%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWW343+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 09:09:58 AM UTC 2026
% Result : Theorem 18.34s 6.26s
% Output : Refutation 19.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 88
% Syntax : Number of formulae : 178 ( 80 unt; 0 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 : 0 ( 0 >; 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_decl,type,
v_Q: $i > $i > $o ).
thf(v_Z_decl,type,
v_Z: $i ).
thf(hAPP_decl,type,
hAPP: $i > $i > $i ).
thf(c_Natural_Oupdate_decl,type,
c_Natural_Oupdate: $i ).
thf(c_Natural_Osetlocs_decl,type,
c_Natural_Osetlocs: $i ).
thf(v_s1_decl,type,
v_s1: $i ).
thf(c_Natural_Ogetlocs_decl,type,
c_Natural_Ogetlocs: $i ).
thf(v_s_H_decl,type,
v_s_H: $i ).
thf(v_X_decl,type,
v_X: $i ).
thf(c_Com_ORes_decl,type,
c_Com_ORes: $i ).
thf(c_Hoare__Mirabelle_Otriple__valid_decl,type,
c_Hoare__Mirabelle_Otriple__valid: $i > $i > $i > $o ).
thf(c_Hoare__Mirabelle_Otriple_Otriple_decl,type,
c_Hoare__Mirabelle_Otriple_Otriple: $i > $i ).
thf(hBOOL_decl,type,
hBOOL: $i > $o ).
thf(c_Natural_Oevaln_decl,type,
c_Natural_Oevaln: $i > $i > $i > $i > $o ).
thf(c_Nat_OSuc_decl,type,
c_Nat_OSuc: $i ).
thf(c_Natural_Oevalc_decl,type,
c_Natural_Oevalc: $i > $i ).
thf(c_Com_Ovname_OLoc_decl,type,
c_Com_Ovname_OLoc: $i > $i ).
thf(c_Com_Ocom_OLocal_decl,type,
c_Com_Ocom_OLocal: $i > $i > $i > $i ).
thf(c_Product__Type_OPair_decl,type,
c_Product__Type_OPair: $i > $i > $i ).
thf(c_Option_Othe_decl,type,
c_Option_Othe: $i > $i ).
thf(tc_Com_Ocom_decl,type,
tc_Com_Ocom: $i ).
thf(c_Com_Obody_decl,type,
c_Com_Obody: $i ).
thf(c_Com_Ocom_OBODY_decl,type,
c_Com_Ocom_OBODY: $i ).
thf(c_Com_Ocom_OAss_decl,type,
c_Com_Ocom_OAss: $i > $i > $i ).
thf(c_Com_Ocom_OCall_decl,type,
c_Com_Ocom_OCall: $i > $i > $i > $i ).
thf(c_Nitpick_Opair__box_OPairBox_decl,type,
c_Nitpick_Opair__box_OPairBox: $i > $i > $i > $i > $i ).
thf(c_Com_Ovname_OGlb_decl,type,
c_Com_Ovname_OGlb: $i > $i ).
thf(c_Com_Ovname_Ovname__case_decl,type,
c_Com_Ovname_Ovname__case: $i > $i > $i > $i > $i ).
thf(c_New__Random__Sequence_Opos__empty_decl,type,
c_New__Random__Sequence_Opos__empty: $i > $i > $i > $i > $i ).
thf(c_New__DSequence_Opos__empty_decl,type,
c_New__DSequence_Opos__empty: $i > $i ).
thf(v_pn_decl,type,
v_pn: $i ).
thf(c_Natural_Onewlocs_decl,type,
c_Natural_Onewlocs: $i ).
thf(c_Com_OArg_decl,type,
c_Com_OArg: $i ).
thf(v_a_decl,type,
v_a: $i > $i ).
thf(v_na_decl,type,
v_na: $i ).
thf(c_Com_Ovname_Ovname__rec_decl,type,
c_Com_Ovname_Ovname__rec: $i > $i > $i > $i > $i ).
thf(c_Finite__Set_Ofolding__one__idem_decl,type,
c_Finite__Set_Ofolding__one__idem: $i > $i > $i > $o ).
thf(c_Nitpick_Opair__box_Opair__box__rec_decl,type,
c_Nitpick_Opair__box_Opair__box__rec: $i > $i > $i > $i > $i > $i ).
thf(c_New__Random__Sequence_Oneg__single_decl,type,
c_New__Random__Sequence_Oneg__single: $i > $i ).
thf(c_New__DSequence_Oneg__single_decl,type,
c_New__DSequence_Oneg__single: $i > $i > $i ).
thf(c_FunDef_Oreduction__pair_decl,type,
c_FunDef_Oreduction__pair: $i > $i > $o ).
thf(c_FunDef_Orp__inv__image_decl,type,
c_FunDef_Orp__inv__image: $i > $i > $i ).
thf(c_Lazy__Sequence_Ohb__single_decl,type,
c_Lazy__Sequence_Ohb__single: $i > $i > $i ).
thf(c_New__Random__Sequence_Opos__single_decl,type,
c_New__Random__Sequence_Opos__single: $i > $i ).
thf(c_New__DSequence_Opos__single_decl,type,
c_New__DSequence_Opos__single: $i > $i > $i ).
thf(c_Lazy__Sequence_Osingle_decl,type,
c_Lazy__Sequence_Osingle: $i > $i > $i ).
thf(c_Typedef_Otype__definition_decl,type,
c_Typedef_Otype__definition: $i > $i > $i > $i > $i > $o ).
thf(c_Product__Type_Oprod_Oprod__rec_decl,type,
c_Product__Type_Oprod_Oprod__rec: $i > $i > $i > $i > $i > $i ).
thf(c_New__Random__Sequence_Opos__not__random__dseq_decl,type,
c_New__Random__Sequence_Opos__not__random__dseq: $i > $i > $i > $i > $i ).
thf(c_New__DSequence_Opos__not__seq_decl,type,
c_New__DSequence_Opos__not__seq: $i > $i ).
thf(c_Lazy__Sequence_Oempty_decl,type,
c_Lazy__Sequence_Oempty: $i > $i ).
thf(c_Finite__Set_Ofolding__image__simple__idem_decl,type,
c_Finite__Set_Ofolding__image__simple__idem: $i > $i > $i > $i > $i > $i > $o ).
thf(c_Hoare__Mirabelle_Otriple_Otriple__rec_decl,type,
c_Hoare__Mirabelle_Otriple_Otriple__rec: $i > $i > $i > $i > $i ).
thf(v_P_decl,type,
v_P: $i > $i > $o ).
thf(c_Nitpick_Opair__box_Opair__box__case_decl,type,
c_Nitpick_Opair__box_Opair__box__case: $i > $i > $i > $i > $i > $i ).
thf(c_Int_ORep__Integ_decl,type,
c_Int_ORep__Integ: $i ).
thf(c_Hoare__Mirabelle_Otriple_Otriple__case_decl,type,
c_Hoare__Mirabelle_Otriple_Otriple__case: $i > $i > $i > $i > $i ).
thf(9,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( c_Com_Obody @ hAPP ) @ ( tc_Com_Ocom @ c_Option_Othe @ hAPP ) @ ( C @ ( E @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_Hoare__Mirabelle_Otriple__valid ) ) )
<=> ( A @ ( B @ ( c_Com_Ocom_OBODY @ hAPP ) @ ( C @ ( E @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ ( D @ ( c_Nat_OSuc @ hAPP ) @ ( E @ c_Hoare__Mirabelle_Otriple__valid ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Body__triple__valid__Suc) ).
thf(115,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( A @ ( B @ ( c_Com_Ocom_OBODY @ hAPP ) @ ( C @ ( E @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ ( D @ ( c_Nat_OSuc @ hAPP ) @ ( E @ c_Hoare__Mirabelle_Otriple__valid ) ) )
=> ( A @ ( B @ ( c_Com_Obody @ hAPP ) @ ( tc_Com_Ocom @ c_Option_Othe @ hAPP ) @ ( C @ ( E @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_Hoare__Mirabelle_Otriple__valid ) ) ) )
& ( ( A @ ( B @ ( c_Com_Obody @ hAPP ) @ ( tc_Com_Ocom @ c_Option_Othe @ hAPP ) @ ( C @ ( E @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_Hoare__Mirabelle_Otriple__valid ) ) )
=> ( A @ ( B @ ( c_Com_Ocom_OBODY @ hAPP ) @ ( C @ ( E @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ ( D @ ( c_Nat_OSuc @ hAPP ) @ ( E @ c_Hoare__Mirabelle_Otriple__valid ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(23,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( E @ ( F @ c_Com_Ocom_OLocal ) ) )
!= ( A @ ( B @ ( C @ c_Com_Ocom_OCall ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I42_J) ).
thf(174,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( E @ ( F @ c_Com_Ocom_OLocal ) ) )
!= ( A @ ( B @ ( C @ c_Com_Ocom_OCall ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(66,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_New__Random__Sequence_Opos__single @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) )
= ( D @ ( E @ c_New__DSequence_Opos__single ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__single__def) ).
thf(421,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_New__Random__Sequence_Opos__single @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) )
= ( D @ ( E @ c_New__DSequence_Opos__single ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(73,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_New__DSequence_Opos__empty @ hAPP ) )
= ( B @ c_Lazy__Sequence_Oempty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_New__DSequence_Opos__empty__def) ).
thf(453,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_New__DSequence_Opos__empty @ hAPP ) )
= ( B @ c_Lazy__Sequence_Oempty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(12,axiom,
! [A: $i,B: $i,C: $i] : ( A @ ( B @ hAPP ) @ ( C @ ( A @ ( c_Natural_Oupdate @ hAPP ) @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( C @ c_Com_Ocom_OAss ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evalc_Oequations_I2_J) ).
thf(129,plain,
! [A: $i,B: $i,C: $i] : ( A @ ( B @ hAPP ) @ ( C @ ( A @ ( c_Natural_Oupdate @ hAPP ) @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( C @ c_Com_Ocom_OAss ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(71,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_New__Random__Sequence_Opos__not__random__dseq ) ) ) )
= ( A @ ( B @ ( C @ ( D @ hAPP ) @ hAPP ) @ hAPP ) @ c_New__DSequence_Opos__not__seq ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__not__random__dseq__def) ).
thf(441,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_New__Random__Sequence_Opos__not__random__dseq ) ) ) )
= ( A @ ( B @ ( C @ ( D @ hAPP ) @ hAPP ) @ hAPP ) @ c_New__DSequence_Opos__not__seq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(42,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( E @ c_Com_Ocom_OAss ) )
!= ( A @ ( B @ ( C @ c_Com_Ocom_OLocal ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I22_J) ).
thf(314,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( E @ c_Com_Ocom_OAss ) )
!= ( A @ ( B @ ( C @ c_Com_Ocom_OLocal ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(48,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( C @ ( D @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) )
=> ~ ( ( D = B )
=> ( C != A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pair__inject) ).
thf(346,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( C @ ( D @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) )
=> ~ ( ( D = B )
=> ( C != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(52,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ c_Com_Ovname_OLoc @ ( B @ ( C @ ( D @ c_Com_Ovname_Ovname__rec ) ) ) )
= ( A @ ( B @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vname_Orecs_I2_J) ).
thf(365,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ c_Com_Ovname_OLoc @ ( B @ ( C @ ( D @ c_Com_Ovname_Ovname__rec ) ) ) )
= ( A @ ( B @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( C @ c_Hoare__Mirabelle_Otriple__valid ) ) )
=> ( A @ ( B @ ( C @ c_Hoare__Mirabelle_Otriple__valid ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_triple__valid__Suc) ).
thf(101,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( C @ c_Hoare__Mirabelle_Otriple__valid ) ) )
=> ( A @ ( B @ ( C @ c_Hoare__Mirabelle_Otriple__valid ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(57,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Com_Ocom_OAss ) )
!= ( A @ ( c_Com_Ocom_OBODY @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I30_J) ).
thf(384,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Com_Ocom_OAss ) )
!= ( A @ ( c_Com_Ocom_OBODY @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(18,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_Com_Ocom_OLocal ) ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ! [F: $i] :
( ( A
= ( E @ ( B @ ( c_Natural_Ogetlocs @ hAPP ) @ hAPP ) @ ( E @ c_Com_Ovname_OLoc @ ( F @ ( c_Natural_Oupdate @ hAPP ) @ hAPP ) @ hAPP ) ) )
=> ~ ( F @ ( B @ ( D @ hAPP ) @ ( E @ c_Com_Ovname_OLoc @ ( B @ ( c_Natural_Oupdate @ hAPP ) @ hAPP ) @ hAPP ) @ ( C @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evalc__elim__cases_I3_J) ).
thf(153,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_Com_Ocom_OLocal ) ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ! [F: $i] :
( ( A
= ( E @ ( B @ ( c_Natural_Ogetlocs @ hAPP ) @ hAPP ) @ ( E @ c_Com_Ovname_OLoc @ ( F @ ( c_Natural_Oupdate @ hAPP ) @ hAPP ) @ hAPP ) ) )
=> ~ ( F @ ( B @ ( D @ hAPP ) @ ( E @ c_Com_Ovname_OLoc @ ( B @ ( c_Natural_Oupdate @ hAPP ) @ hAPP ) @ hAPP ) @ ( C @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(47,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( D @ ( C @ hAPP ) @ ( c_Com_OArg @ c_Com_Ovname_OLoc @ ( c_Natural_Onewlocs @ ( D @ ( c_Natural_Osetlocs @ hAPP ) @ hAPP ) @ ( c_Natural_Oupdate @ hAPP ) @ hAPP ) @ hAPP ) @ ( E @ ( c_Com_Ocom_OBODY @ hAPP ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
=> ( c_Com_ORes @ ( B @ ( c_Natural_Ogetlocs @ hAPP ) @ hAPP ) @ ( A @ ( D @ ( c_Natural_Ogetlocs @ hAPP ) @ ( B @ ( c_Natural_Osetlocs @ hAPP ) @ hAPP ) @ ( c_Natural_Oupdate @ hAPP ) @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( E @ ( A @ c_Com_Ocom_OCall ) ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evalc_OCall) ).
thf(344,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( B @ ( D @ ( C @ hAPP ) @ ( c_Com_OArg @ c_Com_Ovname_OLoc @ ( c_Natural_Onewlocs @ ( D @ ( c_Natural_Osetlocs @ hAPP ) @ hAPP ) @ ( c_Natural_Oupdate @ hAPP ) @ hAPP ) @ hAPP ) @ ( E @ ( c_Com_Ocom_OBODY @ hAPP ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
=> ( c_Com_ORes @ ( B @ ( c_Natural_Ogetlocs @ hAPP ) @ hAPP ) @ ( A @ ( D @ ( c_Natural_Ogetlocs @ hAPP ) @ ( B @ ( c_Natural_Osetlocs @ hAPP ) @ hAPP ) @ ( c_Natural_Oupdate @ hAPP ) @ hAPP ) @ hAPP ) @ ( D @ ( C @ ( E @ ( A @ c_Com_Ocom_OCall ) ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(50,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( E @ c_Com_Ocom_OAss ) )
!= ( A @ ( B @ ( C @ c_Com_Ocom_OCall ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I32_J) ).
thf(357,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( E @ c_Com_Ocom_OAss ) )
!= ( A @ ( B @ ( C @ c_Com_Ocom_OCall ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(31,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( C @ ( D @ ( E @ ( F @ c_Nitpick_Opair__box_OPairBox ) ) ) )
= ( A @ ( B @ ( E @ ( F @ c_Nitpick_Opair__box_OPairBox ) ) ) ) )
<=> ( ( C = A )
& ( D = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pair__box_Oinject) ).
thf(238,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ( C = A )
& ( D = B ) )
=> ( ( C @ ( D @ ( E @ ( F @ c_Nitpick_Opair__box_OPairBox ) ) ) )
= ( A @ ( B @ ( E @ ( F @ c_Nitpick_Opair__box_OPairBox ) ) ) ) ) )
& ( ( ( C @ ( D @ ( E @ ( F @ c_Nitpick_Opair__box_OPairBox ) ) ) )
= ( A @ ( B @ ( E @ ( F @ c_Nitpick_Opair__box_OPairBox ) ) ) ) )
=> ( ( C = A )
& ( D = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(10,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com__det) ).
thf(121,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
=> ( ( A @ ( C @ ( D @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(49,axiom,
! [A: $i,B: $i] :
( ( B @ c_Com_Ovname_OGlb )
!= ( A @ c_Com_Ovname_OLoc ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vname_Osimps_I3_J) ).
thf(353,plain,
! [A: $i,B: $i] :
( ( B @ c_Com_Ovname_OGlb )
!= ( A @ c_Com_Ovname_OLoc ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(80,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( F @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ c_Hoare__Mirabelle_Otriple_Otriple__rec ) ) ) )
= ( A @ ( B @ ( C @ ( D @ hAPP ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_triple_Orecs) ).
thf(480,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( F @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ c_Hoare__Mirabelle_Otriple_Otriple__rec ) ) ) )
= ( A @ ( B @ ( C @ ( D @ hAPP ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(40,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_New__Random__Sequence_Opos__empty ) ) ) )
= ( D @ c_New__DSequence_Opos__empty ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pos__empty__def) ).
thf(307,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_New__Random__Sequence_Opos__empty ) ) ) )
= ( D @ c_New__DSequence_Opos__empty ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(56,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_Com_Ocom_OCall ) ) )
!= ( A @ ( c_Com_Ocom_OBODY @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I63_J) ).
thf(380,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_Com_Ocom_OCall ) ) )
!= ( A @ ( c_Com_Ocom_OBODY @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(33,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( c_Com_Ocom_OBODY @ hAPP ) )
= ( A @ ( c_Com_Ocom_OBODY @ hAPP ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I6_J) ).
thf(270,plain,
! [A: $i,B: $i] :
( ( ( B = A )
=> ( ( B @ ( c_Com_Ocom_OBODY @ hAPP ) )
= ( A @ ( c_Com_Ocom_OBODY @ hAPP ) ) ) )
& ( ( ( B @ ( c_Com_Ocom_OBODY @ hAPP ) )
= ( A @ ( c_Com_Ocom_OBODY @ hAPP ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(20,axiom,
! [A: $i,B: $i,C: $i] : ( A @ ( B @ hAPP ) @ ( C @ ( A @ ( c_Natural_Oupdate @ hAPP ) @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( C @ c_Com_Ocom_OAss ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evalc_OAssign) ).
thf(160,plain,
! [A: $i,B: $i,C: $i] : ( A @ ( B @ hAPP ) @ ( C @ ( A @ ( c_Natural_Oupdate @ hAPP ) @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( C @ c_Com_Ocom_OAss ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(67,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_New__DSequence_Opos__single ) @ hAPP ) )
= ( B @ ( C @ c_Lazy__Sequence_Osingle ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_New__DSequence_Opos__single__def) ).
thf(424,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_New__DSequence_Opos__single ) @ hAPP ) )
= ( B @ ( C @ c_Lazy__Sequence_Osingle ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(61,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( E @ ( F @ c_Nitpick_Opair__box_OPairBox ) ) ) @ ( C @ ( D @ ( E @ ( F @ c_Nitpick_Opair__box_Opair__box__rec ) ) ) ) )
= ( A @ ( B @ ( C @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pair__box_Orecs) ).
thf(407,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( E @ ( F @ c_Nitpick_Opair__box_OPairBox ) ) ) @ ( C @ ( D @ ( E @ ( F @ c_Nitpick_Opair__box_Opair__box__rec ) ) ) ) )
= ( A @ ( B @ ( C @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(78,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( B @ ( C @ ( D @ ( E @ ( F @ c_Typedef_Otype__definition ) ) ) ) )
=> ( ( A @ ( D @ hAPP ) @ ( C @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_type__definition_ORep__inverse) ).
thf(467,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( B @ ( C @ ( D @ ( E @ ( F @ c_Typedef_Otype__definition ) ) ) ) )
=> ( ( A @ ( D @ hAPP ) @ ( C @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(82,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( B @ ( C @ ( E @ ( D @ hAPP ) @ ( c_Com_OArg @ c_Com_Ovname_OLoc @ ( c_Natural_Onewlocs @ ( E @ ( c_Natural_Osetlocs @ hAPP ) @ hAPP ) @ ( c_Natural_Oupdate @ hAPP ) @ hAPP ) @ hAPP ) @ ( F @ ( c_Com_Ocom_OBODY @ hAPP ) @ c_Natural_Oevaln ) ) ) )
=> ( c_Com_ORes @ ( B @ ( c_Natural_Ogetlocs @ hAPP ) @ hAPP ) @ ( A @ ( E @ ( c_Natural_Ogetlocs @ hAPP ) @ ( B @ ( c_Natural_Osetlocs @ hAPP ) @ hAPP ) @ ( c_Natural_Oupdate @ hAPP ) @ hAPP ) @ hAPP ) @ ( C @ ( E @ ( D @ ( F @ ( A @ c_Com_Ocom_OCall ) ) @ c_Natural_Oevaln ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evaln_OCall) ).
thf(484,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( B @ ( C @ ( E @ ( D @ hAPP ) @ ( c_Com_OArg @ c_Com_Ovname_OLoc @ ( c_Natural_Onewlocs @ ( E @ ( c_Natural_Osetlocs @ hAPP ) @ hAPP ) @ ( c_Natural_Oupdate @ hAPP ) @ hAPP ) @ hAPP ) @ ( F @ ( c_Com_Ocom_OBODY @ hAPP ) @ c_Natural_Oevaln ) ) ) )
=> ( c_Com_ORes @ ( B @ ( c_Natural_Ogetlocs @ hAPP ) @ hAPP ) @ ( A @ ( E @ ( c_Natural_Ogetlocs @ hAPP ) @ ( B @ ( c_Natural_Osetlocs @ hAPP ) @ hAPP ) @ ( c_Natural_Oupdate @ hAPP ) @ hAPP ) @ hAPP ) @ ( C @ ( E @ ( D @ ( F @ ( A @ c_Com_Ocom_OCall ) ) @ c_Natural_Oevaln ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(32,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( E @ ( F @ c_Com_Ocom_OCall ) ) )
= ( A @ ( B @ ( C @ c_Com_Ocom_OCall ) ) ) )
<=> ( ( D = A )
& ( E = B )
& ( F = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I7_J) ).
thf(252,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ( D = A )
& ( E = B )
& ( F = C ) )
=> ( ( D @ ( E @ ( F @ c_Com_Ocom_OCall ) ) )
= ( A @ ( B @ ( C @ c_Com_Ocom_OCall ) ) ) ) )
& ( ( ( D @ ( E @ ( F @ c_Com_Ocom_OCall ) ) )
= ( A @ ( B @ ( C @ c_Com_Ocom_OCall ) ) ) )
=> ( ( D = A )
& ( E = B )
& ( F = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(51,axiom,
! [A: $i] :
( A
!= ( A @ ( c_Nat_OSuc @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_n__not__Suc__n) ).
thf(361,plain,
! [A: $i] :
( A
!= ( A @ ( c_Nat_OSuc @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(69,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_Com_Ocom_OAss ) @ c_Natural_Oevaln ) ) ) )
=> ( A
= ( C @ ( D @ hAPP ) @ ( E @ ( C @ ( c_Natural_Oupdate @ hAPP ) @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evaln__elim__cases_I2_J) ).
thf(435,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_Com_Ocom_OAss ) @ c_Natural_Oevaln ) ) ) )
=> ( A
= ( C @ ( D @ hAPP ) @ ( E @ ( C @ ( c_Natural_Oupdate @ hAPP ) @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(74,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( E @ ( C @ hAPP ) @ ( D @ c_Com_Ovname_OLoc @ ( E @ ( c_Natural_Oupdate @ hAPP ) @ hAPP ) @ hAPP ) @ ( F @ c_Natural_Oevaln ) ) ) )
=> ( D @ ( E @ ( c_Natural_Ogetlocs @ hAPP ) @ hAPP ) @ ( D @ c_Com_Ovname_OLoc @ ( A @ ( c_Natural_Oupdate @ hAPP ) @ hAPP ) @ hAPP ) @ ( B @ ( E @ ( F @ ( C @ ( D @ c_Com_Ocom_OLocal ) ) @ c_Natural_Oevaln ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evaln_OLocal) ).
thf(456,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( E @ ( C @ hAPP ) @ ( D @ c_Com_Ovname_OLoc @ ( E @ ( c_Natural_Oupdate @ hAPP ) @ hAPP ) @ hAPP ) @ ( F @ c_Natural_Oevaln ) ) ) )
=> ( D @ ( E @ ( c_Natural_Ogetlocs @ hAPP ) @ hAPP ) @ ( D @ c_Com_Ovname_OLoc @ ( A @ ( c_Natural_Oupdate @ hAPP ) @ hAPP ) @ hAPP ) @ ( B @ ( E @ ( F @ ( C @ ( D @ c_Com_Ocom_OLocal ) ) @ c_Natural_Oevaln ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(60,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_Finite__Set_Ofolding__one__idem ) ) )
=> ( ( A @ ( A @ ( C @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__one__idem_Oidem) ).
thf(403,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_Finite__Set_Ofolding__one__idem ) ) )
=> ( ( A @ ( A @ ( C @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(58,axiom,
! [A: $i,B: $i] :
( ( ( B @ c_Com_Ovname_OLoc )
= ( A @ c_Com_Ovname_OLoc ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vname_Osimps_I2_J) ).
thf(388,plain,
! [A: $i,B: $i] :
( ( ( B = A )
=> ( ( B @ c_Com_Ovname_OLoc )
= ( A @ c_Com_Ovname_OLoc ) ) )
& ( ( ( B @ c_Com_Ovname_OLoc )
= ( A @ c_Com_Ovname_OLoc ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(79,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( C @ ( c_Natural_Ogetlocs @ hAPP ) @ hAPP ) @ ( F @ c_Com_Ovname_OLoc @ ( A @ ( c_Natural_Oupdate @ hAPP ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ ( E @ ( F @ c_Com_Ocom_OLocal ) ) @ c_Natural_Oevaln ) ) ) )
<=> ? [G: $i] :
( ( G @ ( B @ ( C @ ( E @ hAPP ) @ ( F @ c_Com_Ovname_OLoc @ ( C @ ( c_Natural_Oupdate @ hAPP ) @ hAPP ) @ hAPP ) @ ( D @ c_Natural_Oevaln ) ) ) )
& ( ( F @ ( C @ ( c_Natural_Ogetlocs @ hAPP ) @ hAPP ) @ ( F @ c_Com_Ovname_OLoc @ ( A @ ( c_Natural_Oupdate @ hAPP ) @ hAPP ) @ hAPP ) )
= ( F @ ( C @ ( c_Natural_Ogetlocs @ hAPP ) @ hAPP ) @ ( F @ c_Com_Ovname_OLoc @ ( G @ ( c_Natural_Oupdate @ hAPP ) @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evaln_Oequations_I3_J) ).
thf(471,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ? [G: $i] :
( ( G @ ( B @ ( C @ ( E @ hAPP ) @ ( F @ c_Com_Ovname_OLoc @ ( C @ ( c_Natural_Oupdate @ hAPP ) @ hAPP ) @ hAPP ) @ ( D @ c_Natural_Oevaln ) ) ) )
& ( ( F @ ( C @ ( c_Natural_Ogetlocs @ hAPP ) @ hAPP ) @ ( F @ c_Com_Ovname_OLoc @ ( A @ ( c_Natural_Oupdate @ hAPP ) @ hAPP ) @ hAPP ) )
= ( F @ ( C @ ( c_Natural_Ogetlocs @ hAPP ) @ hAPP ) @ ( F @ c_Com_Ovname_OLoc @ ( G @ ( c_Natural_Oupdate @ hAPP ) @ hAPP ) @ hAPP ) ) ) )
=> ( F @ ( C @ ( c_Natural_Ogetlocs @ hAPP ) @ hAPP ) @ ( F @ c_Com_Ovname_OLoc @ ( A @ ( c_Natural_Oupdate @ hAPP ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ ( E @ ( F @ c_Com_Ocom_OLocal ) ) @ c_Natural_Oevaln ) ) ) ) )
& ( ( F @ ( C @ ( c_Natural_Ogetlocs @ hAPP ) @ hAPP ) @ ( F @ c_Com_Ovname_OLoc @ ( A @ ( c_Natural_Oupdate @ hAPP ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ ( E @ ( F @ c_Com_Ocom_OLocal ) ) @ c_Natural_Oevaln ) ) ) )
=> ? [G: $i] :
( ( G @ ( B @ ( C @ ( E @ hAPP ) @ ( F @ c_Com_Ovname_OLoc @ ( C @ ( c_Natural_Oupdate @ hAPP ) @ hAPP ) @ hAPP ) @ ( D @ c_Natural_Oevaln ) ) ) )
& ( ( F @ ( C @ ( c_Natural_Ogetlocs @ hAPP ) @ hAPP ) @ ( F @ c_Com_Ovname_OLoc @ ( A @ ( c_Natural_Oupdate @ hAPP ) @ hAPP ) @ hAPP ) )
= ( F @ ( C @ ( c_Natural_Ogetlocs @ hAPP ) @ hAPP ) @ ( F @ c_Com_Ovname_OLoc @ ( G @ ( c_Natural_Oupdate @ hAPP ) @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(11,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ ( c_Com_Ocom_OBODY @ hAPP ) @ c_Natural_Oevaln ) ) ) )
=> ~ ! [E: $i] :
( ( B
= ( E @ ( c_Nat_OSuc @ hAPP ) ) )
=> ~ ( A @ ( E @ ( C @ ( D @ ( c_Com_Obody @ hAPP ) @ ( tc_Com_Ocom @ c_Option_Othe @ hAPP ) @ c_Natural_Oevaln ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evaln__elim__cases_I6_J) ).
thf(124,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ ( c_Com_Ocom_OBODY @ hAPP ) @ c_Natural_Oevaln ) ) ) )
=> ~ ! [E: $i] :
( ( B
= ( E @ ( c_Nat_OSuc @ hAPP ) ) )
=> ~ ( A @ ( E @ ( C @ ( D @ ( c_Com_Obody @ hAPP ) @ ( tc_Com_Ocom @ c_Option_Othe @ hAPP ) @ c_Natural_Oevaln ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(84,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ c_Com_Ocom_OCall ) ) @ c_Natural_Oevaln ) ) ) )
=> ~ ! [G: $i] :
( ( A
= ( c_Com_ORes @ ( G @ ( c_Natural_Ogetlocs @ hAPP ) @ hAPP ) @ ( F @ ( C @ ( c_Natural_Ogetlocs @ hAPP ) @ ( G @ ( c_Natural_Osetlocs @ hAPP ) @ hAPP ) @ ( c_Natural_Oupdate @ hAPP ) @ hAPP ) @ hAPP ) ) )
=> ~ ( G @ ( B @ ( C @ ( D @ hAPP ) @ ( c_Com_OArg @ c_Com_Ovname_OLoc @ ( c_Natural_Onewlocs @ ( C @ ( c_Natural_Osetlocs @ hAPP ) @ hAPP ) @ ( c_Natural_Oupdate @ hAPP ) @ hAPP ) @ hAPP ) @ ( E @ ( c_Com_Ocom_OBODY @ hAPP ) @ c_Natural_Oevaln ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evaln__elim__cases_I7_J) ).
thf(489,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ c_Com_Ocom_OCall ) ) @ c_Natural_Oevaln ) ) ) )
=> ~ ! [G: $i] :
( ( A
= ( c_Com_ORes @ ( G @ ( c_Natural_Ogetlocs @ hAPP ) @ hAPP ) @ ( F @ ( C @ ( c_Natural_Ogetlocs @ hAPP ) @ ( G @ ( c_Natural_Osetlocs @ hAPP ) @ hAPP ) @ ( c_Natural_Oupdate @ hAPP ) @ hAPP ) @ hAPP ) ) )
=> ~ ( G @ ( B @ ( C @ ( D @ hAPP ) @ ( c_Com_OArg @ c_Com_Ovname_OLoc @ ( c_Natural_Onewlocs @ ( C @ ( c_Natural_Osetlocs @ hAPP ) @ hAPP ) @ ( c_Natural_Oupdate @ hAPP ) @ hAPP ) @ hAPP ) @ ( E @ ( c_Com_Ocom_OBODY @ hAPP ) @ c_Natural_Oevaln ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] : ( D @ ( C @ hAPP ) @ hBOOL )
<=> ! [D: $i,E: $i] : ( E @ ( D @ ( A @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_split__paired__All) ).
thf(105,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i,E: $i] : ( E @ ( D @ ( A @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hBOOL )
=> ! [D: $i] : ( D @ ( C @ hAPP ) @ hBOOL ) )
& ( ! [D: $i] : ( D @ ( C @ hAPP ) @ hBOOL )
=> ! [D: $i,E: $i] : ( E @ ( D @ ( A @ ( B @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(59,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ c_Com_Ocom_OLocal ) ) @ c_Natural_Oevaln ) ) ) )
=> ~ ! [G: $i] :
( ( A
= ( F @ ( C @ ( c_Natural_Ogetlocs @ hAPP ) @ hAPP ) @ ( F @ c_Com_Ovname_OLoc @ ( G @ ( c_Natural_Oupdate @ hAPP ) @ hAPP ) @ hAPP ) ) )
=> ~ ( G @ ( B @ ( C @ ( E @ hAPP ) @ ( F @ c_Com_Ovname_OLoc @ ( C @ ( c_Natural_Oupdate @ hAPP ) @ hAPP ) @ hAPP ) @ ( D @ c_Natural_Oevaln ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evaln__elim__cases_I3_J) ).
thf(398,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ c_Com_Ocom_OLocal ) ) @ c_Natural_Oevaln ) ) ) )
=> ~ ! [G: $i] :
( ( A
= ( F @ ( C @ ( c_Natural_Ogetlocs @ hAPP ) @ hAPP ) @ ( F @ c_Com_Ovname_OLoc @ ( G @ ( c_Natural_Oupdate @ hAPP ) @ hAPP ) @ hAPP ) ) )
=> ~ ( G @ ( B @ ( C @ ( E @ hAPP ) @ ( F @ c_Com_Ovname_OLoc @ ( C @ ( c_Natural_Oupdate @ hAPP ) @ hAPP ) @ hAPP ) @ ( D @ c_Natural_Oevaln ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(72,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Com_ORes @ ( A @ ( c_Natural_Ogetlocs @ hAPP ) @ hAPP ) @ ( F @ ( C @ ( c_Natural_Ogetlocs @ hAPP ) @ ( A @ ( c_Natural_Osetlocs @ hAPP ) @ hAPP ) @ ( c_Natural_Oupdate @ hAPP ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ ( E @ ( F @ c_Com_Ocom_OCall ) ) @ c_Natural_Oevaln ) ) ) )
<=> ? [G: $i] :
( ( G @ ( B @ ( C @ ( D @ hAPP ) @ ( c_Com_OArg @ c_Com_Ovname_OLoc @ ( c_Natural_Onewlocs @ ( C @ ( c_Natural_Osetlocs @ hAPP ) @ hAPP ) @ ( c_Natural_Oupdate @ hAPP ) @ hAPP ) @ hAPP ) @ ( E @ ( c_Com_Ocom_OBODY @ hAPP ) @ c_Natural_Oevaln ) ) ) )
& ( ( c_Com_ORes @ ( A @ ( c_Natural_Ogetlocs @ hAPP ) @ hAPP ) @ ( F @ ( C @ ( c_Natural_Ogetlocs @ hAPP ) @ ( A @ ( c_Natural_Osetlocs @ hAPP ) @ hAPP ) @ ( c_Natural_Oupdate @ hAPP ) @ hAPP ) @ hAPP ) )
= ( c_Com_ORes @ ( G @ ( c_Natural_Ogetlocs @ hAPP ) @ hAPP ) @ ( F @ ( C @ ( c_Natural_Ogetlocs @ hAPP ) @ ( G @ ( c_Natural_Osetlocs @ hAPP ) @ hAPP ) @ ( c_Natural_Oupdate @ hAPP ) @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evaln_Oequations_I10_J) ).
thf(444,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ? [G: $i] :
( ( G @ ( B @ ( C @ ( D @ hAPP ) @ ( c_Com_OArg @ c_Com_Ovname_OLoc @ ( c_Natural_Onewlocs @ ( C @ ( c_Natural_Osetlocs @ hAPP ) @ hAPP ) @ ( c_Natural_Oupdate @ hAPP ) @ hAPP ) @ hAPP ) @ ( E @ ( c_Com_Ocom_OBODY @ hAPP ) @ c_Natural_Oevaln ) ) ) )
& ( ( c_Com_ORes @ ( A @ ( c_Natural_Ogetlocs @ hAPP ) @ hAPP ) @ ( F @ ( C @ ( c_Natural_Ogetlocs @ hAPP ) @ ( A @ ( c_Natural_Osetlocs @ hAPP ) @ hAPP ) @ ( c_Natural_Oupdate @ hAPP ) @ hAPP ) @ hAPP ) )
= ( c_Com_ORes @ ( G @ ( c_Natural_Ogetlocs @ hAPP ) @ hAPP ) @ ( F @ ( C @ ( c_Natural_Ogetlocs @ hAPP ) @ ( G @ ( c_Natural_Osetlocs @ hAPP ) @ hAPP ) @ ( c_Natural_Oupdate @ hAPP ) @ hAPP ) @ hAPP ) ) ) )
=> ( c_Com_ORes @ ( A @ ( c_Natural_Ogetlocs @ hAPP ) @ hAPP ) @ ( F @ ( C @ ( c_Natural_Ogetlocs @ hAPP ) @ ( A @ ( c_Natural_Osetlocs @ hAPP ) @ hAPP ) @ ( c_Natural_Oupdate @ hAPP ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ ( E @ ( F @ c_Com_Ocom_OCall ) ) @ c_Natural_Oevaln ) ) ) ) )
& ( ( c_Com_ORes @ ( A @ ( c_Natural_Ogetlocs @ hAPP ) @ hAPP ) @ ( F @ ( C @ ( c_Natural_Ogetlocs @ hAPP ) @ ( A @ ( c_Natural_Osetlocs @ hAPP ) @ hAPP ) @ ( c_Natural_Oupdate @ hAPP ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ ( E @ ( F @ c_Com_Ocom_OCall ) ) @ c_Natural_Oevaln ) ) ) )
=> ? [G: $i] :
( ( G @ ( B @ ( C @ ( D @ hAPP ) @ ( c_Com_OArg @ c_Com_Ovname_OLoc @ ( c_Natural_Onewlocs @ ( C @ ( c_Natural_Osetlocs @ hAPP ) @ hAPP ) @ ( c_Natural_Oupdate @ hAPP ) @ hAPP ) @ hAPP ) @ ( E @ ( c_Com_Ocom_OBODY @ hAPP ) @ c_Natural_Oevaln ) ) ) )
& ( ( c_Com_ORes @ ( A @ ( c_Natural_Ogetlocs @ hAPP ) @ hAPP ) @ ( F @ ( C @ ( c_Natural_Ogetlocs @ hAPP ) @ ( A @ ( c_Natural_Osetlocs @ hAPP ) @ hAPP ) @ ( c_Natural_Oupdate @ hAPP ) @ hAPP ) @ hAPP ) )
= ( c_Com_ORes @ ( G @ ( c_Natural_Ogetlocs @ hAPP ) @ hAPP ) @ ( F @ ( C @ ( c_Natural_Ogetlocs @ hAPP ) @ ( G @ ( c_Natural_Osetlocs @ hAPP ) @ hAPP ) @ ( c_Natural_Oupdate @ hAPP ) @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(16,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( c_Com_Ocom_OBODY @ hAPP ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ ( c_Com_Obody @ hAPP ) @ ( tc_Com_Ocom @ c_Option_Othe @ hAPP ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evalc__elim__cases_I6_J) ).
thf(149,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( c_Com_Ocom_OBODY @ hAPP ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ ( c_Com_Obody @ hAPP ) @ ( tc_Com_Ocom @ c_Option_Othe @ hAPP ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(25,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( C @ ( D @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) )
<=> ( ( C = A )
& ( D = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Pair__eq) ).
thf(180,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ( C = A )
& ( D = B ) )
=> ( ( C @ ( D @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) ) )
& ( ( ( C @ ( D @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) ) )
=> ( ( C = A )
& ( D = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(37,axiom,
! [A: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) )
!= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__n__not__n) ).
thf(296,plain,
! [A: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(36,axiom,
! [A: $i,B: $i] :
( ( ( B @ c_Com_Ovname_OGlb )
= ( A @ c_Com_Ovname_OGlb ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vname_Osimps_I1_J) ).
thf(286,plain,
! [A: $i,B: $i] :
( ( ( B = A )
=> ( ( B @ c_Com_Ovname_OGlb )
= ( A @ c_Com_Ovname_OGlb ) ) )
& ( ( ( B @ c_Com_Ovname_OGlb )
= ( A @ c_Com_Ovname_OGlb ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(63,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_FunDef_Oreduction__pair ) )
=> ( A @ ( C @ ( B @ ( D @ c_FunDef_Orp__inv__image ) @ hAPP ) @ hAPP ) @ ( B @ c_FunDef_Oreduction__pair ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_rp__inv__image__rp) ).
thf(413,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_FunDef_Oreduction__pair ) )
=> ( A @ ( C @ ( B @ ( D @ c_FunDef_Orp__inv__image ) @ hAPP ) @ hAPP ) @ ( B @ c_FunDef_Oreduction__pair ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(87,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( c_Int_ORep__Integ @ hAPP ) )
= ( A @ ( c_Int_ORep__Integ @ hAPP ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Rep__Integ__inject) ).
thf(498,plain,
! [A: $i,B: $i] :
( ( ( B = A )
=> ( ( B @ ( c_Int_ORep__Integ @ hAPP ) )
= ( A @ ( c_Int_ORep__Integ @ hAPP ) ) ) )
& ( ( ( B @ ( c_Int_ORep__Integ @ hAPP ) )
= ( A @ ( c_Int_ORep__Integ @ hAPP ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(46,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Com_ORes @ ( A @ ( c_Natural_Ogetlocs @ hAPP ) @ hAPP ) @ ( E @ ( B @ ( c_Natural_Ogetlocs @ hAPP ) @ ( A @ ( c_Natural_Osetlocs @ hAPP ) @ hAPP ) @ ( c_Natural_Oupdate @ hAPP ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ ( E @ c_Com_Ocom_OCall ) ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
<=> ? [F: $i] :
( ( F @ ( B @ ( C @ hAPP ) @ ( c_Com_OArg @ c_Com_Ovname_OLoc @ ( c_Natural_Onewlocs @ ( B @ ( c_Natural_Osetlocs @ hAPP ) @ hAPP ) @ ( c_Natural_Oupdate @ hAPP ) @ hAPP ) @ hAPP ) @ ( D @ ( c_Com_Ocom_OBODY @ hAPP ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
& ( ( c_Com_ORes @ ( A @ ( c_Natural_Ogetlocs @ hAPP ) @ hAPP ) @ ( E @ ( B @ ( c_Natural_Ogetlocs @ hAPP ) @ ( A @ ( c_Natural_Osetlocs @ hAPP ) @ hAPP ) @ ( c_Natural_Oupdate @ hAPP ) @ hAPP ) @ hAPP ) )
= ( c_Com_ORes @ ( F @ ( c_Natural_Ogetlocs @ hAPP ) @ hAPP ) @ ( E @ ( B @ ( c_Natural_Ogetlocs @ hAPP ) @ ( F @ ( c_Natural_Osetlocs @ hAPP ) @ hAPP ) @ ( c_Natural_Oupdate @ hAPP ) @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evalc_Oequations_I10_J) ).
thf(335,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ? [F: $i] :
( ( F @ ( B @ ( C @ hAPP ) @ ( c_Com_OArg @ c_Com_Ovname_OLoc @ ( c_Natural_Onewlocs @ ( B @ ( c_Natural_Osetlocs @ hAPP ) @ hAPP ) @ ( c_Natural_Oupdate @ hAPP ) @ hAPP ) @ hAPP ) @ ( D @ ( c_Com_Ocom_OBODY @ hAPP ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
& ( ( c_Com_ORes @ ( A @ ( c_Natural_Ogetlocs @ hAPP ) @ hAPP ) @ ( E @ ( B @ ( c_Natural_Ogetlocs @ hAPP ) @ ( A @ ( c_Natural_Osetlocs @ hAPP ) @ hAPP ) @ ( c_Natural_Oupdate @ hAPP ) @ hAPP ) @ hAPP ) )
= ( c_Com_ORes @ ( F @ ( c_Natural_Ogetlocs @ hAPP ) @ hAPP ) @ ( E @ ( B @ ( c_Natural_Ogetlocs @ hAPP ) @ ( F @ ( c_Natural_Osetlocs @ hAPP ) @ hAPP ) @ ( c_Natural_Oupdate @ hAPP ) @ hAPP ) @ hAPP ) ) ) )
=> ( c_Com_ORes @ ( A @ ( c_Natural_Ogetlocs @ hAPP ) @ hAPP ) @ ( E @ ( B @ ( c_Natural_Ogetlocs @ hAPP ) @ ( A @ ( c_Natural_Osetlocs @ hAPP ) @ hAPP ) @ ( c_Natural_Oupdate @ hAPP ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ ( E @ c_Com_Ocom_OCall ) ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( c_Com_ORes @ ( A @ ( c_Natural_Ogetlocs @ hAPP ) @ hAPP ) @ ( E @ ( B @ ( c_Natural_Ogetlocs @ hAPP ) @ ( A @ ( c_Natural_Osetlocs @ hAPP ) @ hAPP ) @ ( c_Natural_Oupdate @ hAPP ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ ( E @ c_Com_Ocom_OCall ) ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
=> ? [F: $i] :
( ( F @ ( B @ ( C @ hAPP ) @ ( c_Com_OArg @ c_Com_Ovname_OLoc @ ( c_Natural_Onewlocs @ ( B @ ( c_Natural_Osetlocs @ hAPP ) @ hAPP ) @ ( c_Natural_Oupdate @ hAPP ) @ hAPP ) @ hAPP ) @ ( D @ ( c_Com_Ocom_OBODY @ hAPP ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
& ( ( c_Com_ORes @ ( A @ ( c_Natural_Ogetlocs @ hAPP ) @ hAPP ) @ ( E @ ( B @ ( c_Natural_Ogetlocs @ hAPP ) @ ( A @ ( c_Natural_Osetlocs @ hAPP ) @ hAPP ) @ ( c_Natural_Oupdate @ hAPP ) @ hAPP ) @ hAPP ) )
= ( c_Com_ORes @ ( F @ ( c_Natural_Ogetlocs @ hAPP ) @ hAPP ) @ ( E @ ( B @ ( c_Natural_Ogetlocs @ hAPP ) @ ( F @ ( c_Natural_Osetlocs @ hAPP ) @ hAPP ) @ ( c_Natural_Oupdate @ hAPP ) @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(8,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Natural_Oevaln ) ) ) )
=> ( A @ ( C @ ( D @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evaln__evalc) ).
thf(113,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Natural_Oevaln ) ) ) )
=> ( A @ ( C @ ( D @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(55,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( c_Nat_OSuc @ hAPP ) )
= ( A @ ( c_Nat_OSuc @ hAPP ) ) )
=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_Suc__inject) ).
thf(377,plain,
! [A: $i,B: $i] :
( ( ( B @ ( c_Nat_OSuc @ hAPP ) )
= ( A @ ( c_Nat_OSuc @ hAPP ) ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(30,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( c_Nat_OSuc @ hAPP ) )
= ( A @ ( c_Nat_OSuc @ hAPP ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_nat_Oinject) ).
thf(230,plain,
! [A: $i,B: $i] :
( ( ( B = A )
=> ( ( B @ ( c_Nat_OSuc @ hAPP ) )
= ( A @ ( c_Nat_OSuc @ hAPP ) ) ) )
& ( ( ( B @ ( c_Nat_OSuc @ hAPP ) )
= ( A @ ( c_Nat_OSuc @ hAPP ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(43,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( E @ ( F @ c_Com_Ocom_OCall ) ) )
!= ( A @ ( B @ ( C @ c_Com_Ocom_OLocal ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I43_J) ).
thf(318,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( E @ ( F @ c_Com_Ocom_OCall ) ) )
!= ( A @ ( B @ ( C @ c_Com_Ocom_OLocal ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(89,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ c_Com_Ovname_OGlb @ ( B @ ( C @ ( D @ c_Com_Ovname_Ovname__case ) ) ) )
= ( A @ ( C @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vname_Osimps_I5_J) ).
thf(509,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ c_Com_Ovname_OGlb @ ( B @ ( C @ ( D @ c_Com_Ovname_Ovname__case ) ) ) )
= ( A @ ( C @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(28,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( E @ ( F @ c_Com_Ocom_OLocal ) ) )
= ( A @ ( B @ ( C @ c_Com_Ocom_OLocal ) ) ) )
<=> ( ( D = A )
& ( E = B )
& ( F = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I2_J) ).
thf(208,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ( D = A )
& ( E = B )
& ( F = C ) )
=> ( ( D @ ( E @ ( F @ c_Com_Ocom_OLocal ) ) )
= ( A @ ( B @ ( C @ c_Com_Ocom_OLocal ) ) ) ) )
& ( ( ( D @ ( E @ ( F @ c_Com_Ocom_OLocal ) ) )
= ( A @ ( B @ ( C @ c_Com_Ocom_OLocal ) ) ) )
=> ( ( D = A )
& ( E = B )
& ( F = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(85,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ v_P ) )
=> ! [C: $i] :
( ( C @ ( v_na @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( v_pn @ ( c_Com_Ocom_OBODY @ hAPP ) @ c_Natural_Oevaln ) ) ) )
=> ( c_Com_ORes @ ( C @ ( c_Natural_Ogetlocs @ hAPP ) @ hAPP ) @ ( v_X @ ( v_s_H @ ( c_Natural_Ogetlocs @ hAPP ) @ ( C @ ( c_Natural_Osetlocs @ hAPP ) @ hAPP ) @ ( c_Natural_Oupdate @ hAPP ) @ hAPP ) @ hAPP ) @ ( A @ v_Q ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
thf(494,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ v_P ) )
=> ! [C: $i] :
( ( C @ ( v_na @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( v_pn @ ( c_Com_Ocom_OBODY @ hAPP ) @ c_Natural_Oevaln ) ) ) )
=> ( c_Com_ORes @ ( C @ ( c_Natural_Ogetlocs @ hAPP ) @ hAPP ) @ ( v_X @ ( v_s_H @ ( c_Natural_Ogetlocs @ hAPP ) @ ( C @ ( c_Natural_Osetlocs @ hAPP ) @ hAPP ) @ ( c_Natural_Oupdate @ hAPP ) @ hAPP ) @ hAPP ) @ ( A @ v_Q ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( D @ ( B @ hAPP ) @ ( C @ c_Com_Ovname_OLoc @ ( D @ ( c_Natural_Oupdate @ hAPP ) @ hAPP ) @ hAPP ) @ ( E @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( D @ ( c_Natural_Ogetlocs @ hAPP ) @ hAPP ) @ ( C @ c_Com_Ovname_OLoc @ ( A @ ( c_Natural_Oupdate @ hAPP ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( B @ ( C @ c_Com_Ocom_OLocal ) ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evalc_OLocal) ).
thf(103,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( D @ ( B @ hAPP ) @ ( C @ c_Com_Ovname_OLoc @ ( D @ ( c_Natural_Oupdate @ hAPP ) @ hAPP ) @ hAPP ) @ ( E @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
=> ( C @ ( D @ ( c_Natural_Ogetlocs @ hAPP ) @ hAPP ) @ ( C @ c_Com_Ovname_OLoc @ ( A @ ( c_Natural_Oupdate @ hAPP ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( B @ ( C @ c_Com_Ocom_OLocal ) ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(45,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( D @ ( E @ ( F @ ( G @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( G @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) ) )
<=> ( ( D = A )
& ( E = B )
& ( F = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_triple_Oinject) ).
thf(323,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( ( D = A )
& ( E = B )
& ( F = C ) )
=> ( ( D @ ( E @ ( F @ ( G @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( G @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) ) ) )
& ( ( ( D @ ( E @ ( F @ ( G @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( G @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) ) )
=> ( ( D = A )
& ( E = B )
& ( F = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(14,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( C @ ( D @ ( c_Com_Ocom_OBODY @ hAPP ) @ c_Natural_Oevaln ) ) ) )
<=> ( A @ ( B @ ( C @ ( D @ ( c_Com_Obody @ hAPP ) @ ( tc_Com_Ocom @ c_Option_Othe @ hAPP ) @ c_Natural_Oevaln ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evaln_Oequations_I9_J) ).
thf(140,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( A @ ( B @ ( C @ ( D @ ( c_Com_Obody @ hAPP ) @ ( tc_Com_Ocom @ c_Option_Othe @ hAPP ) @ c_Natural_Oevaln ) ) ) )
=> ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( C @ ( D @ ( c_Com_Ocom_OBODY @ hAPP ) @ c_Natural_Oevaln ) ) ) ) )
& ( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( C @ ( D @ ( c_Com_Ocom_OBODY @ hAPP ) @ c_Natural_Oevaln ) ) ) )
=> ( A @ ( B @ ( C @ ( D @ ( c_Com_Obody @ hAPP ) @ ( tc_Com_Ocom @ c_Option_Othe @ hAPP ) @ c_Natural_Oevaln ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(3,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( E @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_Hoare__Mirabelle_Otriple__valid ) ) )
<=> ! [F: $i,G: $i] :
( ( G @ ( F @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [H: $i] :
( ( H @ ( D @ ( G @ ( B @ c_Natural_Oevaln ) ) ) )
=> ( H @ ( F @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_triple__valid__def2) ).
thf(91,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ! [F: $i,G: $i] :
( ( G @ ( F @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [H: $i] :
( ( H @ ( D @ ( G @ ( B @ c_Natural_Oevaln ) ) ) )
=> ( H @ ( F @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ) )
=> ( A @ ( B @ ( C @ ( E @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_Hoare__Mirabelle_Otriple__valid ) ) ) )
& ( ( A @ ( B @ ( C @ ( E @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ c_Hoare__Mirabelle_Otriple__valid ) ) )
=> ! [F: $i,G: $i] :
( ( G @ ( F @ ( C @ hAPP ) @ hAPP ) @ hBOOL )
=> ! [H: $i] :
( ( H @ ( D @ ( G @ ( B @ c_Natural_Oevaln ) ) ) )
=> ( H @ ( F @ ( A @ hAPP ) @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(81,axiom,
v_s_H @ v_a @ ( c_Com_OArg @ c_Com_Ovname_OLoc @ ( c_Natural_Onewlocs @ ( v_s_H @ ( c_Natural_Osetlocs @ hAPP ) @ hAPP ) @ ( c_Natural_Oupdate @ hAPP ) @ hAPP ) @ hAPP ) @ ( v_Z @ v_P ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_2) ).
thf(483,plain,
v_s_H @ v_a @ ( c_Com_OArg @ c_Com_Ovname_OLoc @ ( c_Natural_Onewlocs @ ( v_s_H @ ( c_Natural_Osetlocs @ hAPP ) @ hAPP ) @ ( c_Natural_Oupdate @ hAPP ) @ hAPP ) @ hAPP ) @ ( v_Z @ v_P ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(76,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( C @ ( B @ hAPP ) )
= ( C @ ( A @ hAPP ) ) )
=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_ext) ).
thf(462,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( C @ ( B @ hAPP ) )
= ( C @ ( A @ hAPP ) ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(34,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( c_Com_Ocom_OBODY @ hAPP ) )
!= ( A @ ( B @ c_Com_Ocom_OAss ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I31_J) ).
thf(278,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( c_Com_Ocom_OBODY @ hAPP ) )
!= ( A @ ( B @ c_Com_Ocom_OAss ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(29,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( c_Com_Ocom_OBODY @ hAPP ) )
!= ( A @ ( B @ ( C @ c_Com_Ocom_OCall ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I62_J) ).
thf(226,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( c_Com_Ocom_OBODY @ hAPP ) )
!= ( A @ ( B @ ( C @ c_Com_Ocom_OCall ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(70,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ ( F @ c_Product__Type_Oprod_Oprod__rec ) ) ) ) )
= ( A @ ( B @ ( C @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_prod_Orecs) ).
thf(438,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( E @ ( F @ c_Product__Type_OPair ) @ hAPP ) @ hAPP ) @ ( C @ ( D @ ( E @ ( F @ c_Product__Type_Oprod_Oprod__rec ) ) ) ) )
= ( A @ ( B @ ( C @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(21,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( c_Com_Ocom_OBODY @ hAPP ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
<=> ( A @ ( B @ ( C @ ( c_Com_Obody @ hAPP ) @ ( tc_Com_Ocom @ c_Option_Othe @ hAPP ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evalc_Oequations_I9_J) ).
thf(162,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( B @ ( C @ ( c_Com_Obody @ hAPP ) @ ( tc_Com_Ocom @ c_Option_Othe @ hAPP ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ ( c_Com_Ocom_OBODY @ hAPP ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ ( c_Com_Ocom_OBODY @ hAPP ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ ( c_Com_Obody @ hAPP ) @ ( tc_Com_Ocom @ c_Option_Othe @ hAPP ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(75,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( B @ ( C @ ( D @ ( E @ ( F @ ( G @ c_Finite__Set_Ofolding__image__simple__idem ) ) ) ) ) )
=> ( ( A @ ( A @ ( E @ hAPP ) @ hAPP ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_folding__image__simple__idem_Oidem) ).
thf(458,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( B @ ( C @ ( D @ ( E @ ( F @ ( G @ c_Finite__Set_Ofolding__image__simple__idem ) ) ) ) ) )
=> ( ( A @ ( A @ ( E @ hAPP ) @ hAPP ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(27,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( D @ c_Com_Ocom_OAss ) )
= ( A @ ( B @ c_Com_Ocom_OAss ) ) )
<=> ( ( C = A )
& ( D = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I1_J) ).
thf(194,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( C = A )
& ( D = B ) )
=> ( ( C @ ( D @ c_Com_Ocom_OAss ) )
= ( A @ ( B @ c_Com_Ocom_OAss ) ) ) )
& ( ( ( C @ ( D @ c_Com_Ocom_OAss ) )
= ( A @ ( B @ c_Com_Ocom_OAss ) ) )
=> ( ( C = A )
& ( D = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(35,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Com_Ocom_OLocal ) ) )
!= ( A @ ( B @ c_Com_Ocom_OAss ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I23_J) ).
thf(282,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Com_Ocom_OLocal ) ) )
!= ( A @ ( B @ c_Com_Ocom_OAss ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(41,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_Com_Ocom_OLocal ) ) )
!= ( A @ ( c_Com_Ocom_OBODY @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I40_J) ).
thf(310,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_Com_Ocom_OLocal ) ) )
!= ( A @ ( c_Com_Ocom_OBODY @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(77,axiom,
! [A: $i,B: $i,C: $i,D: $i] : ( B @ ( C @ hAPP ) @ ( D @ ( B @ ( c_Natural_Oupdate @ hAPP ) @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( C @ ( D @ c_Com_Ocom_OAss ) @ c_Natural_Oevaln ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evaln_Oequations_I2_J) ).
thf(465,plain,
! [A: $i,B: $i,C: $i,D: $i] : ( B @ ( C @ hAPP ) @ ( D @ ( B @ ( c_Natural_Oupdate @ hAPP ) @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( C @ ( D @ c_Com_Ocom_OAss ) @ c_Natural_Oevaln ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(53,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_Com_Ocom_OCall ) ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ! [F: $i] :
( ( A
= ( c_Com_ORes @ ( F @ ( c_Natural_Ogetlocs @ hAPP ) @ hAPP ) @ ( E @ ( B @ ( c_Natural_Ogetlocs @ hAPP ) @ ( F @ ( c_Natural_Osetlocs @ hAPP ) @ hAPP ) @ ( c_Natural_Oupdate @ hAPP ) @ hAPP ) @ hAPP ) ) )
=> ~ ( F @ ( B @ ( C @ hAPP ) @ ( c_Com_OArg @ c_Com_Ovname_OLoc @ ( c_Natural_Onewlocs @ ( B @ ( c_Natural_Osetlocs @ hAPP ) @ hAPP ) @ ( c_Natural_Oupdate @ hAPP ) @ hAPP ) @ hAPP ) @ ( D @ ( c_Com_Ocom_OBODY @ hAPP ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evalc__elim__cases_I7_J) ).
thf(368,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_Com_Ocom_OCall ) ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
=> ~ ! [F: $i] :
( ( A
= ( c_Com_ORes @ ( F @ ( c_Natural_Ogetlocs @ hAPP ) @ hAPP ) @ ( E @ ( B @ ( c_Natural_Ogetlocs @ hAPP ) @ ( F @ ( c_Natural_Osetlocs @ hAPP ) @ hAPP ) @ ( c_Natural_Oupdate @ hAPP ) @ hAPP ) @ hAPP ) ) )
=> ~ ( F @ ( B @ ( C @ hAPP ) @ ( c_Com_OArg @ c_Com_Ovname_OLoc @ ( c_Natural_Onewlocs @ ( B @ ( c_Natural_Osetlocs @ hAPP ) @ hAPP ) @ ( c_Natural_Oupdate @ hAPP ) @ hAPP ) @ hAPP ) @ ( D @ ( c_Com_Ocom_OBODY @ hAPP ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(39,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ c_Com_Ovname_OLoc @ ( B @ ( C @ ( D @ c_Com_Ovname_Ovname__case ) ) ) )
= ( A @ ( B @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vname_Osimps_I6_J) ).
thf(304,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ c_Com_Ovname_OLoc @ ( B @ ( C @ ( D @ c_Com_Ovname_Ovname__case ) ) ) )
= ( A @ ( B @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(19,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( c_Com_Obody @ hAPP ) @ ( tc_Com_Ocom @ c_Option_Othe @ hAPP ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ ( c_Com_Ocom_OBODY @ hAPP ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evalc_OBody) ).
thf(158,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( c_Com_Obody @ hAPP ) @ ( tc_Com_Ocom @ c_Option_Othe @ hAPP ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ ( c_Com_Ocom_OBODY @ hAPP ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(65,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_New__DSequence_Oneg__single ) @ hAPP ) )
= ( B @ ( C @ c_Lazy__Sequence_Ohb__single ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_New__DSequence_Oneg__single__def) ).
thf(418,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_New__DSequence_Oneg__single ) @ hAPP ) )
= ( B @ ( C @ c_Lazy__Sequence_Ohb__single ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(17,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
=> ? [D: $i] : ( A @ ( D @ ( B @ ( C @ c_Natural_Oevaln ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evalc__evaln) ).
thf(151,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
=> ? [D: $i] : ( A @ ( D @ ( B @ ( C @ c_Natural_Oevaln ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(38,axiom,
! [A: $i,B: $i] :
( ( B @ c_Com_Ovname_OLoc )
!= ( A @ c_Com_Ovname_OGlb ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vname_Osimps_I4_J) ).
thf(300,plain,
! [A: $i,B: $i] :
( ( B @ c_Com_Ovname_OLoc )
!= ( A @ c_Com_Ovname_OGlb ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(62,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_New__Random__Sequence_Oneg__single @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) )
= ( D @ ( E @ c_New__DSequence_Oneg__single ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_neg__single__def) ).
thf(410,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_New__Random__Sequence_Oneg__single @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) )
= ( D @ ( E @ c_New__DSequence_Oneg__single ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(22,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
<=> ? [D: $i] : ( A @ ( D @ ( B @ ( C @ c_Natural_Oevaln ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_eval__eq) ).
thf(168,plain,
! [A: $i,B: $i,C: $i] :
( ( ? [D: $i] : ( A @ ( D @ ( B @ ( C @ c_Natural_Oevaln ) ) ) )
=> ( A @ ( B @ ( C @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
=> ? [D: $i] : ( A @ ( D @ ( B @ ( C @ c_Natural_Oevaln ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(15,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Com_Ocom_OAss ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A
= ( B @ ( C @ hAPP ) @ ( D @ ( B @ ( c_Natural_Oupdate @ hAPP ) @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evalc__elim__cases_I2_J) ).
thf(146,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Com_Ocom_OAss ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
=> ( A
= ( B @ ( C @ hAPP ) @ ( D @ ( B @ ( c_Natural_Oupdate @ hAPP ) @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(26,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( c_Com_Ocom_OBODY @ hAPP ) )
!= ( A @ ( B @ ( C @ c_Com_Ocom_OLocal ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I41_J) ).
thf(190,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( c_Com_Ocom_OBODY @ hAPP ) )
!= ( A @ ( B @ ( C @ c_Com_Ocom_OLocal ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(54,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Com_Ocom_OCall ) ) )
!= ( A @ ( B @ c_Com_Ocom_OAss ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_com_Osimps_I33_J) ).
thf(373,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Com_Ocom_OCall ) ) )
!= ( A @ ( B @ c_Com_Ocom_OAss ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(88,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( F @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ c_Hoare__Mirabelle_Otriple_Otriple__case ) ) ) )
= ( A @ ( B @ ( C @ ( D @ hAPP ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_triple_Osimps_I2_J) ).
thf(506,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( F @ c_Hoare__Mirabelle_Otriple_Otriple @ hAPP ) @ hAPP ) @ hAPP ) @ ( D @ ( E @ ( F @ c_Hoare__Mirabelle_Otriple_Otriple__case ) ) ) )
= ( A @ ( B @ ( C @ ( D @ hAPP ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(64,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ c_Com_Ovname_OGlb @ ( B @ ( C @ ( D @ c_Com_Ovname_Ovname__rec ) ) ) )
= ( A @ ( C @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_vname_Orecs_I1_J) ).
thf(415,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ c_Com_Ovname_OGlb @ ( B @ ( C @ ( D @ c_Com_Ovname_Ovname__rec ) ) ) )
= ( A @ ( C @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(68,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( C @ ( D @ ( E @ ( F @ ( G @ c_Typedef_Otype__definition ) ) ) ) )
=> ( ( ( B @ ( E @ hAPP ) )
= ( A @ ( E @ hAPP ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_type__definition_ORep__inject) ).
thf(427,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( C @ ( D @ ( E @ ( F @ ( G @ c_Typedef_Otype__definition ) ) ) ) )
=> ( ( ( B = A )
=> ( ( B @ ( E @ hAPP ) )
= ( A @ ( E @ hAPP ) ) ) )
& ( ( ( B @ ( E @ hAPP ) )
= ( A @ ( E @ hAPP ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( B @ ( c_Natural_Ogetlocs @ hAPP ) @ hAPP ) @ ( E @ c_Com_Ovname_OLoc @ ( A @ ( c_Natural_Oupdate @ hAPP ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ ( E @ c_Com_Ocom_OLocal ) ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
<=> ? [F: $i] :
( ( F @ ( B @ ( D @ hAPP ) @ ( E @ c_Com_Ovname_OLoc @ ( B @ ( c_Natural_Oupdate @ hAPP ) @ hAPP ) @ hAPP ) @ ( C @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
& ( ( E @ ( B @ ( c_Natural_Ogetlocs @ hAPP ) @ hAPP ) @ ( E @ c_Com_Ovname_OLoc @ ( A @ ( c_Natural_Oupdate @ hAPP ) @ hAPP ) @ hAPP ) )
= ( E @ ( B @ ( c_Natural_Ogetlocs @ hAPP ) @ hAPP ) @ ( E @ c_Com_Ovname_OLoc @ ( F @ ( c_Natural_Oupdate @ hAPP ) @ hAPP ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evalc_Oequations_I3_J) ).
thf(131,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ? [F: $i] :
( ( F @ ( B @ ( D @ hAPP ) @ ( E @ c_Com_Ovname_OLoc @ ( B @ ( c_Natural_Oupdate @ hAPP ) @ hAPP ) @ hAPP ) @ ( C @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
& ( ( E @ ( B @ ( c_Natural_Ogetlocs @ hAPP ) @ hAPP ) @ ( E @ c_Com_Ovname_OLoc @ ( A @ ( c_Natural_Oupdate @ hAPP ) @ hAPP ) @ hAPP ) )
= ( E @ ( B @ ( c_Natural_Ogetlocs @ hAPP ) @ hAPP ) @ ( E @ c_Com_Ovname_OLoc @ ( F @ ( c_Natural_Oupdate @ hAPP ) @ hAPP ) @ hAPP ) ) ) )
=> ( E @ ( B @ ( c_Natural_Ogetlocs @ hAPP ) @ hAPP ) @ ( E @ c_Com_Ovname_OLoc @ ( A @ ( c_Natural_Oupdate @ hAPP ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ ( E @ c_Com_Ocom_OLocal ) ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL ) )
& ( ( E @ ( B @ ( c_Natural_Ogetlocs @ hAPP ) @ hAPP ) @ ( E @ c_Com_Ovname_OLoc @ ( A @ ( c_Natural_Oupdate @ hAPP ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ ( D @ ( E @ c_Com_Ocom_OLocal ) ) @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
=> ? [F: $i] :
( ( F @ ( B @ ( D @ hAPP ) @ ( E @ c_Com_Ovname_OLoc @ ( B @ ( c_Natural_Oupdate @ hAPP ) @ hAPP ) @ hAPP ) @ ( C @ c_Natural_Oevalc @ hAPP ) @ hAPP ) @ hBOOL )
& ( ( E @ ( B @ ( c_Natural_Ogetlocs @ hAPP ) @ hAPP ) @ ( E @ c_Com_Ovname_OLoc @ ( A @ ( c_Natural_Oupdate @ hAPP ) @ hAPP ) @ hAPP ) )
= ( E @ ( B @ ( c_Natural_Ogetlocs @ hAPP ) @ hAPP ) @ ( E @ c_Com_Ovname_OLoc @ ( F @ ( c_Natural_Oupdate @ hAPP ) @ hAPP ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(24,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Natural_Oevaln ) ) ) )
=> ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( C @ ( D @ c_Natural_Oevaln ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evaln__Suc) ).
thf(178,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Natural_Oevaln ) ) ) )
=> ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( C @ ( D @ c_Natural_Oevaln ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(44,axiom,
v_s1 @ ( v_na @ ( v_s_H @ v_a @ ( c_Com_OArg @ c_Com_Ovname_OLoc @ ( c_Natural_Onewlocs @ ( v_s_H @ ( c_Natural_Osetlocs @ hAPP ) @ hAPP ) @ ( c_Natural_Oupdate @ hAPP ) @ hAPP ) @ hAPP ) @ ( v_pn @ ( c_Com_Obody @ hAPP ) @ ( tc_Com_Ocom @ c_Option_Othe @ hAPP ) @ c_Natural_Oevaln ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_3) ).
thf(322,plain,
v_s1 @ ( v_na @ ( v_s_H @ v_a @ ( c_Com_OArg @ c_Com_Ovname_OLoc @ ( c_Natural_Onewlocs @ ( v_s_H @ ( c_Natural_Osetlocs @ hAPP ) @ hAPP ) @ ( c_Natural_Oupdate @ hAPP ) @ hAPP ) @ hAPP ) @ ( v_pn @ ( c_Com_Obody @ hAPP ) @ ( tc_Com_Ocom @ c_Option_Othe @ hAPP ) @ c_Natural_Oevaln ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(83,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( E @ ( F @ c_Nitpick_Opair__box_OPairBox ) ) ) @ ( C @ ( D @ ( E @ ( F @ c_Nitpick_Opair__box_Opair__box__case ) ) ) ) )
= ( A @ ( B @ ( C @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_pair__box_Osimps_I2_J) ).
thf(486,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( E @ ( F @ c_Nitpick_Opair__box_OPairBox ) ) ) @ ( C @ ( D @ ( E @ ( F @ c_Nitpick_Opair__box_Opair__box__case ) ) ) ) )
= ( A @ ( B @ ( C @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(86,axiom,
! [A: $i,B: $i,C: $i,D: $i] : ( B @ ( C @ hAPP ) @ ( D @ ( B @ ( c_Natural_Oupdate @ hAPP ) @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( C @ ( D @ c_Com_Ocom_OAss ) @ c_Natural_Oevaln ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evaln_OAssign) ).
thf(496,plain,
! [A: $i,B: $i,C: $i,D: $i] : ( B @ ( C @ hAPP ) @ ( D @ ( B @ ( c_Natural_Oupdate @ hAPP ) @ hAPP ) @ hAPP ) @ ( A @ ( B @ ( C @ ( D @ c_Com_Ocom_OAss ) @ c_Natural_Oevaln ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(1,conjecture,
c_Com_ORes @ ( v_s1 @ ( c_Natural_Ogetlocs @ hAPP ) @ hAPP ) @ ( v_X @ ( v_s_H @ ( c_Natural_Ogetlocs @ hAPP ) @ ( v_s1 @ ( c_Natural_Osetlocs @ hAPP ) @ hAPP ) @ ( c_Natural_Oupdate @ hAPP ) @ hAPP ) @ hAPP ) @ ( v_Z @ v_Q ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_4) ).
thf(2,negated_conjecture,
~ ( c_Com_ORes @ ( v_s1 @ ( c_Natural_Ogetlocs @ hAPP ) @ hAPP ) @ ( v_X @ ( v_s_H @ ( c_Natural_Ogetlocs @ hAPP ) @ ( v_s1 @ ( c_Natural_Osetlocs @ hAPP ) @ hAPP ) @ ( c_Natural_Oupdate @ hAPP ) @ hAPP ) @ hAPP ) @ ( v_Z @ v_Q ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(90,plain,
~ ( c_Com_ORes @ ( v_s1 @ ( c_Natural_Ogetlocs @ hAPP ) @ hAPP ) @ ( v_X @ ( v_s_H @ ( c_Natural_Ogetlocs @ hAPP ) @ ( v_s1 @ ( c_Natural_Osetlocs @ hAPP ) @ hAPP ) @ ( c_Natural_Oupdate @ hAPP ) @ hAPP ) @ hAPP ) @ ( v_Z @ v_Q ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ ( c_Com_Obody @ hAPP ) @ ( tc_Com_Ocom @ c_Option_Othe @ hAPP ) @ c_Natural_Oevaln ) ) ) )
=> ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( C @ ( D @ ( c_Com_Ocom_OBODY @ hAPP ) @ c_Natural_Oevaln ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_evaln_OBody) ).
thf(111,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ ( c_Com_Obody @ hAPP ) @ ( tc_Com_Ocom @ c_Option_Othe @ hAPP ) @ c_Natural_Oevaln ) ) ) )
=> ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( C @ ( D @ ( c_Com_Ocom_OBODY @ hAPP ) @ c_Natural_Oevaln ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(573,plain,
$false,
inference(e,[status(thm)],[115,174,421,453,129,441,314,346,365,101,384,153,344,357,238,121,353,480,307,380,270,160,424,407,467,484,252,361,435,456,403,388,471,124,489,105,398,444,149,180,296,286,413,498,335,113,377,230,318,509,208,494,103,323,140,91,483,462,278,226,438,162,458,194,282,310,465,368,304,158,418,151,300,410,168,146,190,373,506,415,427,131,178,322,486,496,90,111]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW343+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.14/0.42 % Computer : n026.cluster.edu
% 0.14/0.42 % Model : x86_64 x86_64
% 0.14/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.42 % Memory : 8046.5625MB
% 0.14/0.42 % OS : Linux 6.8.0-71-generic
% 0.14/0.42 % CPULimit : 300
% 0.14/0.42 % WCLimit : 300
% 0.14/0.42 % DateTime : Sat Sep 26 15:45:11 UTC 2026
% 0.14/0.42 % CPUTime :
% 0.14/0.42 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.88/1.00 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 4.55/2.06 % [INFO] Parsing done (1056ms).
% 4.55/2.08 % [INFO] Running in sequential loop mode.
% 5.34/2.47 % [INFO] eprover registered as external prover.
% 5.34/2.48 % [INFO] Scanning for conjecture ...
% 8.34/3.21 % [INFO] Found a conjecture (or negated_conjecture) and 5208 axioms. Running axiom selection ...
% 10.37/4.14 % [INFO] Axiom selection finished. Selected 87 axioms (removed 5121 axioms).
% 10.77/4.30 % [INFO] Problem is first-order (TPTP FOF).
% 10.77/4.32 % [INFO] Type checking passed.
% 10.77/4.32 % [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 ...
% 18.34/6.25 % External prover 'e' found a proof!
% 18.34/6.25 % [INFO] Killing All external provers ...
% 18.34/6.25 % Time passed: 5689ms (effective reasoning time: 4165ms)
% 18.34/6.25 % 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)>
% 18.34/6.25 % 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
% 18.34/6.25 % No. of inferences in proof: 178
% 18.34/6.26 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 5689 ms resp. 4165 ms w/o parsing
% 19.26/6.41 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 19.26/6.41 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------