TSTP Solution File: SWW343+1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SWW343+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n025.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 12:23:34 EDT 2023
% Result : Theorem 13.00s 4.48s
% Output : Refutation 13.50s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 145
% Syntax : Number of formulae : 235 ( 80 unt; 57 typ; 0 def)
% Number of atoms : 383 ( 211 equ; 0 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 3384 ( 58 ~; 0 |; 61 &;3121 @)
% ( 22 <=>; 122 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 104 ( 104 >; 0 *; 0 +; 0 <<)
% Number of symbols : 59 ( 57 usr; 18 con; 0-6 aty)
% Number of variables : 771 ( 0 ^; 754 !; 17 ?; 771 :)
% Comments :
%------------------------------------------------------------------------------
thf(v_Q_type,type,
v_Q: $i > $i > $o ).
thf(v_Z_type,type,
v_Z: $i ).
thf(hAPP_type,type,
hAPP: $i > $i > $i ).
thf(c_Natural_Oupdate_type,type,
c_Natural_Oupdate: $i ).
thf(c_Natural_Osetlocs_type,type,
c_Natural_Osetlocs: $i ).
thf(v_s1_type,type,
v_s1: $i ).
thf(c_Natural_Ogetlocs_type,type,
c_Natural_Ogetlocs: $i ).
thf(v_s_H_type,type,
v_s_H: $i ).
thf(v_X_type,type,
v_X: $i ).
thf(c_Com_ORes_type,type,
c_Com_ORes: $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(hBOOL_type,type,
hBOOL: $i > $o ).
thf(c_Natural_Oevaln_type,type,
c_Natural_Oevaln: $i > $i > $i > $i > $o ).
thf(c_Nat_OSuc_type,type,
c_Nat_OSuc: $i ).
thf(c_Natural_Oevalc_type,type,
c_Natural_Oevalc: $i > $i ).
thf(c_Com_Ovname_OLoc_type,type,
c_Com_Ovname_OLoc: $i > $i ).
thf(c_Com_Ocom_OLocal_type,type,
c_Com_Ocom_OLocal: $i > $i > $i > $i ).
thf(c_Product__Type_OPair_type,type,
c_Product__Type_OPair: $i > $i > $i ).
thf(c_Option_Othe_type,type,
c_Option_Othe: $i > $i ).
thf(tc_Com_Ocom_type,type,
tc_Com_Ocom: $i ).
thf(c_Com_Obody_type,type,
c_Com_Obody: $i ).
thf(c_Com_Ocom_OBODY_type,type,
c_Com_Ocom_OBODY: $i ).
thf(c_Com_Ocom_OAss_type,type,
c_Com_Ocom_OAss: $i > $i > $i ).
thf(c_Com_Ocom_OCall_type,type,
c_Com_Ocom_OCall: $i > $i > $i > $i ).
thf(c_Nitpick_Opair__box_OPairBox_type,type,
c_Nitpick_Opair__box_OPairBox: $i > $i > $i > $i > $i ).
thf(c_Com_Ovname_OGlb_type,type,
c_Com_Ovname_OGlb: $i > $i ).
thf(c_Com_Ovname_Ovname__case_type,type,
c_Com_Ovname_Ovname__case: $i > $i > $i > $i > $i ).
thf(c_New__Random__Sequence_Opos__empty_type,type,
c_New__Random__Sequence_Opos__empty: $i > $i > $i > $i > $i ).
thf(c_New__DSequence_Opos__empty_type,type,
c_New__DSequence_Opos__empty: $i > $i ).
thf(v_pn_type,type,
v_pn: $i ).
thf(c_Natural_Onewlocs_type,type,
c_Natural_Onewlocs: $i ).
thf(c_Com_OArg_type,type,
c_Com_OArg: $i ).
thf(v_a_type,type,
v_a: $i > $i ).
thf(v_na_type,type,
v_na: $i ).
thf(c_Com_Ovname_Ovname__rec_type,type,
c_Com_Ovname_Ovname__rec: $i > $i > $i > $i > $i ).
thf(c_Finite__Set_Ofolding__one__idem_type,type,
c_Finite__Set_Ofolding__one__idem: $i > $i > $i > $o ).
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_New__Random__Sequence_Oneg__single_type,type,
c_New__Random__Sequence_Oneg__single: $i > $i ).
thf(c_New__DSequence_Oneg__single_type,type,
c_New__DSequence_Oneg__single: $i > $i > $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_Lazy__Sequence_Ohb__single_type,type,
c_Lazy__Sequence_Ohb__single: $i > $i > $i ).
thf(c_New__Random__Sequence_Opos__single_type,type,
c_New__Random__Sequence_Opos__single: $i > $i ).
thf(c_New__DSequence_Opos__single_type,type,
c_New__DSequence_Opos__single: $i > $i > $i ).
thf(c_Lazy__Sequence_Osingle_type,type,
c_Lazy__Sequence_Osingle: $i > $i > $i ).
thf(c_Typedef_Otype__definition_type,type,
c_Typedef_Otype__definition: $i > $i > $i > $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_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_Lazy__Sequence_Oempty_type,type,
c_Lazy__Sequence_Oempty: $i > $i ).
thf(c_Finite__Set_Ofolding__image__simple__idem_type,type,
c_Finite__Set_Ofolding__image__simple__idem: $i > $i > $i > $i > $i > $i > $o ).
thf(c_Hoare__Mirabelle_Otriple_Otriple__rec_type,type,
c_Hoare__Mirabelle_Otriple_Otriple__rec: $i > $i > $i > $i > $i ).
thf(v_P_type,type,
v_P: $i > $i > $o ).
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_Int_ORep__Integ_type,type,
c_Int_ORep__Integ: $i ).
thf(c_Hoare__Mirabelle_Otriple_Otriple__case_type,type,
c_Hoare__Mirabelle_Otriple_Otriple__case: $i > $i > $i > $i > $i ).
thf(57,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Com_Ocom_OAss @ C @ B )
!= ( hAPP @ c_Com_Ocom_OBODY @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I30_J) ).
thf(352,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Com_Ocom_OAss @ C @ B )
!= ( hAPP @ c_Com_Ocom_OBODY @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(20,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/sandbox/benchmark/theBenchmark.p',fact_evalc_OAssign) ).
thf(153,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)],[20]) ).
thf(34,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ c_Com_Ocom_OBODY @ C )
!= ( c_Com_Ocom_OAss @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I31_J) ).
thf(252,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ c_Com_Ocom_OBODY @ C )
!= ( c_Com_Ocom_OAss @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(86,axiom,
! [A: $i,B: $i,C: $i,D: $i] : ( 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/sandbox/benchmark/theBenchmark.p',fact_evaln_OAssign) ).
thf(457,plain,
! [A: $i,B: $i,C: $i,D: $i] : ( 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)],[86]) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OLocal @ E @ D @ C ) ) @ B ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oupdate @ A ) @ ( c_Com_Ovname_OLoc @ E ) ) @ ( hAPP @ ( hAPP @ c_Natural_Ogetlocs @ B ) @ E ) ) ) )
<=> ? [F: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oupdate @ A ) @ ( c_Com_Ovname_OLoc @ E ) ) @ ( hAPP @ ( hAPP @ c_Natural_Ogetlocs @ B ) @ E ) )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oupdate @ F ) @ ( c_Com_Ovname_OLoc @ E ) ) @ ( hAPP @ ( hAPP @ c_Natural_Ogetlocs @ B ) @ E ) ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ C ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oupdate @ B ) @ ( c_Com_Ovname_OLoc @ E ) ) @ ( hAPP @ D @ B ) ) ) @ F ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc_Oequations_I3_J) ).
thf(127,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OLocal @ E @ D @ C ) ) @ B ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oupdate @ A ) @ ( c_Com_Ovname_OLoc @ E ) ) @ ( hAPP @ ( hAPP @ c_Natural_Ogetlocs @ B ) @ E ) ) ) )
=> ? [F: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oupdate @ A ) @ ( c_Com_Ovname_OLoc @ E ) ) @ ( hAPP @ ( hAPP @ c_Natural_Ogetlocs @ B ) @ E ) )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oupdate @ F ) @ ( c_Com_Ovname_OLoc @ E ) ) @ ( hAPP @ ( hAPP @ c_Natural_Ogetlocs @ B ) @ E ) ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ C ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oupdate @ B ) @ ( c_Com_Ovname_OLoc @ E ) ) @ ( hAPP @ D @ B ) ) ) @ F ) ) ) )
& ( ? [F: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oupdate @ A ) @ ( c_Com_Ovname_OLoc @ E ) ) @ ( hAPP @ ( hAPP @ c_Natural_Ogetlocs @ B ) @ E ) )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oupdate @ F ) @ ( c_Com_Ovname_OLoc @ E ) ) @ ( hAPP @ ( hAPP @ c_Natural_Ogetlocs @ B ) @ E ) ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ C ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oupdate @ B ) @ ( c_Com_Ovname_OLoc @ E ) ) @ ( hAPP @ D @ B ) ) ) @ F ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OLocal @ E @ D @ C ) ) @ B ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oupdate @ A ) @ ( c_Com_Ovname_OLoc @ E ) ) @ ( hAPP @ ( hAPP @ c_Natural_Ogetlocs @ B ) @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(25,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/sandbox/benchmark/theBenchmark.p',fact_Pair__eq) ).
thf(171,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)],[25]) ).
thf(72,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OCall @ F @ E @ D ) @ C @ B @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oupdate @ ( hAPP @ ( hAPP @ c_Natural_Osetlocs @ A ) @ ( hAPP @ c_Natural_Ogetlocs @ C ) ) ) @ F ) @ ( hAPP @ ( hAPP @ c_Natural_Ogetlocs @ A ) @ c_Com_ORes ) ) )
<=> ? [G: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oupdate @ ( hAPP @ ( hAPP @ c_Natural_Osetlocs @ A ) @ ( hAPP @ c_Natural_Ogetlocs @ C ) ) ) @ F ) @ ( hAPP @ ( hAPP @ c_Natural_Ogetlocs @ A ) @ c_Com_ORes ) )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oupdate @ ( hAPP @ ( hAPP @ c_Natural_Osetlocs @ G ) @ ( hAPP @ c_Natural_Ogetlocs @ C ) ) ) @ F ) @ ( hAPP @ ( hAPP @ c_Natural_Ogetlocs @ G ) @ c_Com_ORes ) ) )
& ( c_Natural_Oevaln @ ( hAPP @ c_Com_Ocom_OBODY @ E ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oupdate @ ( hAPP @ ( hAPP @ c_Natural_Osetlocs @ C ) @ c_Natural_Onewlocs ) ) @ ( c_Com_Ovname_OLoc @ c_Com_OArg ) ) @ ( hAPP @ D @ C ) ) @ B @ G ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln_Oequations_I10_J) ).
thf(408,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OCall @ F @ E @ D ) @ C @ B @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oupdate @ ( hAPP @ ( hAPP @ c_Natural_Osetlocs @ A ) @ ( hAPP @ c_Natural_Ogetlocs @ C ) ) ) @ F ) @ ( hAPP @ ( hAPP @ c_Natural_Ogetlocs @ A ) @ c_Com_ORes ) ) )
=> ? [G: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oupdate @ ( hAPP @ ( hAPP @ c_Natural_Osetlocs @ A ) @ ( hAPP @ c_Natural_Ogetlocs @ C ) ) ) @ F ) @ ( hAPP @ ( hAPP @ c_Natural_Ogetlocs @ A ) @ c_Com_ORes ) )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oupdate @ ( hAPP @ ( hAPP @ c_Natural_Osetlocs @ G ) @ ( hAPP @ c_Natural_Ogetlocs @ C ) ) ) @ F ) @ ( hAPP @ ( hAPP @ c_Natural_Ogetlocs @ G ) @ c_Com_ORes ) ) )
& ( c_Natural_Oevaln @ ( hAPP @ c_Com_Ocom_OBODY @ E ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oupdate @ ( hAPP @ ( hAPP @ c_Natural_Osetlocs @ C ) @ c_Natural_Onewlocs ) ) @ ( c_Com_Ovname_OLoc @ c_Com_OArg ) ) @ ( hAPP @ D @ C ) ) @ B @ G ) ) )
& ( ? [G: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oupdate @ ( hAPP @ ( hAPP @ c_Natural_Osetlocs @ A ) @ ( hAPP @ c_Natural_Ogetlocs @ C ) ) ) @ F ) @ ( hAPP @ ( hAPP @ c_Natural_Ogetlocs @ A ) @ c_Com_ORes ) )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oupdate @ ( hAPP @ ( hAPP @ c_Natural_Osetlocs @ G ) @ ( hAPP @ c_Natural_Ogetlocs @ C ) ) ) @ F ) @ ( hAPP @ ( hAPP @ c_Natural_Ogetlocs @ G ) @ c_Com_ORes ) ) )
& ( c_Natural_Oevaln @ ( hAPP @ c_Com_Ocom_OBODY @ E ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oupdate @ ( hAPP @ ( hAPP @ c_Natural_Osetlocs @ C ) @ c_Natural_Onewlocs ) ) @ ( c_Com_Ovname_OLoc @ c_Com_OArg ) ) @ ( hAPP @ D @ C ) ) @ B @ G ) )
=> ( c_Natural_Oevaln @ ( c_Com_Ocom_OCall @ F @ E @ D ) @ C @ B @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oupdate @ ( hAPP @ ( hAPP @ c_Natural_Osetlocs @ A ) @ ( hAPP @ c_Natural_Ogetlocs @ C ) ) ) @ F ) @ ( hAPP @ ( hAPP @ c_Natural_Ogetlocs @ A ) @ c_Com_ORes ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(39,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Com_Ovname_Ovname__case @ D @ C @ B @ ( c_Com_Ovname_OLoc @ A ) )
= ( hAPP @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vname_Osimps_I6_J) ).
thf(276,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Com_Ovname_Ovname__case @ D @ C @ B @ ( c_Com_Ovname_OLoc @ A ) )
= ( hAPP @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(67,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_New__DSequence_Opos__single @ C @ B ) @ A )
= ( c_Lazy__Sequence_Osingle @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_New__DSequence_Opos__single__def) ).
thf(389,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_New__DSequence_Opos__single @ C @ B ) @ A )
= ( c_Lazy__Sequence_Osingle @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(27,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/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I1_J) ).
thf(184,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)],[27]) ).
thf(61,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/sandbox/benchmark/theBenchmark.p',fact_pair__box_Orecs) ).
thf(372,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)],[61]) ).
thf(12,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/sandbox/benchmark/theBenchmark.p',fact_evalc_Oequations_I2_J) ).
thf(125,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)],[12]) ).
thf(75,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( c_Finite__Set_Ofolding__image__simple__idem @ G @ F @ E @ D @ C @ B )
=> ( ( hAPP @ ( hAPP @ E @ A ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple__idem_Oidem) ).
thf(421,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( c_Finite__Set_Ofolding__image__simple__idem @ G @ F @ E @ D @ C @ B )
=> ( ( hAPP @ ( hAPP @ E @ A ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(73,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_New__DSequence_Opos__empty @ B ) @ A )
= ( c_Lazy__Sequence_Oempty @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_New__DSequence_Opos__empty__def) ).
thf(416,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_New__DSequence_Opos__empty @ B ) @ A )
= ( c_Lazy__Sequence_Oempty @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(83,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/sandbox/benchmark/theBenchmark.p',fact_pair__box_Osimps_I2_J) ).
thf(448,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)],[83]) ).
thf(48,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/sandbox/benchmark/theBenchmark.p',fact_Pair__inject) ).
thf(316,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)],[48]) ).
thf(11,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Natural_Oevaln @ ( hAPP @ c_Com_Ocom_OBODY @ D ) @ C @ B @ A )
=> ~ ! [E: $i] :
( ( B
= ( hAPP @ c_Nat_OSuc @ E ) )
=> ~ ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ D ) ) @ C @ E @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln__elim__cases_I6_J) ).
thf(121,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Natural_Oevaln @ ( hAPP @ c_Com_Ocom_OBODY @ D ) @ C @ B @ A )
=> ~ ! [E: $i] :
( ( B
= ( hAPP @ c_Nat_OSuc @ E ) )
=> ~ ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ D ) ) @ C @ E @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(56,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Com_Ocom_OCall @ D @ C @ B )
!= ( hAPP @ c_Com_Ocom_OBODY @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I63_J) ).
thf(348,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Com_Ocom_OCall @ D @ C @ B )
!= ( hAPP @ c_Com_Ocom_OBODY @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(18,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OLocal @ E @ D @ C ) ) @ B ) @ A ) )
=> ~ ! [F: $i] :
( ( A
= ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oupdate @ F ) @ ( c_Com_Ovname_OLoc @ E ) ) @ ( hAPP @ ( hAPP @ c_Natural_Ogetlocs @ B ) @ E ) ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ C ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oupdate @ B ) @ ( c_Com_Ovname_OLoc @ E ) ) @ ( hAPP @ D @ B ) ) ) @ F ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc__elim__cases_I3_J) ).
thf(147,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OLocal @ E @ D @ C ) ) @ B ) @ A ) )
=> ~ ! [F: $i] :
( ( A
= ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oupdate @ F ) @ ( c_Com_Ovname_OLoc @ E ) ) @ ( hAPP @ ( hAPP @ c_Natural_Ogetlocs @ B ) @ E ) ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ C ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oupdate @ B ) @ ( c_Com_Ovname_OLoc @ E ) ) @ ( hAPP @ D @ B ) ) ) @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(77,axiom,
! [A: $i,B: $i,C: $i,D: $i] : ( 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/sandbox/benchmark/theBenchmark.p',fact_evaln_Oequations_I2_J) ).
thf(428,plain,
! [A: $i,B: $i,C: $i,D: $i] : ( 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)],[77]) ).
thf(64,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/sandbox/benchmark/theBenchmark.p',fact_vname_Orecs_I1_J) ).
thf(380,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)],[64]) ).
thf(31,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/sandbox/benchmark/theBenchmark.p',fact_pair__box_Oinject) ).
thf(220,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)],[31]) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ E ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oupdate @ D ) @ ( c_Com_Ovname_OLoc @ C ) ) @ ( hAPP @ B @ D ) ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OLocal @ C @ B @ E ) ) @ D ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oupdate @ A ) @ ( c_Com_Ovname_OLoc @ C ) ) @ ( hAPP @ ( hAPP @ c_Natural_Ogetlocs @ D ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc_OLocal) ).
thf(102,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ E ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oupdate @ D ) @ ( c_Com_Ovname_OLoc @ C ) ) @ ( hAPP @ B @ D ) ) ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OLocal @ C @ B @ E ) ) @ D ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oupdate @ A ) @ ( c_Com_Ovname_OLoc @ C ) ) @ ( hAPP @ ( hAPP @ c_Natural_Ogetlocs @ D ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(52,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Com_Ovname_Ovname__rec @ D @ C @ B @ ( c_Com_Ovname_OLoc @ A ) )
= ( hAPP @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vname_Orecs_I2_J) ).
thf(334,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Com_Ovname_Ovname__rec @ D @ C @ B @ ( c_Com_Ovname_OLoc @ A ) )
= ( hAPP @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(36,axiom,
! [A: $i,B: $i] :
( ( ( c_Com_Ovname_OGlb @ B )
= ( c_Com_Ovname_OGlb @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vname_Osimps_I1_J) ).
thf(260,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)],[36]) ).
thf(22,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ C ) @ B ) @ A ) )
<=> ? [D: $i] : ( c_Natural_Oevaln @ C @ B @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eval__eq) ).
thf(160,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ C ) @ B ) @ A ) )
=> ? [D: $i] : ( c_Natural_Oevaln @ C @ B @ D @ A ) )
& ( ? [D: $i] : ( c_Natural_Oevaln @ C @ B @ D @ A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ C ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(68,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/sandbox/benchmark/theBenchmark.p',fact_type__definition_ORep__inject) ).
thf(392,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)],[68]) ).
thf(23,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Com_Ocom_OLocal @ F @ E @ D )
!= ( c_Com_Ocom_OCall @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I42_J) ).
thf(165,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Com_Ocom_OLocal @ F @ E @ D )
!= ( c_Com_Ocom_OCall @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(58,axiom,
! [A: $i,B: $i] :
( ( ( c_Com_Ovname_OLoc @ B )
= ( c_Com_Ovname_OLoc @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vname_Osimps_I2_J) ).
thf(356,plain,
! [A: $i,B: $i] :
( ( ( ( c_Com_Ovname_OLoc @ B )
= ( c_Com_Ovname_OLoc @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( c_Com_Ovname_OLoc @ B )
= ( c_Com_Ovname_OLoc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(24,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Natural_Oevaln @ D @ C @ B @ A )
=> ( c_Natural_Oevaln @ D @ C @ ( hAPP @ c_Nat_OSuc @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln__Suc) ).
thf(169,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Natural_Oevaln @ D @ C @ B @ A )
=> ( c_Natural_Oevaln @ D @ C @ ( hAPP @ c_Nat_OSuc @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ D ) ) @ C @ B @ A )
=> ( c_Natural_Oevaln @ ( hAPP @ c_Com_Ocom_OBODY @ D ) @ C @ ( hAPP @ c_Nat_OSuc @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln_OBody) ).
thf(109,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ D ) ) @ C @ B @ A )
=> ( c_Natural_Oevaln @ ( hAPP @ c_Com_Ocom_OBODY @ D ) @ C @ ( hAPP @ c_Nat_OSuc @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(35,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Com_Ocom_OLocal @ E @ D @ C )
!= ( c_Com_Ocom_OAss @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I23_J) ).
thf(256,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Com_Ocom_OLocal @ E @ D @ C )
!= ( c_Com_Ocom_OAss @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(76,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( hAPP @ B @ C )
= ( hAPP @ A @ C ) )
=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ext) ).
thf(425,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( hAPP @ B @ C )
= ( hAPP @ A @ C ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(78,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/sandbox/benchmark/theBenchmark.p',fact_type__definition_ORep__inverse) ).
thf(430,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)],[78]) ).
thf(40,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_New__Random__Sequence_Opos__empty @ D @ C @ B @ A )
= ( c_New__DSequence_Opos__empty @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__empty__def) ).
thf(279,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_New__Random__Sequence_Opos__empty @ D @ C @ B @ A )
= ( c_New__DSequence_Opos__empty @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(26,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ c_Com_Ocom_OBODY @ D )
!= ( c_Com_Ocom_OLocal @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I41_J) ).
thf(180,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ c_Com_Ocom_OBODY @ D )
!= ( c_Com_Ocom_OLocal @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(62,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_New__Random__Sequence_Oneg__single @ E ) @ D ) @ C ) @ B ) @ A )
= ( c_New__DSequence_Oneg__single @ E @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__single__def) ).
thf(375,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_New__Random__Sequence_Oneg__single @ E ) @ D ) @ C ) @ B ) @ A )
= ( c_New__DSequence_Oneg__single @ E @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(70,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/sandbox/benchmark/theBenchmark.p',fact_prod_Orecs) ).
thf(402,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)],[70]) ).
thf(42,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Com_Ocom_OAss @ E @ D )
!= ( c_Com_Ocom_OLocal @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I22_J) ).
thf(286,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Com_Ocom_OAss @ E @ D )
!= ( c_Com_Ocom_OLocal @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(10,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/sandbox/benchmark/theBenchmark.p',fact_com__det) ).
thf(118,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)],[10]) ).
thf(81,axiom,
v_P @ v_Z @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oupdate @ ( hAPP @ ( hAPP @ c_Natural_Osetlocs @ v_s_H ) @ c_Natural_Onewlocs ) ) @ ( c_Com_Ovname_OLoc @ c_Com_OArg ) ) @ ( v_a @ v_s_H ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_2) ).
thf(445,plain,
v_P @ v_Z @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oupdate @ ( hAPP @ ( hAPP @ c_Natural_Osetlocs @ v_s_H ) @ c_Natural_Onewlocs ) ) @ ( c_Com_Ovname_OLoc @ c_Com_OArg ) ) @ ( v_a @ v_s_H ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(88,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Hoare__Mirabelle_Otriple_Otriple__case @ 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/sandbox/benchmark/theBenchmark.p',fact_triple_Osimps_I2_J) ).
thf(466,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Hoare__Mirabelle_Otriple_Otriple__case @ 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)],[88]) ).
thf(9,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 ) @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ B ) ) ) @ A ) )
<=> ( c_Hoare__Mirabelle_Otriple__valid @ E @ ( hAPP @ c_Nat_OSuc @ D ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ E ) @ C ) @ ( hAPP @ c_Com_Ocom_OBODY @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Body__triple__valid__Suc) ).
thf(113,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 ) @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ B ) ) ) @ A ) )
=> ( c_Hoare__Mirabelle_Otriple__valid @ E @ ( hAPP @ c_Nat_OSuc @ D ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ E ) @ C ) @ ( hAPP @ c_Com_Ocom_OBODY @ B ) ) @ A ) ) )
& ( ( c_Hoare__Mirabelle_Otriple__valid @ E @ ( hAPP @ c_Nat_OSuc @ D ) @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ E ) @ C ) @ ( hAPP @ c_Com_Ocom_OBODY @ B ) ) @ A ) )
=> ( c_Hoare__Mirabelle_Otriple__valid @ E @ D @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_Hoare__Mirabelle_Otriple_Otriple @ E ) @ C ) @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ B ) ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(74,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Natural_Oevaln @ F @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oupdate @ E ) @ ( c_Com_Ovname_OLoc @ D ) ) @ ( hAPP @ C @ E ) ) @ B @ A )
=> ( c_Natural_Oevaln @ ( c_Com_Ocom_OLocal @ D @ C @ F ) @ E @ B @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oupdate @ A ) @ ( c_Com_Ovname_OLoc @ D ) ) @ ( hAPP @ ( hAPP @ c_Natural_Ogetlocs @ E ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln_OLocal) ).
thf(419,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Natural_Oevaln @ F @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oupdate @ E ) @ ( c_Com_Ovname_OLoc @ D ) ) @ ( hAPP @ C @ E ) ) @ B @ A )
=> ( c_Natural_Oevaln @ ( c_Com_Ocom_OLocal @ D @ C @ F ) @ E @ B @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oupdate @ A ) @ ( c_Com_Ovname_OLoc @ D ) ) @ ( hAPP @ ( hAPP @ c_Natural_Ogetlocs @ E ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(84,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OCall @ F @ E @ D ) @ C @ B @ A )
=> ~ ! [G: $i] :
( ( A
= ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oupdate @ ( hAPP @ ( hAPP @ c_Natural_Osetlocs @ G ) @ ( hAPP @ c_Natural_Ogetlocs @ C ) ) ) @ F ) @ ( hAPP @ ( hAPP @ c_Natural_Ogetlocs @ G ) @ c_Com_ORes ) ) )
=> ~ ( c_Natural_Oevaln @ ( hAPP @ c_Com_Ocom_OBODY @ E ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oupdate @ ( hAPP @ ( hAPP @ c_Natural_Osetlocs @ C ) @ c_Natural_Onewlocs ) ) @ ( c_Com_Ovname_OLoc @ c_Com_OArg ) ) @ ( hAPP @ D @ C ) ) @ B @ G ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln__elim__cases_I7_J) ).
thf(451,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OCall @ F @ E @ D ) @ C @ B @ A )
=> ~ ! [G: $i] :
( ( A
= ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oupdate @ ( hAPP @ ( hAPP @ c_Natural_Osetlocs @ G ) @ ( hAPP @ c_Natural_Ogetlocs @ C ) ) ) @ F ) @ ( hAPP @ ( hAPP @ c_Natural_Ogetlocs @ G ) @ c_Com_ORes ) ) )
=> ~ ( c_Natural_Oevaln @ ( hAPP @ c_Com_Ocom_OBODY @ E ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oupdate @ ( hAPP @ ( hAPP @ c_Natural_Osetlocs @ C ) @ c_Natural_Onewlocs ) ) @ ( c_Com_Ovname_OLoc @ c_Com_OArg ) ) @ ( hAPP @ D @ C ) ) @ B @ G ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(33,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ c_Com_Ocom_OBODY @ B )
= ( hAPP @ c_Com_Ocom_OBODY @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I6_J) ).
thf(245,plain,
! [A: $i,B: $i] :
( ( ( ( hAPP @ c_Com_Ocom_OBODY @ B )
= ( hAPP @ c_Com_Ocom_OBODY @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( hAPP @ c_Com_Ocom_OBODY @ B )
= ( hAPP @ c_Com_Ocom_OBODY @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(79,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OLocal @ F @ E @ D ) @ C @ B @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oupdate @ A ) @ ( c_Com_Ovname_OLoc @ F ) ) @ ( hAPP @ ( hAPP @ c_Natural_Ogetlocs @ C ) @ F ) ) )
<=> ? [G: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oupdate @ A ) @ ( c_Com_Ovname_OLoc @ F ) ) @ ( hAPP @ ( hAPP @ c_Natural_Ogetlocs @ C ) @ F ) )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oupdate @ G ) @ ( c_Com_Ovname_OLoc @ F ) ) @ ( hAPP @ ( hAPP @ c_Natural_Ogetlocs @ C ) @ F ) ) )
& ( c_Natural_Oevaln @ D @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oupdate @ C ) @ ( c_Com_Ovname_OLoc @ F ) ) @ ( hAPP @ E @ C ) ) @ B @ G ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln_Oequations_I3_J) ).
thf(434,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OLocal @ F @ E @ D ) @ C @ B @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oupdate @ A ) @ ( c_Com_Ovname_OLoc @ F ) ) @ ( hAPP @ ( hAPP @ c_Natural_Ogetlocs @ C ) @ F ) ) )
=> ? [G: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oupdate @ A ) @ ( c_Com_Ovname_OLoc @ F ) ) @ ( hAPP @ ( hAPP @ c_Natural_Ogetlocs @ C ) @ F ) )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oupdate @ G ) @ ( c_Com_Ovname_OLoc @ F ) ) @ ( hAPP @ ( hAPP @ c_Natural_Ogetlocs @ C ) @ F ) ) )
& ( c_Natural_Oevaln @ D @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oupdate @ C ) @ ( c_Com_Ovname_OLoc @ F ) ) @ ( hAPP @ E @ C ) ) @ B @ G ) ) )
& ( ? [G: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oupdate @ A ) @ ( c_Com_Ovname_OLoc @ F ) ) @ ( hAPP @ ( hAPP @ c_Natural_Ogetlocs @ C ) @ F ) )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oupdate @ G ) @ ( c_Com_Ovname_OLoc @ F ) ) @ ( hAPP @ ( hAPP @ c_Natural_Ogetlocs @ C ) @ F ) ) )
& ( c_Natural_Oevaln @ D @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oupdate @ C ) @ ( c_Com_Ovname_OLoc @ F ) ) @ ( hAPP @ E @ C ) ) @ B @ G ) )
=> ( c_Natural_Oevaln @ ( c_Com_Ocom_OLocal @ F @ E @ D ) @ C @ B @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oupdate @ A ) @ ( c_Com_Ovname_OLoc @ F ) ) @ ( hAPP @ ( hAPP @ c_Natural_Ogetlocs @ C ) @ F ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(55,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ c_Nat_OSuc @ B )
= ( hAPP @ c_Nat_OSuc @ A ) )
=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__inject) ).
thf(345,plain,
! [A: $i,B: $i] :
( ( ( hAPP @ c_Nat_OSuc @ B )
= ( hAPP @ c_Nat_OSuc @ A ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(15,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/sandbox/benchmark/theBenchmark.p',fact_evalc__elim__cases_I2_J) ).
thf(140,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)],[15]) ).
thf(30,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ c_Nat_OSuc @ B )
= ( hAPP @ c_Nat_OSuc @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat_Oinject) ).
thf(213,plain,
! [A: $i,B: $i] :
( ( ( ( hAPP @ c_Nat_OSuc @ B )
= ( hAPP @ c_Nat_OSuc @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( hAPP @ c_Nat_OSuc @ B )
= ( hAPP @ c_Nat_OSuc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(3,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] :
( ( c_Natural_Oevaln @ B @ G @ D @ H )
=> ( hBOOL @ ( hAPP @ ( hAPP @ A @ F ) @ H ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_triple__valid__def2) ).
thf(91,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] :
( ( 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] :
( ( 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)],[3]) ).
thf(21,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( hAPP @ c_Com_Ocom_OBODY @ C ) ) @ B ) @ A ) )
<=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ C ) ) ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc_Oequations_I9_J) ).
thf(155,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( hAPP @ c_Com_Ocom_OBODY @ C ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ C ) ) ) @ B ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ C ) ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( hAPP @ c_Com_Ocom_OBODY @ C ) ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(51,axiom,
! [A: $i] :
( A
!= ( hAPP @ c_Nat_OSuc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_n__not__Suc__n) ).
thf(330,plain,
! [A: $i] :
( A
!= ( hAPP @ c_Nat_OSuc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(69,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( 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/sandbox/benchmark/theBenchmark.p',fact_evaln__elim__cases_I2_J) ).
thf(399,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( 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)],[69]) ).
thf(85,axiom,
! [A: $i,B: $i] :
( ( v_P @ A @ B )
=> ! [C: $i] :
( ( c_Natural_Oevaln @ ( hAPP @ c_Com_Ocom_OBODY @ v_pn ) @ B @ ( hAPP @ c_Nat_OSuc @ v_na ) @ C )
=> ( v_Q @ A @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oupdate @ ( hAPP @ ( hAPP @ c_Natural_Osetlocs @ C ) @ ( hAPP @ c_Natural_Ogetlocs @ v_s_H ) ) ) @ v_X ) @ ( hAPP @ ( hAPP @ c_Natural_Ogetlocs @ C ) @ c_Com_ORes ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
thf(455,plain,
! [A: $i,B: $i] :
( ( v_P @ A @ B )
=> ! [C: $i] :
( ( c_Natural_Oevaln @ ( hAPP @ c_Com_Ocom_OBODY @ v_pn ) @ B @ ( hAPP @ c_Nat_OSuc @ v_na ) @ C )
=> ( v_Q @ A @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oupdate @ ( hAPP @ ( hAPP @ c_Natural_Osetlocs @ C ) @ ( hAPP @ c_Natural_Ogetlocs @ v_s_H ) ) ) @ v_X ) @ ( hAPP @ ( hAPP @ c_Natural_Ogetlocs @ C ) @ c_Com_ORes ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(46,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCall @ E @ D @ C ) ) @ B ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oupdate @ ( hAPP @ ( hAPP @ c_Natural_Osetlocs @ A ) @ ( hAPP @ c_Natural_Ogetlocs @ B ) ) ) @ E ) @ ( hAPP @ ( hAPP @ c_Natural_Ogetlocs @ A ) @ c_Com_ORes ) ) ) )
<=> ? [F: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oupdate @ ( hAPP @ ( hAPP @ c_Natural_Osetlocs @ A ) @ ( hAPP @ c_Natural_Ogetlocs @ B ) ) ) @ E ) @ ( hAPP @ ( hAPP @ c_Natural_Ogetlocs @ A ) @ c_Com_ORes ) )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oupdate @ ( hAPP @ ( hAPP @ c_Natural_Osetlocs @ F ) @ ( hAPP @ c_Natural_Ogetlocs @ B ) ) ) @ E ) @ ( hAPP @ ( hAPP @ c_Natural_Ogetlocs @ F ) @ c_Com_ORes ) ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( hAPP @ c_Com_Ocom_OBODY @ D ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oupdate @ ( hAPP @ ( hAPP @ c_Natural_Osetlocs @ B ) @ c_Natural_Onewlocs ) ) @ ( c_Com_Ovname_OLoc @ c_Com_OArg ) ) @ ( hAPP @ C @ B ) ) ) @ F ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc_Oequations_I10_J) ).
thf(306,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCall @ E @ D @ C ) ) @ B ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oupdate @ ( hAPP @ ( hAPP @ c_Natural_Osetlocs @ A ) @ ( hAPP @ c_Natural_Ogetlocs @ B ) ) ) @ E ) @ ( hAPP @ ( hAPP @ c_Natural_Ogetlocs @ A ) @ c_Com_ORes ) ) ) )
=> ? [F: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oupdate @ ( hAPP @ ( hAPP @ c_Natural_Osetlocs @ A ) @ ( hAPP @ c_Natural_Ogetlocs @ B ) ) ) @ E ) @ ( hAPP @ ( hAPP @ c_Natural_Ogetlocs @ A ) @ c_Com_ORes ) )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oupdate @ ( hAPP @ ( hAPP @ c_Natural_Osetlocs @ F ) @ ( hAPP @ c_Natural_Ogetlocs @ B ) ) ) @ E ) @ ( hAPP @ ( hAPP @ c_Natural_Ogetlocs @ F ) @ c_Com_ORes ) ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( hAPP @ c_Com_Ocom_OBODY @ D ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oupdate @ ( hAPP @ ( hAPP @ c_Natural_Osetlocs @ B ) @ c_Natural_Onewlocs ) ) @ ( c_Com_Ovname_OLoc @ c_Com_OArg ) ) @ ( hAPP @ C @ B ) ) ) @ F ) ) ) )
& ( ? [F: $i] :
( ( ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oupdate @ ( hAPP @ ( hAPP @ c_Natural_Osetlocs @ A ) @ ( hAPP @ c_Natural_Ogetlocs @ B ) ) ) @ E ) @ ( hAPP @ ( hAPP @ c_Natural_Ogetlocs @ A ) @ c_Com_ORes ) )
= ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oupdate @ ( hAPP @ ( hAPP @ c_Natural_Osetlocs @ F ) @ ( hAPP @ c_Natural_Ogetlocs @ B ) ) ) @ E ) @ ( hAPP @ ( hAPP @ c_Natural_Ogetlocs @ F ) @ c_Com_ORes ) ) )
& ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( hAPP @ c_Com_Ocom_OBODY @ D ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oupdate @ ( hAPP @ ( hAPP @ c_Natural_Osetlocs @ B ) @ c_Natural_Onewlocs ) ) @ ( c_Com_Ovname_OLoc @ c_Com_OArg ) ) @ ( hAPP @ C @ B ) ) ) @ F ) ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCall @ E @ D @ C ) ) @ B ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oupdate @ ( hAPP @ ( hAPP @ c_Natural_Osetlocs @ A ) @ ( hAPP @ c_Natural_Ogetlocs @ B ) ) ) @ E ) @ ( hAPP @ ( hAPP @ c_Natural_Ogetlocs @ A ) @ c_Com_ORes ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(14,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Natural_Oevaln @ ( hAPP @ c_Com_Ocom_OBODY @ D ) @ C @ ( hAPP @ c_Nat_OSuc @ B ) @ A )
<=> ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ D ) ) @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln_Oequations_I9_J) ).
thf(135,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_Natural_Oevaln @ ( hAPP @ c_Com_Ocom_OBODY @ D ) @ C @ ( hAPP @ c_Nat_OSuc @ B ) @ A )
=> ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ D ) ) @ C @ B @ A ) )
& ( ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ D ) ) @ C @ B @ A )
=> ( c_Natural_Oevaln @ ( hAPP @ c_Com_Ocom_OBODY @ D ) @ C @ ( hAPP @ c_Nat_OSuc @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(29,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ c_Com_Ocom_OBODY @ D )
!= ( c_Com_Ocom_OCall @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I62_J) ).
thf(209,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ c_Com_Ocom_OBODY @ D )
!= ( c_Com_Ocom_OCall @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(17,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ C ) @ B ) @ A ) )
=> ? [D: $i] : ( c_Natural_Oevaln @ C @ B @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc__evaln) ).
thf(145,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ C ) @ B ) @ A ) )
=> ? [D: $i] : ( c_Natural_Oevaln @ C @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(45,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/sandbox/benchmark/theBenchmark.p',fact_triple_Oinject) ).
thf(295,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)],[45]) ).
thf(41,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Com_Ocom_OLocal @ D @ C @ B )
!= ( hAPP @ c_Com_Ocom_OBODY @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I40_J) ).
thf(282,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Com_Ocom_OLocal @ D @ C @ B )
!= ( hAPP @ c_Com_Ocom_OBODY @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(66,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_New__Random__Sequence_Opos__single @ E ) @ D ) @ C ) @ B ) @ A )
= ( c_New__DSequence_Opos__single @ E @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__single__def) ).
thf(386,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_New__Random__Sequence_Opos__single @ E ) @ D ) @ C ) @ B ) @ A )
= ( c_New__DSequence_Opos__single @ E @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(47,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( hAPP @ c_Com_Ocom_OBODY @ E ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oupdate @ ( hAPP @ ( hAPP @ c_Natural_Osetlocs @ D ) @ c_Natural_Onewlocs ) ) @ ( c_Com_Ovname_OLoc @ c_Com_OArg ) ) @ ( hAPP @ C @ D ) ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCall @ A @ E @ C ) ) @ D ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oupdate @ ( hAPP @ ( hAPP @ c_Natural_Osetlocs @ B ) @ ( hAPP @ c_Natural_Ogetlocs @ D ) ) ) @ A ) @ ( hAPP @ ( hAPP @ c_Natural_Ogetlocs @ B ) @ c_Com_ORes ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc_OCall) ).
thf(314,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( hAPP @ c_Com_Ocom_OBODY @ E ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oupdate @ ( hAPP @ ( hAPP @ c_Natural_Osetlocs @ D ) @ c_Natural_Onewlocs ) ) @ ( c_Com_Ovname_OLoc @ c_Com_OArg ) ) @ ( hAPP @ C @ D ) ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCall @ A @ E @ C ) ) @ D ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oupdate @ ( hAPP @ ( hAPP @ c_Natural_Osetlocs @ B ) @ ( hAPP @ c_Natural_Ogetlocs @ D ) ) ) @ A ) @ ( hAPP @ ( hAPP @ c_Natural_Ogetlocs @ B ) @ c_Com_ORes ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(82,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Natural_Oevaln @ ( hAPP @ c_Com_Ocom_OBODY @ F ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oupdate @ ( hAPP @ ( hAPP @ c_Natural_Osetlocs @ E ) @ c_Natural_Onewlocs ) ) @ ( c_Com_Ovname_OLoc @ c_Com_OArg ) ) @ ( hAPP @ D @ E ) ) @ C @ B )
=> ( c_Natural_Oevaln @ ( c_Com_Ocom_OCall @ A @ F @ D ) @ E @ C @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oupdate @ ( hAPP @ ( hAPP @ c_Natural_Osetlocs @ B ) @ ( hAPP @ c_Natural_Ogetlocs @ E ) ) ) @ A ) @ ( hAPP @ ( hAPP @ c_Natural_Ogetlocs @ B ) @ c_Com_ORes ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln_OCall) ).
thf(446,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Natural_Oevaln @ ( hAPP @ c_Com_Ocom_OBODY @ F ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oupdate @ ( hAPP @ ( hAPP @ c_Natural_Osetlocs @ E ) @ c_Natural_Onewlocs ) ) @ ( c_Com_Ovname_OLoc @ c_Com_OArg ) ) @ ( hAPP @ D @ E ) ) @ C @ B )
=> ( c_Natural_Oevaln @ ( c_Com_Ocom_OCall @ A @ F @ D ) @ E @ C @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oupdate @ ( hAPP @ ( hAPP @ c_Natural_Osetlocs @ B ) @ ( hAPP @ c_Natural_Ogetlocs @ E ) ) ) @ A ) @ ( hAPP @ ( hAPP @ c_Natural_Ogetlocs @ B ) @ c_Com_ORes ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(16,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( hAPP @ c_Com_Ocom_OBODY @ C ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ C ) ) ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc__elim__cases_I6_J) ).
thf(143,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( hAPP @ c_Com_Ocom_OBODY @ C ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ C ) ) ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(32,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( c_Com_Ocom_OCall @ F @ E @ D )
= ( c_Com_Ocom_OCall @ C @ B @ A ) )
<=> ( ( F = C )
& ( E = B )
& ( D = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I7_J) ).
thf(231,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ( c_Com_Ocom_OCall @ F @ E @ D )
= ( c_Com_Ocom_OCall @ C @ B @ A ) )
=> ( ( F = C )
& ( E = B )
& ( D = A ) ) )
& ( ( ( F = C )
& ( E = B )
& ( D = A ) )
=> ( ( c_Com_Ocom_OCall @ F @ E @ D )
= ( c_Com_Ocom_OCall @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(6,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/sandbox/benchmark/theBenchmark.p',fact_split__paired__All) ).
thf(104,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)],[6]) ).
thf(60,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/sandbox/benchmark/theBenchmark.p',fact_folding__one__idem_Oidem) ).
thf(368,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)],[60]) ).
thf(38,axiom,
! [A: $i,B: $i] :
( ( c_Com_Ovname_OLoc @ B )
!= ( c_Com_Ovname_OGlb @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vname_Osimps_I4_J) ).
thf(272,plain,
! [A: $i,B: $i] :
( ( c_Com_Ovname_OLoc @ B )
!= ( c_Com_Ovname_OGlb @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(65,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_New__DSequence_Oneg__single @ C @ B ) @ A )
= ( c_Lazy__Sequence_Ohb__single @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_New__DSequence_Oneg__single__def) ).
thf(383,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_New__DSequence_Oneg__single @ C @ B ) @ A )
= ( c_Lazy__Sequence_Ohb__single @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(43,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Com_Ocom_OCall @ F @ E @ D )
!= ( c_Com_Ocom_OLocal @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I43_J) ).
thf(290,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Com_Ocom_OCall @ F @ E @ D )
!= ( c_Com_Ocom_OLocal @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(63,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/sandbox/benchmark/theBenchmark.p',fact_rp__inv__image__rp) ).
thf(378,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)],[63]) ).
thf(19,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ C ) ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( hAPP @ c_Com_Ocom_OBODY @ C ) ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc_OBody) ).
thf(151,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ C ) ) ) @ B ) @ A ) )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( hAPP @ c_Com_Ocom_OBODY @ C ) ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(71,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/sandbox/benchmark/theBenchmark.p',fact_pos__not__random__dseq__def) ).
thf(405,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)],[71]) ).
thf(50,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Com_Ocom_OAss @ E @ D )
!= ( c_Com_Ocom_OCall @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I32_J) ).
thf(326,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Com_Ocom_OAss @ E @ D )
!= ( c_Com_Ocom_OCall @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(44,axiom,
c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ v_pn ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oupdate @ ( hAPP @ ( hAPP @ c_Natural_Osetlocs @ v_s_H ) @ c_Natural_Onewlocs ) ) @ ( c_Com_Ovname_OLoc @ c_Com_OArg ) ) @ ( v_a @ v_s_H ) ) @ v_na @ v_s1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_3) ).
thf(294,plain,
c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ v_pn ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oupdate @ ( hAPP @ ( hAPP @ c_Natural_Osetlocs @ v_s_H ) @ c_Natural_Onewlocs ) ) @ ( c_Com_Ovname_OLoc @ c_Com_OArg ) ) @ ( v_a @ v_s_H ) ) @ v_na @ v_s1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(54,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Com_Ocom_OCall @ E @ D @ C )
!= ( c_Com_Ocom_OAss @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I33_J) ).
thf(341,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Com_Ocom_OCall @ E @ D @ C )
!= ( c_Com_Ocom_OAss @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(37,axiom,
! [A: $i] :
( ( hAPP @ c_Nat_OSuc @ A )
!= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__n__not__n) ).
thf(268,plain,
! [A: $i] :
( ( hAPP @ c_Nat_OSuc @ A )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(28,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( c_Com_Ocom_OLocal @ F @ E @ D )
= ( c_Com_Ocom_OLocal @ C @ B @ A ) )
<=> ( ( F = C )
& ( E = B )
& ( D = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I2_J) ).
thf(195,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ( c_Com_Ocom_OLocal @ F @ E @ D )
= ( c_Com_Ocom_OLocal @ C @ B @ A ) )
=> ( ( F = C )
& ( E = B )
& ( D = A ) ) )
& ( ( ( F = C )
& ( E = B )
& ( D = A ) )
=> ( ( c_Com_Ocom_OLocal @ F @ E @ D )
= ( c_Com_Ocom_OLocal @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(87,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ c_Int_ORep__Integ @ B )
= ( hAPP @ c_Int_ORep__Integ @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Rep__Integ__inject) ).
thf(459,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)],[87]) ).
thf(80,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/sandbox/benchmark/theBenchmark.p',fact_triple_Orecs) ).
thf(442,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)],[80]) ).
thf(49,axiom,
! [A: $i,B: $i] :
( ( c_Com_Ovname_OGlb @ B )
!= ( c_Com_Ovname_OLoc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_vname_Osimps_I3_J) ).
thf(322,plain,
! [A: $i,B: $i] :
( ( c_Com_Ovname_OGlb @ B )
!= ( c_Com_Ovname_OLoc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(53,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCall @ E @ D @ C ) ) @ B ) @ A ) )
=> ~ ! [F: $i] :
( ( A
= ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oupdate @ ( hAPP @ ( hAPP @ c_Natural_Osetlocs @ F ) @ ( hAPP @ c_Natural_Ogetlocs @ B ) ) ) @ E ) @ ( hAPP @ ( hAPP @ c_Natural_Ogetlocs @ F ) @ c_Com_ORes ) ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( hAPP @ c_Com_Ocom_OBODY @ D ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oupdate @ ( hAPP @ ( hAPP @ c_Natural_Osetlocs @ B ) @ c_Natural_Onewlocs ) ) @ ( c_Com_Ovname_OLoc @ c_Com_OArg ) ) @ ( hAPP @ C @ B ) ) ) @ F ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc__elim__cases_I7_J) ).
thf(337,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( c_Com_Ocom_OCall @ E @ D @ C ) ) @ B ) @ A ) )
=> ~ ! [F: $i] :
( ( A
= ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oupdate @ ( hAPP @ ( hAPP @ c_Natural_Osetlocs @ F ) @ ( hAPP @ c_Natural_Ogetlocs @ B ) ) ) @ E ) @ ( hAPP @ ( hAPP @ c_Natural_Ogetlocs @ F ) @ c_Com_ORes ) ) )
=> ~ ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ ( hAPP @ c_Com_Ocom_OBODY @ D ) ) @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oupdate @ ( hAPP @ ( hAPP @ c_Natural_Osetlocs @ B ) @ c_Natural_Onewlocs ) ) @ ( c_Com_Ovname_OLoc @ c_Com_OArg ) ) @ ( hAPP @ C @ B ) ) ) @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(89,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/sandbox/benchmark/theBenchmark.p',fact_vname_Osimps_I5_J) ).
thf(469,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)],[89]) ).
thf(59,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OLocal @ F @ E @ D ) @ C @ B @ A )
=> ~ ! [G: $i] :
( ( A
= ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oupdate @ G ) @ ( c_Com_Ovname_OLoc @ F ) ) @ ( hAPP @ ( hAPP @ c_Natural_Ogetlocs @ C ) @ F ) ) )
=> ~ ( c_Natural_Oevaln @ D @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oupdate @ C ) @ ( c_Com_Ovname_OLoc @ F ) ) @ ( hAPP @ E @ C ) ) @ B @ G ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln__elim__cases_I3_J) ).
thf(364,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OLocal @ F @ E @ D ) @ C @ B @ A )
=> ~ ! [G: $i] :
( ( A
= ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oupdate @ G ) @ ( c_Com_Ovname_OLoc @ F ) ) @ ( hAPP @ ( hAPP @ c_Natural_Ogetlocs @ C ) @ F ) ) )
=> ~ ( c_Natural_Oevaln @ D @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oupdate @ C ) @ ( c_Com_Ovname_OLoc @ F ) ) @ ( hAPP @ E @ C ) ) @ B @ G ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Hoare__Mirabelle_Otriple__valid @ C @ ( hAPP @ c_Nat_OSuc @ B ) @ A )
=> ( c_Hoare__Mirabelle_Otriple__valid @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_triple__valid__Suc) ).
thf(100,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Hoare__Mirabelle_Otriple__valid @ C @ ( hAPP @ c_Nat_OSuc @ B ) @ A )
=> ( c_Hoare__Mirabelle_Otriple__valid @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(1,conjecture,
v_Q @ v_Z @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oupdate @ ( hAPP @ ( hAPP @ c_Natural_Osetlocs @ v_s1 ) @ ( hAPP @ c_Natural_Ogetlocs @ v_s_H ) ) ) @ v_X ) @ ( hAPP @ ( hAPP @ c_Natural_Ogetlocs @ v_s1 ) @ c_Com_ORes ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_4) ).
thf(2,negated_conjecture,
~ ( v_Q @ v_Z @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oupdate @ ( hAPP @ ( hAPP @ c_Natural_Osetlocs @ v_s1 ) @ ( hAPP @ c_Natural_Ogetlocs @ v_s_H ) ) ) @ v_X ) @ ( hAPP @ ( hAPP @ c_Natural_Ogetlocs @ v_s1 ) @ c_Com_ORes ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(90,plain,
~ ( v_Q @ v_Z @ ( hAPP @ ( hAPP @ ( hAPP @ c_Natural_Oupdate @ ( hAPP @ ( hAPP @ c_Natural_Osetlocs @ v_s1 ) @ ( hAPP @ c_Natural_Ogetlocs @ v_s_H ) ) ) @ v_X ) @ ( hAPP @ ( hAPP @ c_Natural_Ogetlocs @ v_s1 ) @ c_Com_ORes ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(8,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Natural_Oevaln @ D @ C @ B @ A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ D ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln__evalc) ).
thf(111,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Natural_Oevaln @ D @ C @ B @ A )
=> ( hBOOL @ ( hAPP @ ( hAPP @ ( c_Natural_Oevalc @ D ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(475,plain,
$false,
inference(cvc4,[status(thm)],[352,153,252,457,127,171,408,276,389,184,372,125,421,416,448,316,121,348,147,428,380,220,102,334,260,160,392,165,356,169,109,256,425,430,279,180,375,402,286,118,445,466,113,419,451,245,434,345,140,213,91,155,330,399,455,306,135,209,145,295,282,386,314,446,143,231,104,368,272,383,290,378,151,405,326,294,341,268,195,459,442,322,337,469,364,100,90,111]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.14 % Problem : SWW343+1 : TPTP v8.1.2. Released v5.2.0.
% 0.07/0.17 % Command : run_Leo-III %s %d
% 0.15/0.38 % Computer : n025.cluster.edu
% 0.15/0.38 % Model : x86_64 x86_64
% 0.15/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.38 % Memory : 8042.1875MB
% 0.15/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.38 % CPULimit : 300
% 0.15/0.38 % WCLimit : 300
% 0.15/0.38 % DateTime : Thu May 18 22:35:34 EDT 2023
% 0.15/0.38 % CPUTime :
% 0.92/0.87 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 3.01/1.56 % [INFO] Parsing done (687ms).
% 3.17/1.58 % [INFO] Running in sequential loop mode.
% 3.48/1.81 % [INFO] eprover registered as external prover.
% 3.60/1.81 % [INFO] cvc4 registered as external prover.
% 3.60/1.82 % [INFO] Scanning for conjecture ...
% 4.94/2.26 % [INFO] Found a conjecture and 5208 axioms. Running axiom selection ...
% 6.53/2.89 % [INFO] Axiom selection finished. Selected 87 axioms (removed 5121 axioms).
% 6.71/3.01 % [INFO] Problem is first-order (TPTP FOF).
% 6.71/3.03 % [INFO] Type checking passed.
% 6.71/3.03 % [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 ...
% 13.00/4.47 % External prover 'cvc4' found a proof!
% 13.00/4.47 % [INFO] Killing All external provers ...
% 13.00/4.47 % Time passed: 3937ms (effective reasoning time: 2893ms)
% 13.00/4.47 % 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)>
% 13.00/4.48 % Axioms used in derivation (87): conj_2, fact_pos__single__def, fact_evalc_OBody, conj_1, fact_com_Osimps_I1_J, fact_evalc__evaln, fact_com__det, fact_com_Osimps_I40_J, fact_prod_Orecs, fact_com_Osimps_I22_J, fact_com_Osimps_I31_J, fact_pair__box_Oinject, fact_com_Osimps_I2_J, fact_evaln_OAssign, conj_3, fact_evalc__elim__cases_I6_J, fact_evaln_OCall, fact_evaln__Suc, fact_triple__valid__def2, fact_neg__single__def, fact_split__paired__All, fact_evalc__elim__cases_I2_J, fact_com_Osimps_I62_J, fact_triple_Oinject, fact_vname_Orecs_I1_J, fact_nat_Oinject, fact_vname_Osimps_I5_J, fact_vname_Osimps_I3_J, fact_com_Osimps_I23_J, fact_evaln_Oequations_I2_J, fact_vname_Osimps_I6_J, fact_pos__empty__def, fact_Rep__Integ__inject, fact_com_Osimps_I41_J, fact_vname_Osimps_I1_J, fact_evaln_OBody, fact_com_Osimps_I30_J, fact_evaln_Oequations_I3_J, fact_triple__valid__Suc, fact_com_Osimps_I63_J, fact_New__DSequence_Oneg__single__def, fact_evalc__elim__cases_I3_J, fact_folding__one__idem_Oidem, fact_com_Osimps_I7_J, fact_rp__inv__image__rp, fact_com_Osimps_I32_J, fact_pair__box_Orecs, fact_com_Osimps_I6_J, fact_evalc_Oequations_I9_J, fact_evaln__elim__cases_I7_J, fact_Pair__inject, fact_evalc_Oequations_I10_J, fact_Suc__inject, fact_ext, fact_com_Osimps_I42_J, fact_com_Osimps_I33_J, fact_vname_Osimps_I4_J, fact_triple_Osimps_I2_J, fact_n__not__Suc__n, fact_evaln__elim__cases_I2_J, fact_Body__triple__valid__Suc, fact_New__DSequence_Opos__empty__def, fact_evalc_OCall, fact_vname_Orecs_I2_J, fact_Pair__eq, fact_evaln__elim__cases_I6_J, fact_evaln_Oequations_I9_J, fact_evalc_OLocal, fact_evalc_Oequations_I3_J, fact_New__DSequence_Opos__single__def, fact_type__definition_ORep__inject, fact_vname_Osimps_I2_J, fact_com_Osimps_I43_J, fact_evalc_Oequations_I2_J, fact_pair__box_Osimps_I2_J, fact_Suc__n__not__n, fact_pos__not__random__dseq__def, fact_triple_Orecs, fact_evaln__elim__cases_I3_J, fact_type__definition_ORep__inverse, fact_evaln_OLocal, fact_evalc_OAssign, fact_folding__image__simple__idem_Oidem, fact_eval__eq, fact_evaln_Oequations_I10_J, fact_evaln__evalc, fact_evalc__elim__cases_I7_J
% 13.00/4.48 % No. of inferences in proof: 178
% 13.00/4.48 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 3937 ms resp. 2893 ms w/o parsing
% 13.50/4.56 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 13.50/4.56 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------