,680,525,855,1025,1400,409,993,1053,1452,791,338,359,1285,643,1038,370,1358,336,1257,613,1221,600,1140,1008,446,859,1372,595,845,465,1459,482,581,1448,1010,363,556,1253,1385,517,632,1077,800,752,1229,1395,1303,865,603,1436,918,1363,807,767,1056,960,886,1033,400,740,1236,332,1268,427,1378,528,723,691,982,1431,1004,803,1320,1367,354,543,1416,491,1468,708,496,1069]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWW350+1 : TPTP v8.1.2. Released v5.2.0.
% 0.06/0.15 % Command : run_Leo-III %s %d
% 0.14/0.36 % Computer : n017.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Thu May 18 21:43:31 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.84/0.86 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.72/1.39 % [INFO] Parsing done (532ms).
% 2.72/1.41 % [INFO] Running in sequential loop mode.
% 3.00/1.60 % [INFO] eprover registered as external prover.
% 3.00/1.61 % [INFO] cvc4 registered as external prover.
% 3.00/1.61 % [INFO] Scanning for conjecture ...
% 4.60/1.99 % [INFO] Found a conjecture and 5228 axioms. Running axiom selection ...
% 6.93/2.71 % [INFO] Axiom selection finished. Selected 289 axioms (removed 4939 axioms).
% 7.38/2.91 % [INFO] Problem is first-order (TPTP FOF).
% 7.38/2.93 % [INFO] Type checking passed.
% 7.38/2.93 % [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 ...
% 16.27/4.93 % External prover 'e' found a proof!
% 16.27/4.93 % [INFO] Killing All external provers ...
% 16.27/4.93 % Time passed: 4412ms (effective reasoning time: 3517ms)
% 16.27/4.93 % 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)>
% 16.27/4.93 % 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
% 16.27/4.93 % No. of inferences in proof: 582
% 16.27/4.93 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 4412 ms resp. 3517 ms w/o parsing
% 17.08/5.10 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 17.08/5.10 % [INFO] Killing All external provers ...
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