%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWW295+1 : TPTP v9.3.1. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n005.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 09:09:51 AM UTC 2026
% Result : Theorem 62.56s 17.08s
% Output : Refutation 55.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 218
% Syntax : Number of formulae : 518 ( 284 unt; 0 typ; 8 def)
% Number of atoms : 1152 ( 564 equ; 0 cnn)
% Maximal formula atoms : 20 ( 2 avg)
% Number of connectives : 6076 ( 360 ~; 113 |; 154 &;5106 @)
% ( 41 <=>; 302 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 2 ( 2 >; 0 *; 0 +; 0 <<)
% Number of symbols : 77 ( 74 usr; 20 con; 0-10 aty)
% Number of variables : 2192 ( 7 ^;2104 !; 73 ?;2192 :)
% ( 0 !>; 0 ?*; 0 @-; 8 @+)
% Comments :
%------------------------------------------------------------------------------
thf(v_P_decl,type,
v_P: $i > $i > $o ).
thf(c_Natural_Oevaln_decl,type,
c_Natural_Oevaln: $i > $i > $i > $i > $o ).
thf(hAPP_decl,type,
hAPP: $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(v_pn_decl,type,
v_pn: $i ).
thf(v_n_decl,type,
v_n: $i ).
thf(v_Q_decl,type,
v_Q: $i > $i > $o ).
thf(c_Com_Ocom_OBODY_decl,type,
c_Com_Ocom_OBODY: $i > $i ).
thf(c_Nat_OSuc_decl,type,
c_Nat_OSuc: $i ).
thf(c_Map_Omap__comp_decl,type,
c_Map_Omap__comp: $i > $i > $i > $i > $i > $i > $i ).
thf(c_Option_Ooption_OSome_decl,type,
c_Option_Ooption_OSome: $i > $i ).
thf(c_Option_Ooption_ONone_decl,type,
c_Option_Ooption_ONone: $i > $i ).
thf(c_Com_Ocom_OWhile_decl,type,
c_Com_Ocom_OWhile: $i > $i > $i ).
thf(c_Com_Ocom_OSemi_decl,type,
c_Com_Ocom_OSemi: $i > $i > $i ).
thf(c_Com_Ocom_OLocal_decl,type,
c_Com_Ocom_OLocal: $i > $i > $i > $i ).
thf(hBOOL_decl,type,
hBOOL: $i > $o ).
thf(c_Natural_Oevalc_decl,type,
c_Natural_Oevalc: $i > $i > $i > $o ).
thf(c_Com_Ocom_OCond_decl,type,
c_Com_Ocom_OCond: $i > $i > $i > $i ).
thf(c_Com_OWT_decl,type,
c_Com_OWT: $i ).
thf(c_Com_Ocom_OCall_decl,type,
c_Com_Ocom_OCall: $i > $i > $i > $i ).
thf(c_Com_Ocom_OSKIP_decl,type,
c_Com_Ocom_OSKIP: $i ).
thf(c_Com_Ocom_Ocom__rec_decl,type,
c_Com_Ocom_Ocom__rec: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i ).
thf(c_Sum__Type_Osum_Osum__case_decl,type,
c_Sum__Type_Osum_Osum__case: $i > $i > $i > $i > $i > $i ).
thf(c_Sum__Type_OInl_decl,type,
c_Sum__Type_OInl: $i > $i > $i ).
thf(c_Product__Type_OPair_decl,type,
c_Product__Type_OPair: $i > $i > $i ).
thf(c_Com_Ocom_OAss_decl,type,
c_Com_Ocom_OAss: $i > $i > $i ).
thf(c_Sum__Type_OInr_decl,type,
c_Sum__Type_OInr: $i > $i > $i ).
thf(c_Natural_Oupdate_decl,type,
c_Natural_Oupdate: $i > $i > $i > $i ).
thf(c_List_Orotate1_decl,type,
c_List_Orotate1: $i > $i ).
thf(c_List_Orotate_decl,type,
c_List_Orotate: $i > $i > $i ).
thf(c_Nitpick_Opair__box_OPairBox_decl,type,
c_Nitpick_Opair__box_OPairBox: $i > $i > $i > $i > $i ).
thf(c_Com_Ocom_Ocom__case_decl,type,
c_Com_Ocom_Ocom__case: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i ).
thf(c_Com_OWT__bodies_decl,type,
c_Com_OWT__bodies: $o ).
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(c_Finite__Set_Ofolding__one__idem_decl,type,
c_Finite__Set_Ofolding__one__idem: $i > $i > $i > $o ).
thf(c_Typedef_Otype__definition_decl,type,
c_Typedef_Otype__definition: $i > $i > $i > $i > $i > $o ).
thf(c_Sum__Type_OProjr_decl,type,
c_Sum__Type_OProjr: $i > $i > $i > $i ).
thf(c_Nitpick_Opair__box_Opair__box__rec_decl,type,
c_Nitpick_Opair__box_Opair__box__rec: $i > $i > $i > $i > $i > $i ).
thf(c_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_Lazy__Sequence_Ohb__single_decl,type,
c_Lazy__Sequence_Ohb__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_Map_Omap__of_decl,type,
c_Map_Omap__of: $i > $i > $i > $i ).
thf(tc_Com_Opname_decl,type,
tc_Com_Opname: $i ).
thf(c_Com_Obodies_decl,type,
c_Com_Obodies: $i ).
thf(c_Sum__Type_OProjl_decl,type,
c_Sum__Type_OProjl: $i > $i > $i > $i ).
thf(c_Nitpick_Opair__box_Opair__box__case_decl,type,
c_Nitpick_Opair__box_Opair__box__case: $i > $i > $i > $i > $i > $i ).
thf(c_Nat_Onat_Onat__rec_decl,type,
c_Nat_Onat_Onat__rec: $i > $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_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_Product__Type_Oprod_Oprod__rec_decl,type,
c_Product__Type_Oprod_Oprod__rec: $i > $i > $i > $i > $i > $i ).
thf(c_Nat_Onat_Onat__case_decl,type,
c_Nat_Onat_Onat__case: $i > $i > $i > $i > $i ).
thf(c_Int_ORep__Integ_decl,type,
c_Int_ORep__Integ: $i ).
thf(c_Power_Opower_Opower_decl,type,
c_Power_Opower_Opower: $i > $i > $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(class_Rings_Osemiring__1_decl,type,
class_Rings_Osemiring__1: $i > $o ).
thf(c_Nat_Osemiring__1__class_Oof__nat__aux_decl,type,
c_Nat_Osemiring__1__class_Oof__nat__aux: $i > $i > $i > $i > $i ).
thf(c_Lazy__Sequence_Oempty_decl,type,
c_Lazy__Sequence_Oempty: $i > $i ).
thf(sk1_decl,type,
sk1: $o ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: $i ).
thf(sk4_decl,type,
sk4: $i ).
thf(sk5_decl,type,
sk5: $i ).
thf(sk6_decl,type,
sk6: $i ).
thf(sk7_decl,type,
sk7: $i ).
thf(sk8_decl,type,
sk8: $i > $i > $i > $i > $i > $i > $i > $i ).
thf(sk50_decl,type,
sk50: $i > $i ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ! [B: $i] :
( ( B @ ( A @ v_P ) )
=> ! [C: $i] :
( ( C @ ( v_n @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( v_pn @ c_Com_Ocom_OBODY @ c_Natural_Oevaln ) ) ) )
=> ( C @ ( A @ v_Q ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
~ ( ( A @ ( sk2 @ v_P ) )
=> ! [B: $i] :
( ( B @ ( v_n @ ( c_Nat_OSuc @ hAPP ) @ ( A @ ( v_pn @ c_Com_Ocom_OBODY @ c_Natural_Oevaln ) ) ) )
=> ( B @ ( sk2 @ v_Q ) ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: $i] :
~ ( ( A @ ( v_n @ ( c_Nat_OSuc @ hAPP ) @ ( sk3 @ ( v_pn @ c_Com_Ocom_OBODY @ c_Natural_Oevaln ) ) ) )
=> ( A @ ( sk2 @ v_Q ) ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( @+[A: $i] :
~ ! [B: $i] :
( ( B @ ( A @ v_P ) )
=> ! [C: $i] :
( ( C @ ( v_n @ ( B @ ( v_pn @ ( c_Com_Obody @ hAPP ) @ ( tc_Com_Ocom @ c_Option_Othe @ hAPP ) @ c_Natural_Oevaln ) ) ) )
=> ( C @ ( A @ v_Q ) ) ) ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( @+[A: $i] :
~ ( ( A @ ( sk5 @ v_P ) )
=> ! [B: $i] :
( ( B @ ( v_n @ ( A @ ( v_pn @ ( c_Com_Obody @ hAPP ) @ ( tc_Com_Ocom @ c_Option_Othe @ hAPP ) @ c_Natural_Oevaln ) ) ) )
=> ( B @ ( sk5 @ v_Q ) ) ) ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( @+[A: $i] :
~ ( ( A @ ( v_n @ ( sk6 @ ( v_pn @ ( c_Com_Obody @ hAPP ) @ ( tc_Com_Ocom @ c_Option_Othe @ hAPP ) @ c_Natural_Oevaln ) ) ) )
=> ( A @ ( sk5 @ v_Q ) ) ) ) ) ).
thf(sk8_def,definition,
( sk8
= ( ^ [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
@+[H: $i] :
( ( ( H @ ( D @ hAPP ) )
= ( G @ ( B @ c_Option_Ooption_OSome @ hAPP ) ) )
& ( ( F @ ( E @ hAPP ) )
= ( H @ ( A @ c_Option_Ooption_OSome @ hAPP ) ) ) ) ) ) ).
thf(sk50_def,definition,
( sk50
= ( @+[A: $i > $i] :
! [B: $i] :
( ( B @ c_Com_Ocom_OBODY @ A )
= B ) ) ) ).
thf(112,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( E @ c_Com_Ocom_OAss ) )
!= ( A @ ( B @ ( C @ c_Com_Ocom_OCond ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I26_J) ).
thf(809,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( E @ c_Com_Ocom_OAss ) )
!= ( A @ ( B @ ( C @ c_Com_Ocom_OCond ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(210,axiom,
! [A: $i,B: $i,C: $i,D: $i] : ( B @ ( C @ hAPP ) @ ( D @ ( B @ c_Natural_Oupdate ) ) @ ( A @ ( B @ ( C @ ( D @ c_Com_Ocom_OAss ) @ c_Natural_Oevaln ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln_Oequations_I2_J) ).
thf(1190,plain,
! [A: $i,B: $i,C: $i,D: $i] : ( B @ ( C @ hAPP ) @ ( D @ ( B @ c_Natural_Oupdate ) ) @ ( A @ ( B @ ( C @ ( D @ c_Com_Ocom_OAss ) @ c_Natural_Oevaln ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(189,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Com_Ocom_OBODY @ c_Natural_Oevalc ) ) )
=> ( A @ ( B @ ( C @ ( c_Com_Obody @ hAPP ) @ ( tc_Com_Ocom @ c_Option_Othe @ hAPP ) @ c_Natural_Oevalc ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc__elim__cases_I6_J) ).
thf(1105,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Com_Ocom_OBODY @ c_Natural_Oevalc ) ) )
=> ( A @ ( B @ ( C @ ( c_Com_Obody @ hAPP ) @ ( tc_Com_Ocom @ c_Option_Othe @ hAPP ) @ c_Natural_Oevalc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(1,conjecture,
( ! [A: $i,B: $i] :
( ( B @ ( A @ v_P ) )
=> ! [C: $i] :
( ( C @ ( v_n @ ( B @ ( v_pn @ ( c_Com_Obody @ hAPP ) @ ( tc_Com_Ocom @ c_Option_Othe @ hAPP ) @ c_Natural_Oevaln ) ) ) )
=> ( C @ ( A @ v_Q ) ) ) )
<=> ! [A: $i,B: $i] :
( ( B @ ( A @ v_P ) )
=> ! [C: $i] :
( ( C @ ( v_n @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( v_pn @ c_Com_Ocom_OBODY @ c_Natural_Oevaln ) ) ) )
=> ( C @ ( A @ v_Q ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( ! [A: $i,B: $i] :
( ( B @ ( A @ v_P ) )
=> ! [C: $i] :
( ( C @ ( v_n @ ( B @ ( v_pn @ ( c_Com_Obody @ hAPP ) @ ( tc_Com_Ocom @ c_Option_Othe @ hAPP ) @ c_Natural_Oevaln ) ) ) )
=> ( C @ ( A @ v_Q ) ) ) )
<=> ! [A: $i,B: $i] :
( ( B @ ( A @ v_P ) )
=> ! [C: $i] :
( ( C @ ( v_n @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( v_pn @ c_Com_Ocom_OBODY @ c_Natural_Oevaln ) ) ) )
=> ( C @ ( A @ v_Q ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(212,plain,
~ ( ( ! [A: $i,B: $i] :
( ( B @ ( A @ v_P ) )
=> ! [C: $i] :
( ( C @ ( v_n @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( v_pn @ c_Com_Ocom_OBODY @ c_Natural_Oevaln ) ) ) )
=> ( C @ ( A @ v_Q ) ) ) )
=> ! [A: $i,B: $i] :
( ( B @ ( A @ v_P ) )
=> ! [C: $i] :
( ( C @ ( v_n @ ( B @ ( v_pn @ ( c_Com_Obody @ hAPP ) @ ( tc_Com_Ocom @ c_Option_Othe @ hAPP ) @ c_Natural_Oevaln ) ) ) )
=> ( C @ ( A @ v_Q ) ) ) ) )
& ( ! [A: $i,B: $i] :
( ( B @ ( A @ v_P ) )
=> ! [C: $i] :
( ( C @ ( v_n @ ( B @ ( v_pn @ ( c_Com_Obody @ hAPP ) @ ( tc_Com_Ocom @ c_Option_Othe @ hAPP ) @ c_Natural_Oevaln ) ) ) )
=> ( C @ ( A @ v_Q ) ) ) )
=> ! [A: $i,B: $i] :
( ( B @ ( A @ v_P ) )
=> ! [C: $i] :
( ( C @ ( v_n @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( v_pn @ c_Com_Ocom_OBODY @ c_Natural_Oevaln ) ) ) )
=> ( C @ ( A @ v_Q ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(213,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ~ ( sk7 @ ( sk5 @ v_Q ) )
| sk1 )
& ( ( sk7 @ ( v_n @ ( sk6 @ ( v_pn @ ( c_Com_Obody @ hAPP ) @ ( tc_Com_Ocom @ c_Option_Othe @ hAPP ) @ c_Natural_Oevaln ) ) ) )
| sk1 )
& ( ( sk6 @ ( sk5 @ v_P ) )
| sk1 )
& ( ( F @ ( D @ v_Q ) )
| ~ ( F @ ( v_n @ ( c_Nat_OSuc @ hAPP ) @ ( E @ ( v_pn @ c_Com_Ocom_OBODY @ c_Natural_Oevaln ) ) ) )
| ~ ( E @ ( D @ v_P ) )
| sk1 )
& ( ~ sk1
| ~ ( sk4 @ ( sk2 @ v_Q ) ) )
& ( ~ sk1
| ( sk4 @ ( v_n @ ( c_Nat_OSuc @ hAPP ) @ ( sk3 @ ( v_pn @ c_Com_Ocom_OBODY @ c_Natural_Oevaln ) ) ) ) )
& ( ~ sk1
| ( sk3 @ ( sk2 @ v_P ) ) )
& ( ~ sk1
| ( C @ ( A @ v_Q ) )
| ~ ( C @ ( v_n @ ( B @ ( v_pn @ ( c_Com_Obody @ hAPP ) @ ( tc_Com_Ocom @ c_Option_Othe @ hAPP ) @ c_Natural_Oevaln ) ) ) )
| ~ ( B @ ( A @ v_P ) ) ) ),
inference(cnf,[status(esa)],[212]) ).
thf(217,plain,
( ( sk6 @ ( sk5 @ v_P ) )
| sk1 ),
inference(cnfConj,[status(thm)],[213]) ).
thf(218,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ v_Q ) )
| ~ ( C @ ( v_n @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( v_pn @ c_Com_Ocom_OBODY @ c_Natural_Oevaln ) ) ) )
| ~ ( B @ ( A @ v_P ) )
| sk1 ),
inference(cnfConj,[status(thm)],[213]) ).
thf(222,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ v_Q ) )
| ~ ( C @ ( v_n @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( v_pn @ c_Com_Ocom_OBODY @ c_Natural_Oevaln ) ) ) )
| ~ ( B @ ( A @ v_P ) )
| sk1 ),
inference(simp,[status(thm)],[218]) ).
thf(1229,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk6 @ ( sk5 @ v_P ) )
!= ( B @ ( A @ v_P ) ) )
| ( C @ ( A @ v_Q ) )
| ~ ( C @ ( v_n @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( v_pn @ c_Com_Ocom_OBODY @ c_Natural_Oevaln ) ) ) )
| ~ $true
| sk1
| sk1 ),
inference(paramod_ordered,[status(thm)],[217,222]) ).
thf(1230,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk6 @ ( sk5 @ v_P ) )
!= ( B @ ( A @ v_P ) ) )
| ( C @ ( A @ v_Q ) )
| ~ ( C @ ( v_n @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( v_pn @ c_Com_Ocom_OBODY @ c_Natural_Oevaln ) ) ) )
| sk1 ),
inference(simp,[status(thm)],[1229]) ).
thf(1231,plain,
! [A: $i] :
( ( A @ ( sk5 @ v_Q ) )
| ~ ( A @ ( v_n @ ( c_Nat_OSuc @ hAPP ) @ ( sk6 @ ( v_pn @ c_Com_Ocom_OBODY @ c_Natural_Oevaln ) ) ) )
| sk1 ),
inference(pattern_uni,[status(thm)],[1230:[bind(A,$thf( sk5 )),bind(B,$thf( sk6 ))]]) ).
thf(1237,plain,
! [A: $i] :
( ( A @ ( sk5 @ v_Q ) )
| ~ ( A @ ( v_n @ ( c_Nat_OSuc @ hAPP ) @ ( sk6 @ ( v_pn @ c_Com_Ocom_OBODY @ c_Natural_Oevaln ) ) ) )
| sk1 ),
inference(simp,[status(thm)],[1231]) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( E @ c_Com_Ocom_OSemi ) )
!= ( A @ ( B @ ( C @ c_Com_Ocom_OCond ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I44_J) ).
thf(249,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( E @ c_Com_Ocom_OSemi ) )
!= ( A @ ( B @ ( C @ c_Com_Ocom_OCond ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(50,axiom,
c_Com_Ocom_OSKIP @ ( c_Com_OWT @ hAPP ) @ hBOOL,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_WT_OSkip) ).
thf(468,plain,
c_Com_Ocom_OSKIP @ ( c_Com_OWT @ hAPP ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(104,axiom,
! [A: $i,B: $i] :
( ( B @ ( c_Com_OWT @ hAPP ) @ hBOOL )
=> ( ( A @ ( c_Com_OWT @ hAPP ) @ hBOOL )
=> ( A @ ( B @ c_Com_Ocom_OSemi ) @ ( c_Com_OWT @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_WT_OSemi) ).
thf(777,plain,
! [A: $i,B: $i] :
( ( B @ ( c_Com_OWT @ hAPP ) @ hBOOL )
=> ( ( A @ ( c_Com_OWT @ hAPP ) @ hBOOL )
=> ( A @ ( B @ c_Com_Ocom_OSemi ) @ ( c_Com_OWT @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(152,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ ( B @ c_Sum__Type_OInr ) @ hAPP ) @ ( B @ ( C @ c_Sum__Type_OProjr ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Projr_Osimps) ).
thf(977,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( C @ ( B @ c_Sum__Type_OInr ) @ hAPP ) @ ( B @ ( C @ c_Sum__Type_OProjr ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(162,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Sum__Type_OInl ) @ hAPP ) @ ( B @ ( C @ c_Sum__Type_OProjl ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Projl_Osimps) ).
thf(1005,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Sum__Type_OInl ) @ hAPP ) @ ( B @ ( C @ c_Sum__Type_OProjl ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(157,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/sandbox/benchmark/theBenchmark.p',fact_New__DSequence_Oneg__single__def) ).
thf(994,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)],[157]) ).
thf(8,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( E @ hAPP ) @ hBOOL )
=> ( ( B @ ( D @ ( C @ c_Natural_Oevalc ) ) )
=> ( ( A @ ( B @ ( C @ ( E @ c_Com_Ocom_OWhile ) @ c_Natural_Oevalc ) ) )
=> ( A @ ( D @ ( C @ ( E @ c_Com_Ocom_OWhile ) @ c_Natural_Oevalc ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc_OWhileTrue) ).
thf(247,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( E @ hAPP ) @ hBOOL )
=> ( ( B @ ( D @ ( C @ c_Natural_Oevalc ) ) )
=> ( ( A @ ( B @ ( C @ ( E @ c_Com_Ocom_OWhile ) @ c_Natural_Oevalc ) ) )
=> ( A @ ( D @ ( C @ ( E @ c_Com_Ocom_OWhile ) @ c_Natural_Oevalc ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(85,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Com_Ocom_OCall ) ) )
!= ( A @ ( B @ c_Com_Ocom_OSemi ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I51_J) ).
thf(677,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Com_Ocom_OCall ) ) )
!= ( A @ ( B @ c_Com_Ocom_OSemi ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(125,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ c_Com_Ocom_OCond ) ) @ c_Natural_Oevaln ) ) ) )
<=> ( ( ( A @ ( B @ ( C @ ( D @ c_Natural_Oevaln ) ) ) )
& ~ ( C @ ( F @ hAPP ) @ hBOOL ) )
| ( ( A @ ( B @ ( C @ ( E @ c_Natural_Oevaln ) ) ) )
& ( C @ ( F @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln_Oequations_I5_J) ).
thf(861,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ( ( A @ ( B @ ( C @ ( D @ c_Natural_Oevaln ) ) ) )
& ~ ( C @ ( F @ hAPP ) @ hBOOL ) )
| ( ( A @ ( B @ ( C @ ( E @ c_Natural_Oevaln ) ) ) )
& ( C @ ( F @ hAPP ) @ hBOOL ) ) )
=> ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ c_Com_Ocom_OCond ) ) @ c_Natural_Oevaln ) ) ) ) )
& ( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ c_Com_Ocom_OCond ) ) @ c_Natural_Oevaln ) ) ) )
=> ( ( ( A @ ( B @ ( C @ ( D @ c_Natural_Oevaln ) ) ) )
& ~ ( C @ ( F @ hAPP ) @ hBOOL ) )
| ( ( A @ ( B @ ( C @ ( E @ c_Natural_Oevaln ) ) ) )
& ( C @ ( F @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(205,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Com_Ocom_OSemi ) )
!= ( A @ c_Com_Ocom_OBODY ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I48_J) ).
thf(1170,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Com_Ocom_OSemi ) )
!= ( A @ c_Com_Ocom_OBODY ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(1171,plain,
~ ? [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Com_Ocom_OSemi ) )
= ( A @ c_Com_Ocom_OBODY ) ),
inference(miniscope,[status(thm)],[1170]) ).
thf(1172,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ c_Com_Ocom_OSemi ) )
!= ( A @ c_Com_Ocom_OBODY ) ),
inference(cnf,[status(esa)],[1171]) ).
thf(1173,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ c_Com_Ocom_OSemi ) )
!= ( A @ c_Com_Ocom_OBODY ) ),
inference(lifteq,[status(thm)],[1172]) ).
thf(63,axiom,
! [A: $i,B: $i] :
( ( B @ c_Option_Ooption_ONone )
!= ( A @ ( B @ c_Option_Ooption_OSome @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_option_Osimps_I2_J) ).
thf(523,plain,
! [A: $i,B: $i] :
( ( B @ c_Option_Ooption_ONone )
!= ( A @ ( B @ c_Option_Ooption_OSome @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(74,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Com_Ocom_OAss ) )
!= ( A @ ( B @ c_Com_Ocom_OSemi ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I24_J) ).
thf(582,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Com_Ocom_OAss ) )
!= ( A @ ( B @ c_Com_Ocom_OSemi ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(95,axiom,
! [A: $i,B: $i] : ( A @ ( B @ c_Com_Ocom_OAss ) @ ( c_Com_OWT @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_WT_Oequations_I2_J) ).
thf(730,plain,
! [A: $i,B: $i] : ( A @ ( B @ c_Com_Ocom_OAss ) @ ( c_Com_OWT @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Com_Ocom_OWhile ) )
!= c_Com_Ocom_OSKIP ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I17_J) ).
thf(273,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Com_Ocom_OWhile ) )
!= c_Com_Ocom_OSKIP ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(274,plain,
~ ? [A: $i,B: $i] :
( ( A @ ( B @ c_Com_Ocom_OWhile ) )
= c_Com_Ocom_OSKIP ),
inference(miniscope,[status(thm)],[273]) ).
thf(275,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ c_Com_Ocom_OWhile ) )
!= c_Com_Ocom_OSKIP ),
inference(cnf,[status(esa)],[274]) ).
thf(276,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ c_Com_Ocom_OWhile ) )
!= c_Com_Ocom_OSKIP ),
inference(lifteq,[status(thm)],[275]) ).
thf(136,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i] :
( ( A @ ( B @ c_Com_Ocom_OSemi ) @ ( C @ ( D @ ( E @ ( F @ ( G @ ( H @ ( I @ ( J @ ( K @ c_Com_Ocom_Ocom__rec ) ) ) ) ) ) ) ) ) )
= ( A @ ( C @ ( D @ ( E @ ( F @ ( G @ ( H @ ( I @ ( J @ ( K @ c_Com_Ocom_Ocom__rec ) ) ) ) ) ) ) ) ) @ ( B @ ( C @ ( D @ ( E @ ( F @ ( G @ ( H @ ( I @ ( J @ ( K @ c_Com_Ocom_Ocom__rec ) ) ) ) ) ) ) ) ) @ ( A @ ( B @ ( G @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Orecs_I4_J) ).
thf(913,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i] :
( ( A @ ( B @ c_Com_Ocom_OSemi ) @ ( C @ ( D @ ( E @ ( F @ ( G @ ( H @ ( I @ ( J @ ( K @ c_Com_Ocom_Ocom__rec ) ) ) ) ) ) ) ) ) )
= ( A @ ( C @ ( D @ ( E @ ( F @ ( G @ ( H @ ( I @ ( J @ ( K @ c_Com_Ocom_Ocom__rec ) ) ) ) ) ) ) ) ) @ ( B @ ( C @ ( D @ ( E @ ( F @ ( G @ ( H @ ( I @ ( J @ ( K @ c_Com_Ocom_Ocom__rec ) ) ) ) ) ) ) ) ) @ ( A @ ( B @ ( G @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(65,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Com_Ocom_OWhile ) @ ( c_Com_OWT @ hAPP ) @ hBOOL )
=> ( A @ ( c_Com_OWT @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_WTs__elim__cases_I6_J) ).
thf(538,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Com_Ocom_OWhile ) @ ( c_Com_OWT @ hAPP ) @ hBOOL )
=> ( A @ ( c_Com_OWT @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(160,axiom,
( c_Com_Obody
= ( c_Com_Obodies @ ( tc_Com_Ocom @ ( tc_Com_Opname @ c_Map_Omap__of ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_body__def) ).
thf(1001,plain,
( c_Com_Obody
= ( c_Com_Obodies @ ( tc_Com_Ocom @ ( tc_Com_Opname @ c_Map_Omap__of ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(28,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Com_Ocom_OAss ) )
!= c_Com_Ocom_OSKIP ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I9_J) ).
thf(320,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Com_Ocom_OAss ) )
!= c_Com_Ocom_OSKIP ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(12,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i,L: $i] :
( ( A @ ( B @ ( C @ c_Com_Ocom_OCall ) ) @ ( D @ ( E @ ( F @ ( G @ ( H @ ( I @ ( J @ ( K @ ( L @ c_Com_Ocom_Ocom__rec ) ) ) ) ) ) ) ) ) )
= ( A @ ( B @ ( C @ ( D @ hAPP ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Orecs_I8_J) ).
thf(257,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i,L: $i] :
( ( A @ ( B @ ( C @ c_Com_Ocom_OCall ) ) @ ( D @ ( E @ ( F @ ( G @ ( H @ ( I @ ( J @ ( K @ ( L @ c_Com_Ocom_Ocom__rec ) ) ) ) ) ) ) ) ) )
= ( A @ ( B @ ( C @ ( D @ hAPP ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(151,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/sandbox/benchmark/theBenchmark.p',fact_type__definition_ORep__inverse) ).
thf(973,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)],[151]) ).
thf(130,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_Natural_Oevalc ) ) )
=> ( ( A @ ( C @ ( D @ c_Natural_Oevalc ) ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com__det) ).
thf(885,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_Natural_Oevalc ) ) )
=> ( ( A @ ( C @ ( D @ c_Natural_Oevalc ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(93,axiom,
! [A: $i,B: $i] :
( c_Com_Ocom_OSKIP
!= ( A @ ( B @ c_Com_Ocom_OWhile ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I16_J) ).
thf(724,plain,
! [A: $i,B: $i] :
( c_Com_Ocom_OSKIP
!= ( A @ ( B @ c_Com_Ocom_OWhile ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(107,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Com_Ocom_OSemi ) @ c_Natural_Oevalc ) ) )
<=> ? [E: $i] :
( ( A @ ( E @ ( C @ c_Natural_Oevalc ) ) )
& ( E @ ( B @ ( D @ c_Natural_Oevalc ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc_Oequations_I4_J) ).
thf(785,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ? [E: $i] :
( ( A @ ( E @ ( C @ c_Natural_Oevalc ) ) )
& ( E @ ( B @ ( D @ c_Natural_Oevalc ) ) ) )
=> ( A @ ( B @ ( C @ ( D @ c_Com_Ocom_OSemi ) @ c_Natural_Oevalc ) ) ) )
& ( ( A @ ( B @ ( C @ ( D @ c_Com_Ocom_OSemi ) @ c_Natural_Oevalc ) ) )
=> ? [E: $i] :
( ( A @ ( E @ ( C @ c_Natural_Oevalc ) ) )
& ( E @ ( B @ ( D @ c_Natural_Oevalc ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(142,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_Com_Ocom_OCond ) ) )
!= ( A @ c_Com_Ocom_OBODY ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I54_J) ).
thf(934,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_Com_Ocom_OCond ) ) )
!= ( A @ c_Com_Ocom_OBODY ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(196,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/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple__idem_Oidem) ).
thf(1132,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)],[196]) ).
thf(146,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Natural_Oevalc ) ) )
<=> ? [D: $i] : ( A @ ( D @ ( B @ ( C @ c_Natural_Oevaln ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eval__eq) ).
thf(949,plain,
! [A: $i,B: $i,C: $i] :
( ( ? [D: $i] : ( A @ ( D @ ( B @ ( C @ c_Natural_Oevaln ) ) ) )
=> ( A @ ( B @ ( C @ c_Natural_Oevalc ) ) ) )
& ( ( A @ ( B @ ( C @ c_Natural_Oevalc ) ) )
=> ? [D: $i] : ( A @ ( D @ ( B @ ( C @ c_Natural_Oevaln ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(123,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/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I22_J) ).
thf(853,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)],[123]) ).
thf(182,axiom,
! [A: $i] :
( ( A @ c_Com_Ocom_OBODY )
!= c_Com_Ocom_OSKIP ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I19_J) ).
thf(1084,plain,
! [A: $i] :
( ( A @ c_Com_Ocom_OBODY )
!= c_Com_Ocom_OSKIP ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(1085,plain,
~ ? [A: $i] :
( ( A @ c_Com_Ocom_OBODY )
= c_Com_Ocom_OSKIP ),
inference(miniscope,[status(thm)],[1084]) ).
thf(1086,plain,
! [A: $i] :
( ( A @ c_Com_Ocom_OBODY )
!= c_Com_Ocom_OSKIP ),
inference(cnf,[status(esa)],[1085]) ).
thf(1087,plain,
! [A: $i] :
( ( A @ c_Com_Ocom_OBODY )
!= c_Com_Ocom_OSKIP ),
inference(lifteq,[status(thm)],[1086]) ).
thf(48,axiom,
! [A: $i,B: $i,C: $i] : ( A @ ( B @ hAPP ) @ ( C @ ( A @ c_Natural_Oupdate ) ) @ ( A @ ( B @ ( C @ c_Com_Ocom_OAss ) @ c_Natural_Oevalc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc_Oequations_I2_J) ).
thf(448,plain,
! [A: $i,B: $i,C: $i] : ( A @ ( B @ hAPP ) @ ( C @ ( A @ c_Natural_Oupdate ) ) @ ( A @ ( B @ ( C @ c_Com_Ocom_OAss ) @ c_Natural_Oevalc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(187,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( c_Com_Obody @ hAPP ) @ ( tc_Com_Ocom @ c_Option_Othe @ hAPP ) @ c_Natural_Oevalc ) ) )
=> ( A @ ( B @ ( C @ c_Com_Ocom_OBODY @ c_Natural_Oevalc ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc_OBody) ).
thf(1100,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( c_Com_Obody @ hAPP ) @ ( tc_Com_Ocom @ c_Option_Othe @ hAPP ) @ c_Natural_Oevalc ) ) )
=> ( A @ ( B @ ( C @ c_Com_Ocom_OBODY @ c_Natural_Oevalc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(216,plain,
( ~ sk1
| ~ ( sk4 @ ( sk2 @ v_Q ) ) ),
inference(cnfConj,[status(thm)],[213]) ).
thf(139,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i] :
( ( A @ ( B @ c_Com_Ocom_OSemi ) @ ( C @ ( D @ ( E @ ( F @ ( G @ ( H @ ( I @ ( J @ ( K @ c_Com_Ocom_Ocom__case ) ) ) ) ) ) ) ) ) )
= ( A @ ( B @ ( G @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I67_J) ).
thf(924,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i] :
( ( A @ ( B @ c_Com_Ocom_OSemi ) @ ( C @ ( D @ ( E @ ( F @ ( G @ ( H @ ( I @ ( J @ ( K @ c_Com_Ocom_Ocom__case ) ) ) ) ) ) ) ) ) )
= ( A @ ( B @ ( G @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(147,axiom,
! [A: $i,B: $i] : ( B @ ( A @ ( B @ ( c_Com_Ocom_OSKIP @ c_Natural_Oevaln ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln_OSkip) ).
thf(955,plain,
! [A: $i,B: $i] : ( B @ ( A @ ( B @ ( c_Com_Ocom_OSKIP @ c_Natural_Oevaln ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(956,plain,
! [B: $i,A: $i] : ( B @ ( A @ ( B @ ( c_Com_Ocom_OSKIP @ c_Natural_Oevaln ) ) ) ),
inference(cnf,[status(esa)],[955]) ).
thf(221,plain,
( ~ sk1
| ( sk3 @ ( sk2 @ v_P ) ) ),
inference(cnfConj,[status(thm)],[213]) ).
thf(215,plain,
! [C: $i,B: $i,A: $i] :
( ~ sk1
| ( C @ ( A @ v_Q ) )
| ~ ( C @ ( v_n @ ( B @ ( v_pn @ ( c_Com_Obody @ hAPP ) @ ( tc_Com_Ocom @ c_Option_Othe @ hAPP ) @ c_Natural_Oevaln ) ) ) )
| ~ ( B @ ( A @ v_P ) ) ),
inference(cnfConj,[status(thm)],[213]) ).
thf(1201,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk3 @ ( sk2 @ v_P ) )
!= ( B @ ( A @ v_P ) ) )
| ~ sk1
| ( C @ ( A @ v_Q ) )
| ~ ( C @ ( v_n @ ( B @ ( v_pn @ ( c_Com_Obody @ hAPP ) @ ( tc_Com_Ocom @ c_Option_Othe @ hAPP ) @ c_Natural_Oevaln ) ) ) )
| ~ $true
| ~ sk1 ),
inference(paramod_ordered,[status(thm)],[221,215]) ).
thf(1202,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk3 @ ( sk2 @ v_P ) )
!= ( B @ ( A @ v_P ) ) )
| ( C @ ( A @ v_Q ) )
| ~ ( C @ ( v_n @ ( B @ ( v_pn @ ( c_Com_Obody @ hAPP ) @ ( tc_Com_Ocom @ c_Option_Othe @ hAPP ) @ c_Natural_Oevaln ) ) ) )
| ~ sk1 ),
inference(simp,[status(thm)],[1201]) ).
thf(1203,plain,
! [A: $i] :
( ( A @ ( sk2 @ v_Q ) )
| ~ ( A @ ( v_n @ ( sk3 @ ( v_pn @ ( c_Com_Obody @ hAPP ) @ ( tc_Com_Ocom @ c_Option_Othe @ hAPP ) @ c_Natural_Oevaln ) ) ) )
| ~ sk1 ),
inference(pattern_uni,[status(thm)],[1202:[bind(A,$thf( sk2 )),bind(B,$thf( sk3 ))]]) ).
thf(1206,plain,
! [A: $i] :
( ( A @ ( sk2 @ v_Q ) )
| ~ ( A @ ( v_n @ ( sk3 @ ( v_pn @ ( c_Com_Obody @ hAPP ) @ ( tc_Com_Ocom @ c_Option_Othe @ hAPP ) @ c_Natural_Oevaln ) ) ) )
| ~ sk1 ),
inference(simp,[status(thm)],[1203]) ).
thf(1291,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ( B @ ( c_Com_Ocom_OSKIP @ c_Natural_Oevaln ) ) ) )
!= ( C @ ( v_n @ ( sk3 @ ( v_pn @ ( c_Com_Obody @ hAPP ) @ ( tc_Com_Ocom @ c_Option_Othe @ hAPP ) @ c_Natural_Oevaln ) ) ) ) )
| ( C @ ( sk2 @ v_Q ) )
| ~ $true
| ~ sk1 ),
inference(paramod_ordered,[status(thm)],[956,1206]) ).
thf(1292,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ ( B @ ( c_Com_Ocom_OSKIP @ c_Natural_Oevaln ) ) ) )
!= ( C @ ( v_n @ ( sk3 @ ( v_pn @ ( c_Com_Obody @ hAPP ) @ ( tc_Com_Ocom @ c_Option_Othe @ hAPP ) @ c_Natural_Oevaln ) ) ) ) )
| ( C @ ( sk2 @ v_Q ) )
| ~ sk1 ),
inference(simp,[status(thm)],[1291]) ).
thf(1298,plain,
! [C: $i,B: $i,A: $i] :
( ( B != C )
| ( A != v_n )
| ( B != sk3 )
| ( ( v_pn @ ( c_Com_Obody @ hAPP ) @ ( tc_Com_Ocom @ c_Option_Othe @ hAPP ) )
!= c_Com_Ocom_OSKIP )
| ~ sk1
| ( C @ ( sk2 @ v_Q ) ) ),
inference(simp,[status(thm)],[1292]) ).
thf(1302,plain,
( ( ( v_pn @ ( c_Com_Obody @ hAPP ) @ ( tc_Com_Ocom @ c_Option_Othe @ hAPP ) )
!= c_Com_Ocom_OSKIP )
| ~ sk1
| ( sk3 @ ( sk2 @ v_Q ) ) ),
inference(simp,[status(thm)],[1298]) ).
thf(191,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 ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln__elim__cases_I2_J) ).
thf(1109,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 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(10,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Com_Ocom_OCall ) ) @ ( c_Com_OWT @ hAPP ) @ hBOOL )
=> ( B @ c_Com_Ocom_OBODY @ ( c_Com_OWT @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_WTs__elim__cases_I8_J) ).
thf(253,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Com_Ocom_OCall ) ) @ ( c_Com_OWT @ hAPP ) @ hBOOL )
=> ( B @ c_Com_Ocom_OBODY @ ( c_Com_OWT @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(197,axiom,
! [A: $i,B: $i] :
( ( ( B @ c_Com_Ocom_OBODY )
= ( A @ c_Com_Ocom_OBODY ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I6_J) ).
thf(1136,plain,
! [A: $i,B: $i] :
( ( ( B = A )
=> ( ( B @ c_Com_Ocom_OBODY )
= ( A @ c_Com_Ocom_OBODY ) ) )
& ( ( ( B @ c_Com_Ocom_OBODY )
= ( A @ c_Com_Ocom_OBODY ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(60,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( C @ ( D @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( C @ ( B @ ( D @ c_Com_Ocom_OWhile ) @ c_Natural_Oevaln ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln_OWhileFalse) ).
thf(514,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( C @ ( D @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( C @ ( B @ ( D @ c_Com_Ocom_OWhile ) @ c_Natural_Oevaln ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(111,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i] :
( ( A @ ( B @ c_Com_Ocom_OAss ) @ ( C @ ( D @ ( E @ ( F @ ( G @ ( H @ ( I @ ( J @ ( K @ c_Com_Ocom_Ocom__rec ) ) ) ) ) ) ) ) ) )
= ( A @ ( B @ ( I @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Orecs_I2_J) ).
thf(806,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i] :
( ( A @ ( B @ c_Com_Ocom_OAss ) @ ( C @ ( D @ ( E @ ( F @ ( G @ ( H @ ( I @ ( J @ ( K @ c_Com_Ocom_Ocom__rec ) ) ) ) ) ) ) ) ) )
= ( A @ ( B @ ( I @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(88,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Com_Ocom_OSemi ) )
!= ( A @ ( B @ c_Com_Ocom_OWhile ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I46_J) ).
thf(692,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Com_Ocom_OSemi ) )
!= ( A @ ( B @ c_Com_Ocom_OWhile ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(179,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( C @ c_List_Orotate ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_List_Orotate ) @ hAPP ) @ ( C @ c_List_Orotate1 @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rotate__Suc) ).
thf(1072,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( C @ c_List_Orotate ) @ hAPP ) )
= ( A @ ( B @ ( C @ c_List_Orotate ) @ hAPP ) @ ( C @ c_List_Orotate1 @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(83,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Com_Ocom_OLocal ) ) @ ( c_Com_OWT @ hAPP ) @ hBOOL )
=> ( A @ ( c_Com_OWT @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_WTs__elim__cases_I3_J) ).
thf(660,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Com_Ocom_OLocal ) ) @ ( c_Com_OWT @ hAPP ) @ hBOOL )
=> ( A @ ( c_Com_OWT @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( E @ c_Com_Ocom_OWhile ) )
!= ( A @ ( B @ ( C @ c_Com_Ocom_OLocal ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I39_J) ).
thf(243,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( E @ c_Com_Ocom_OWhile ) )
!= ( A @ ( B @ ( C @ c_Com_Ocom_OLocal ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(45,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ~ ( D @ ( E @ hAPP ) @ hBOOL )
=> ( ( B @ ( D @ ( C @ c_Natural_Oevalc ) ) )
=> ( B @ ( D @ ( C @ ( A @ ( E @ c_Com_Ocom_OCond ) ) @ c_Natural_Oevalc ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc_OIfFalse) ).
thf(428,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ~ ( D @ ( E @ hAPP ) @ hBOOL )
=> ( ( B @ ( D @ ( C @ c_Natural_Oevalc ) ) )
=> ( B @ ( D @ ( C @ ( A @ ( E @ c_Com_Ocom_OCond ) ) @ c_Natural_Oevalc ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(15,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( c_Com_OWT @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( B @ c_Com_Ocom_OLocal ) ) @ ( c_Com_OWT @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_WT_OLocal) ).
thf(265,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( c_Com_OWT @ hAPP ) @ hBOOL )
=> ( C @ ( A @ ( B @ c_Com_Ocom_OLocal ) ) @ ( c_Com_OWT @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(64,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_Com_Ocom_OWhile ) @ c_Natural_Oevaln ) ) ) )
=> ( ( ( A = C )
=> ( C @ ( E @ hAPP ) @ hBOOL ) )
=> ~ ( ( C @ ( E @ hAPP ) @ hBOOL )
=> ! [F: $i] :
( ( F @ ( B @ ( C @ ( D @ c_Natural_Oevaln ) ) ) )
=> ~ ( A @ ( B @ ( F @ ( D @ ( E @ c_Com_Ocom_OWhile ) @ c_Natural_Oevaln ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln__WHILE__case) ).
thf(527,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_Com_Ocom_OWhile ) @ c_Natural_Oevaln ) ) ) )
=> ( ( ( A = C )
=> ( C @ ( E @ hAPP ) @ hBOOL ) )
=> ~ ( ( C @ ( E @ hAPP ) @ hBOOL )
=> ! [F: $i] :
( ( F @ ( B @ ( C @ ( D @ c_Natural_Oevaln ) ) ) )
=> ~ ( A @ ( B @ ( F @ ( D @ ( E @ c_Com_Ocom_OWhile ) @ c_Natural_Oevaln ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(138,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_Sum__Type_OInr ) @ hAPP ) )
!= ( A @ ( D @ ( C @ c_Sum__Type_OInl ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inr__not__Inl) ).
thf(920,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_Sum__Type_OInr ) @ hAPP ) )
!= ( A @ ( D @ ( C @ c_Sum__Type_OInl ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(144,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( G = F )
=> ( ( G @ ( A @ ( B @ ( C @ ( D @ ( E @ c_Sum__Type_Osum_Osum__case ) ) ) ) @ hAPP ) )
= ( F @ ( A @ ( B @ ( C @ ( D @ ( E @ c_Sum__Type_Osum_Osum__case ) ) ) ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum__case__weak__cong) ).
thf(942,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( G = F )
=> ( ( G @ ( A @ ( B @ ( C @ ( D @ ( E @ c_Sum__Type_Osum_Osum__case ) ) ) ) @ hAPP ) )
= ( F @ ( A @ ( B @ ( C @ ( D @ ( E @ c_Sum__Type_Osum_Osum__case ) ) ) ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(220,plain,
( ~ sk1
| ( sk4 @ ( v_n @ ( c_Nat_OSuc @ hAPP ) @ ( sk3 @ ( v_pn @ c_Com_Ocom_OBODY @ c_Natural_Oevaln ) ) ) ) ),
inference(cnfConj,[status(thm)],[213]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( F @ ( G @ hAPP ) )
= ( D @ ( E @ c_Option_Ooption_OSome @ hAPP ) ) )
=> ( ( F @ ( G @ ( A @ ( B @ ( C @ ( E @ c_Map_Omap__comp ) ) ) ) ) )
= ( D @ ( A @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__comp__simps_I2_J) ).
thf(233,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( F @ ( G @ hAPP ) )
= ( D @ ( E @ c_Option_Ooption_OSome @ hAPP ) ) )
=> ( ( F @ ( G @ ( A @ ( B @ ( C @ ( E @ c_Map_Omap__comp ) ) ) ) ) )
= ( D @ ( A @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(200,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ c_Com_Ocom_OBODY )
!= ( A @ ( B @ ( C @ c_Com_Ocom_OCond ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I55_J) ).
thf(1153,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ c_Com_Ocom_OBODY )
!= ( A @ ( B @ ( C @ c_Com_Ocom_OCond ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(101,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ c_Com_Ocom_OCond ) ) @ c_Natural_Oevaln ) ) ) )
=> ( ( ( C @ ( F @ hAPP ) @ hBOOL )
=> ~ ( A @ ( B @ ( C @ ( E @ c_Natural_Oevaln ) ) ) ) )
=> ~ ( ~ ( C @ ( F @ hAPP ) @ hBOOL )
=> ~ ( A @ ( B @ ( C @ ( D @ c_Natural_Oevaln ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln__elim__cases_I5_J) ).
thf(761,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ c_Com_Ocom_OCond ) ) @ c_Natural_Oevaln ) ) ) )
=> ( ( ( C @ ( F @ hAPP ) @ hBOOL )
=> ~ ( A @ ( B @ ( C @ ( E @ c_Natural_Oevaln ) ) ) ) )
=> ~ ( ~ ( C @ ( F @ hAPP ) @ hBOOL )
=> ~ ( A @ ( B @ ( C @ ( D @ c_Natural_Oevaln ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(172,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/sandbox/benchmark/theBenchmark.p',fact_pos__single__def) ).
thf(1047,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)],[172]) ).
thf(109,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/sandbox/benchmark/theBenchmark.p',fact_split__paired__All) ).
thf(798,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)],[109]) ).
thf(184,axiom,
! [A: $i,B: $i,C: $i,D: $i] : ( B @ ( C @ hAPP ) @ ( D @ ( B @ c_Natural_Oupdate ) ) @ ( A @ ( B @ ( C @ ( D @ c_Com_Ocom_OAss ) @ c_Natural_Oevaln ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln_OAssign) ).
thf(1091,plain,
! [A: $i,B: $i,C: $i,D: $i] : ( B @ ( C @ hAPP ) @ ( D @ ( B @ c_Natural_Oupdate ) ) @ ( A @ ( B @ ( C @ ( D @ c_Com_Ocom_OAss ) @ c_Natural_Oevaln ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(26,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( C @ ( D @ ( E @ ( F @ ( G @ c_Sum__Type_Osum_Osum__case ) ) ) ) )
= ( A @ ( B @ ( E @ ( F @ ( G @ c_Sum__Type_Osum_Osum__case ) ) ) ) ) )
=> ~ ( ( D = B )
=> ( C != A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum__case__inject) ).
thf(302,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( C @ ( D @ ( E @ ( F @ ( G @ c_Sum__Type_Osum_Osum__case ) ) ) ) )
= ( A @ ( B @ ( E @ ( F @ ( G @ c_Sum__Type_Osum_Osum__case ) ) ) ) ) )
=> ~ ( ( D = B )
=> ( C != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( D @ ( F @ c_Sum__Type_OInl ) @ hAPP ) @ ( B @ ( C @ ( D @ ( E @ ( F @ c_Sum__Type_Osum_Osum__case ) ) ) ) @ hAPP ) )
= ( A @ ( C @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum_Osimps_I5_J) ).
thf(260,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( D @ ( F @ c_Sum__Type_OInl ) @ hAPP ) @ ( B @ ( C @ ( D @ ( E @ ( F @ c_Sum__Type_Osum_Osum__case ) ) ) ) @ hAPP ) )
= ( A @ ( C @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(206,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_Com_Ocom_OSemi ) @ c_Natural_Oevaln ) ) ) )
<=> ? [F: $i] :
( ( A @ ( B @ ( F @ ( D @ c_Natural_Oevaln ) ) ) )
& ( F @ ( B @ ( C @ ( E @ c_Natural_Oevaln ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln_Oequations_I4_J) ).
thf(1174,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ? [F: $i] :
( ( A @ ( B @ ( F @ ( D @ c_Natural_Oevaln ) ) ) )
& ( F @ ( B @ ( C @ ( E @ c_Natural_Oevaln ) ) ) ) )
=> ( A @ ( B @ ( C @ ( D @ ( E @ c_Com_Ocom_OSemi ) @ c_Natural_Oevaln ) ) ) ) )
& ( ( A @ ( B @ ( C @ ( D @ ( E @ c_Com_Ocom_OSemi ) @ c_Natural_Oevaln ) ) ) )
=> ? [F: $i] :
( ( A @ ( B @ ( F @ ( D @ c_Natural_Oevaln ) ) ) )
& ( F @ ( B @ ( C @ ( E @ c_Natural_Oevaln ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(44,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( E @ ( F @ c_Com_Ocom_OCond ) ) )
!= ( A @ ( B @ ( C @ c_Com_Ocom_OLocal ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I37_J) ).
thf(424,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( E @ ( F @ c_Com_Ocom_OCond ) ) )
!= ( A @ ( B @ ( C @ c_Com_Ocom_OLocal ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(1137,plain,
( ! [A: $i,B: $i] :
( ( B = A )
=> ( ( B @ c_Com_Ocom_OBODY )
= ( A @ c_Com_Ocom_OBODY ) ) )
& ! [A: $i,B: $i] :
( ( ( B @ c_Com_Ocom_OBODY )
= ( A @ c_Com_Ocom_OBODY ) )
=> ( B = A ) ) ),
inference(miniscope,[status(thm)],[1136]) ).
thf(1138,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( ( D @ c_Com_Ocom_OBODY )
= ( C @ c_Com_Ocom_OBODY ) )
| ( D != C ) )
& ( ( B = A )
| ( ( B @ c_Com_Ocom_OBODY )
!= ( A @ c_Com_Ocom_OBODY ) ) ) ),
inference(cnf,[status(esa)],[1137]) ).
thf(1139,plain,
! [B: $i,A: $i] :
( ( B = A )
| ( ( B @ c_Com_Ocom_OBODY )
!= ( A @ c_Com_Ocom_OBODY ) ) ),
inference(cnfConj,[status(thm)],[1138]) ).
thf(1141,plain,
! [B: $i,A: $i] :
( ( B = A )
| ( ( B @ c_Com_Ocom_OBODY )
!= ( A @ c_Com_Ocom_OBODY ) ) ),
inference(lifteq,[status(thm)],[1139]) ).
thf(1142,plain,
? [A: $i > $i] :
! [B: $i] :
( ( B @ c_Com_Ocom_OBODY @ A )
= B ),
inference(detectInverse,[status(thm)],[1141]) ).
thf(1143,plain,
! [A: $i] :
( ( A @ c_Com_Ocom_OBODY @ sk50 )
= A ),
inference(cnf,[status(esa)],[1142]) ).
thf(1238,plain,
! [A: $i] :
( ( A @ c_Com_Ocom_OBODY @ sk50 )
= A ),
inference(lifteq,[status(thm)],[1143]) ).
thf(148,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_Com_Ocom_OCall ) ) )
!= ( A @ c_Com_Ocom_OBODY ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I63_J) ).
thf(957,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_Com_Ocom_OCall ) ) )
!= ( A @ c_Com_Ocom_OBODY ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(133,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i] :
( ( A @ ( B @ c_Com_Ocom_OAss ) @ ( C @ ( D @ ( E @ ( F @ ( G @ ( H @ ( I @ ( J @ ( K @ c_Com_Ocom_Ocom__case ) ) ) ) ) ) ) ) ) )
= ( A @ ( B @ ( I @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I65_J) ).
thf(894,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i] :
( ( A @ ( B @ c_Com_Ocom_OAss ) @ ( C @ ( D @ ( E @ ( F @ ( G @ ( H @ ( I @ ( J @ ( K @ c_Com_Ocom_Ocom__case ) ) ) ) ) ) ) ) ) )
= ( A @ ( B @ ( I @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(137,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Com_Ocom_OLocal ) ) )
!= ( A @ ( B @ c_Com_Ocom_OSemi ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I34_J) ).
thf(916,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Com_Ocom_OLocal ) ) )
!= ( A @ ( B @ c_Com_Ocom_OSemi ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(128,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Com_Ocom_OSemi ) )
!= c_Com_Ocom_OSKIP ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I13_J) ).
thf(879,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Com_Ocom_OSemi ) )
!= c_Com_Ocom_OSKIP ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(55,axiom,
! [A: $i,B: $i] : ( A @ ( B @ c_Com_Ocom_OAss ) @ ( c_Com_OWT @ hAPP ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_WT_OAssign) ).
thf(493,plain,
! [A: $i,B: $i] : ( A @ ( B @ c_Com_Ocom_OAss ) @ ( c_Com_OWT @ hAPP ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(100,axiom,
! [A: $i,B: $i] :
( c_Com_OWT__bodies
=> ( ( ( B @ ( c_Com_Obody @ hAPP ) )
= ( A @ ( tc_Com_Ocom @ c_Option_Ooption_OSome @ hAPP ) ) )
=> ( A @ ( c_Com_OWT @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_WT__bodiesD) ).
thf(757,plain,
! [A: $i,B: $i] :
( c_Com_OWT__bodies
=> ( ( ( B @ ( c_Com_Obody @ hAPP ) )
= ( A @ ( tc_Com_Ocom @ c_Option_Ooption_OSome @ hAPP ) ) )
=> ( A @ ( c_Com_OWT @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(119,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i,L: $i] :
( ( A @ ( B @ ( C @ c_Com_Ocom_OCond ) ) @ ( D @ ( E @ ( F @ ( G @ ( H @ ( I @ ( J @ ( K @ ( L @ c_Com_Ocom_Ocom__case ) ) ) ) ) ) ) ) ) )
= ( A @ ( B @ ( C @ ( G @ hAPP ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I68_J) ).
thf(842,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i,L: $i] :
( ( A @ ( B @ ( C @ c_Com_Ocom_OCond ) ) @ ( D @ ( E @ ( F @ ( G @ ( H @ ( I @ ( J @ ( K @ ( L @ c_Com_Ocom_Ocom__case ) ) ) ) ) ) ) ) ) )
= ( A @ ( B @ ( C @ ( G @ hAPP ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(29,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( C @ ( D @ c_Sum__Type_OInr ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Sum__Type_OInr ) @ hAPP ) ) )
=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inr__inject) ).
thf(324,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( C @ ( D @ c_Sum__Type_OInr ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Sum__Type_OInr ) @ hAPP ) ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(3,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( B @ ( C @ ( D @ ( E @ ( F @ ( G @ c_Map_Omap__comp ) ) ) ) ) )
= ( A @ ( F @ c_Option_Ooption_OSome @ hAPP ) ) )
<=> ? [H: $i] :
( ( ( H @ ( D @ hAPP ) )
= ( A @ ( F @ c_Option_Ooption_OSome @ hAPP ) ) )
& ( ( B @ ( C @ hAPP ) )
= ( H @ ( G @ c_Option_Ooption_OSome @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__comp__Some__iff) ).
thf(223,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ? [H: $i] :
( ( ( H @ ( D @ hAPP ) )
= ( A @ ( F @ c_Option_Ooption_OSome @ hAPP ) ) )
& ( ( B @ ( C @ hAPP ) )
= ( H @ ( G @ c_Option_Ooption_OSome @ hAPP ) ) ) )
=> ( ( B @ ( C @ ( D @ ( E @ ( F @ ( G @ c_Map_Omap__comp ) ) ) ) ) )
= ( A @ ( F @ c_Option_Ooption_OSome @ hAPP ) ) ) )
& ( ( ( B @ ( C @ ( D @ ( E @ ( F @ ( G @ c_Map_Omap__comp ) ) ) ) ) )
= ( A @ ( F @ c_Option_Ooption_OSome @ hAPP ) ) )
=> ? [H: $i] :
( ( ( H @ ( D @ hAPP ) )
= ( A @ ( F @ c_Option_Ooption_OSome @ hAPP ) ) )
& ( ( B @ ( C @ hAPP ) )
= ( H @ ( G @ c_Option_Ooption_OSome @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(224,plain,
( ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ? [H: $i] :
( ( ( H @ ( D @ hAPP ) )
= ( A @ ( F @ c_Option_Ooption_OSome @ hAPP ) ) )
& ( ( B @ ( C @ hAPP ) )
= ( H @ ( G @ c_Option_Ooption_OSome @ hAPP ) ) ) )
=> ( ( B @ ( C @ ( D @ ( E @ ( F @ ( G @ c_Map_Omap__comp ) ) ) ) ) )
= ( A @ ( F @ c_Option_Ooption_OSome @ hAPP ) ) ) )
& ! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( B @ ( C @ ( D @ ( E @ ( F @ ( G @ c_Map_Omap__comp ) ) ) ) ) )
= ( A @ ( F @ c_Option_Ooption_OSome @ hAPP ) ) )
=> ? [H: $i] :
( ( ( H @ ( D @ hAPP ) )
= ( A @ ( F @ c_Option_Ooption_OSome @ hAPP ) ) )
& ( ( B @ ( C @ hAPP ) )
= ( H @ ( G @ c_Option_Ooption_OSome @ hAPP ) ) ) ) ) ),
inference(miniscope,[status(thm)],[223]) ).
thf(225,plain,
! [O: $i,N: $i,M: $i,L: $i,K: $i,J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( ( I @ ( J @ ( K @ ( L @ ( M @ ( N @ c_Map_Omap__comp ) ) ) ) ) )
= ( H @ ( M @ c_Option_Ooption_OSome @ hAPP ) ) )
| ( ( O @ ( K @ hAPP ) )
!= ( H @ ( M @ c_Option_Ooption_OSome @ hAPP ) ) )
| ( ( I @ ( J @ hAPP ) )
!= ( O @ ( N @ c_Option_Ooption_OSome @ hAPP ) ) ) )
& ( ( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ ( G @ sk8 ) ) ) ) ) ) @ ( D @ hAPP ) )
= ( A @ ( F @ c_Option_Ooption_OSome @ hAPP ) ) )
| ( ( B @ ( C @ ( D @ ( E @ ( F @ ( G @ c_Map_Omap__comp ) ) ) ) ) )
!= ( A @ ( F @ c_Option_Ooption_OSome @ hAPP ) ) ) )
& ( ( ( B @ ( C @ hAPP ) )
= ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ ( G @ sk8 ) ) ) ) ) ) @ ( G @ c_Option_Ooption_OSome @ hAPP ) ) )
| ( ( B @ ( C @ ( D @ ( E @ ( F @ ( G @ c_Map_Omap__comp ) ) ) ) ) )
!= ( A @ ( F @ c_Option_Ooption_OSome @ hAPP ) ) ) ) ),
inference(cnf,[status(esa)],[224]) ).
thf(226,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ hAPP ) )
= ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ ( G @ sk8 ) ) ) ) ) ) @ ( G @ c_Option_Ooption_OSome @ hAPP ) ) )
| ( ( B @ ( C @ ( D @ ( E @ ( F @ ( G @ c_Map_Omap__comp ) ) ) ) ) )
!= ( A @ ( F @ c_Option_Ooption_OSome @ hAPP ) ) ) ),
inference(cnfConj,[status(thm)],[225]) ).
thf(229,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ hAPP ) )
= ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ ( G @ sk8 ) ) ) ) ) ) @ ( G @ c_Option_Ooption_OSome @ hAPP ) ) )
| ( ( B @ ( C @ ( D @ ( E @ ( F @ ( G @ c_Map_Omap__comp ) ) ) ) ) )
!= ( A @ ( F @ c_Option_Ooption_OSome @ hAPP ) ) ) ),
inference(lifteq,[status(thm)],[226]) ).
thf(53,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Com_Ocom_OCond ) ) @ ( c_Com_OWT @ hAPP ) @ hBOOL )
=> ~ ( ( B @ ( c_Com_OWT @ hAPP ) @ hBOOL )
=> ~ ( A @ ( c_Com_OWT @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_WTs__elim__cases_I5_J) ).
thf(484,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Com_Ocom_OCond ) ) @ ( c_Com_OWT @ hAPP ) @ hBOOL )
=> ~ ( ( B @ ( c_Com_OWT @ hAPP ) @ hBOOL )
=> ~ ( A @ ( c_Com_OWT @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(68,axiom,
! [A: $i,B: $i] :
( c_Com_Ocom_OSKIP
!= ( A @ ( B @ c_Com_Ocom_OSemi ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I12_J) ).
thf(548,plain,
! [A: $i,B: $i] :
( c_Com_Ocom_OSKIP
!= ( A @ ( B @ c_Com_Ocom_OSemi ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(549,plain,
~ ? [A: $i,B: $i] :
( c_Com_Ocom_OSKIP
= ( A @ ( B @ c_Com_Ocom_OSemi ) ) ),
inference(miniscope,[status(thm)],[548]) ).
thf(550,plain,
! [B: $i,A: $i] :
( c_Com_Ocom_OSKIP
!= ( A @ ( B @ c_Com_Ocom_OSemi ) ) ),
inference(cnf,[status(esa)],[549]) ).
thf(551,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ c_Com_Ocom_OSemi ) )
!= c_Com_Ocom_OSKIP ),
inference(lifteq,[status(thm)],[550]) ).
thf(195,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_Com_Ocom_OLocal ) ) )
!= ( A @ c_Com_Ocom_OBODY ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I40_J) ).
thf(1128,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_Com_Ocom_OLocal ) ) )
!= ( A @ c_Com_Ocom_OBODY ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(78,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Com_Ocom_OAss ) @ c_Natural_Oevalc ) ) )
=> ( A
= ( B @ ( C @ hAPP ) @ ( D @ ( B @ c_Natural_Oupdate ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc__elim__cases_I2_J) ).
thf(615,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Com_Ocom_OAss ) @ c_Natural_Oevalc ) ) )
=> ( A
= ( B @ ( C @ hAPP ) @ ( D @ ( B @ c_Natural_Oupdate ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(176,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Natural_Oevaln ) ) ) )
=> ( A @ ( C @ ( D @ c_Natural_Oevalc ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln__evalc) ).
thf(1064,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Natural_Oevaln ) ) ) )
=> ( A @ ( C @ ( D @ c_Natural_Oevalc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(153,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/sandbox/benchmark/theBenchmark.p',fact_pair__box_Orecs) ).
thf(980,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)],[153]) ).
thf(186,axiom,
! [A: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) )
!= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__n__not__n) ).
thf(1096,plain,
! [A: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(57,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i,L: $i] :
( ( A @ ( B @ ( C @ c_Com_Ocom_OLocal ) ) @ ( D @ ( E @ ( F @ ( G @ ( H @ ( I @ ( J @ ( K @ ( L @ c_Com_Ocom_Ocom__rec ) ) ) ) ) ) ) ) ) )
= ( A @ ( D @ ( E @ ( F @ ( G @ ( H @ ( I @ ( J @ ( K @ ( L @ c_Com_Ocom_Ocom__rec ) ) ) ) ) ) ) ) ) @ ( A @ ( B @ ( C @ ( I @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Orecs_I3_J) ).
thf(499,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i,L: $i] :
( ( A @ ( B @ ( C @ c_Com_Ocom_OLocal ) ) @ ( D @ ( E @ ( F @ ( G @ ( H @ ( I @ ( J @ ( K @ ( L @ c_Com_Ocom_Ocom__rec ) ) ) ) ) ) ) ) ) )
= ( A @ ( D @ ( E @ ( F @ ( G @ ( H @ ( I @ ( J @ ( K @ ( L @ c_Com_Ocom_Ocom__rec ) ) ) ) ) ) ) ) ) @ ( A @ ( B @ ( C @ ( I @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(155,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ c_Com_Ocom_OBODY )
!= ( A @ ( B @ c_Com_Ocom_OAss ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I31_J) ).
thf(986,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ c_Com_Ocom_OBODY )
!= ( A @ ( B @ c_Com_Ocom_OAss ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(987,plain,
~ ? [A: $i,B: $i,C: $i] :
( ( C @ c_Com_Ocom_OBODY )
= ( A @ ( B @ c_Com_Ocom_OAss ) ) ),
inference(miniscope,[status(thm)],[986]) ).
thf(988,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ c_Com_Ocom_OBODY )
!= ( A @ ( B @ c_Com_Ocom_OAss ) ) ),
inference(cnf,[status(esa)],[987]) ).
thf(989,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ c_Com_Ocom_OBODY )
!= ( A @ ( B @ c_Com_Ocom_OAss ) ) ),
inference(lifteq,[status(thm)],[988]) ).
thf(124,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/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I43_J) ).
thf(857,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)],[124]) ).
thf(129,axiom,
! [A: $i] : ( A @ ( A @ ( c_Com_Ocom_OSKIP @ c_Natural_Oevalc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc_Oequations_I1_J) ).
thf(883,plain,
! [A: $i] : ( A @ ( A @ ( c_Com_Ocom_OSKIP @ c_Natural_Oevalc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(884,plain,
! [A: $i] : ( A @ ( A @ ( c_Com_Ocom_OSKIP @ c_Natural_Oevalc ) ) ),
inference(cnf,[status(esa)],[883]) ).
thf(202,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 @ c_Natural_Oevaln ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln_OBody) ).
thf(1160,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 @ c_Natural_Oevaln ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(180,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Com_Ocom_OBODY @ c_Natural_Oevalc ) ) )
<=> ( A @ ( B @ ( C @ ( c_Com_Obody @ hAPP ) @ ( tc_Com_Ocom @ c_Option_Othe @ hAPP ) @ c_Natural_Oevalc ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc_Oequations_I9_J) ).
thf(1075,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( B @ ( C @ ( c_Com_Obody @ hAPP ) @ ( tc_Com_Ocom @ c_Option_Othe @ hAPP ) @ c_Natural_Oevalc ) ) )
=> ( A @ ( B @ ( C @ c_Com_Ocom_OBODY @ c_Natural_Oevalc ) ) ) )
& ( ( A @ ( B @ ( C @ c_Com_Ocom_OBODY @ c_Natural_Oevalc ) ) )
=> ( A @ ( B @ ( C @ ( c_Com_Obody @ hAPP ) @ ( tc_Com_Ocom @ c_Option_Othe @ hAPP ) @ c_Natural_Oevalc ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(54,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Com_Ocom_OWhile ) )
!= ( A @ ( B @ c_Com_Ocom_OAss ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I29_J) ).
thf(489,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Com_Ocom_OWhile ) )
!= ( A @ ( B @ c_Com_Ocom_OAss ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(30,axiom,
! [A: $i,B: $i,C: $i] :
( c_Com_Ocom_OSKIP
!= ( A @ ( B @ ( C @ c_Com_Ocom_OCall ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I20_J) ).
thf(328,plain,
! [A: $i,B: $i,C: $i] :
( c_Com_Ocom_OSKIP
!= ( A @ ( B @ ( C @ c_Com_Ocom_OCall ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(11,axiom,
c_Com_Ocom_OSKIP @ ( c_Com_OWT @ hAPP ) @ hBOOL,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_WT_Oequations_I1_J) ).
thf(256,plain,
c_Com_Ocom_OSKIP @ ( c_Com_OWT @ hAPP ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(211,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( C @ ( B @ hAPP ) )
= ( C @ ( A @ hAPP ) ) )
=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ext) ).
thf(1192,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( C @ ( B @ hAPP ) )
= ( C @ ( A @ hAPP ) ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(173,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/sandbox/benchmark/theBenchmark.p',fact_New__DSequence_Opos__single__def) ).
thf(1050,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)],[173]) ).
thf(1002,plain,
( ( c_Com_Obodies @ ( tc_Com_Ocom @ ( tc_Com_Opname @ c_Map_Omap__of ) ) )
= c_Com_Obody ),
inference(lifteq,[status(thm)],[1001]) ).
thf(105,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( E @ ( F @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ ( E @ ( D @ c_Natural_Oevaln ) ) ) )
=> ( B @ ( C @ ( E @ ( A @ ( D @ ( F @ c_Com_Ocom_OCond ) ) @ c_Natural_Oevaln ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln_OIfTrue) ).
thf(779,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( E @ ( F @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ ( E @ ( D @ c_Natural_Oevaln ) ) ) )
=> ( B @ ( C @ ( E @ ( A @ ( D @ ( F @ c_Com_Ocom_OCond ) ) @ c_Natural_Oevaln ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(81,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( A @ ( B @ ( C @ c_Com_Ocom_OWhile ) @ c_Natural_Oevalc ) ) )
<=> ( ( A @ ( C @ hAPP ) @ hBOOL )
=> ? [D: $i] :
( ( A @ ( D @ ( B @ ( C @ c_Com_Ocom_OWhile ) @ c_Natural_Oevalc ) ) )
& ( D @ ( A @ ( B @ c_Natural_Oevalc ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc_Oequations_I7_J) ).
thf(647,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( A @ ( C @ hAPP ) @ hBOOL )
=> ? [D: $i] :
( ( A @ ( D @ ( B @ ( C @ c_Com_Ocom_OWhile ) @ c_Natural_Oevalc ) ) )
& ( D @ ( A @ ( B @ c_Natural_Oevalc ) ) ) ) )
=> ( A @ ( A @ ( B @ ( C @ c_Com_Ocom_OWhile ) @ c_Natural_Oevalc ) ) ) )
& ( ( A @ ( A @ ( B @ ( C @ c_Com_Ocom_OWhile ) @ c_Natural_Oevalc ) ) )
=> ( ( A @ ( C @ hAPP ) @ hBOOL )
=> ? [D: $i] :
( ( A @ ( D @ ( B @ ( C @ c_Com_Ocom_OWhile ) @ c_Natural_Oevalc ) ) )
& ( D @ ( A @ ( B @ c_Natural_Oevalc ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(158,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/sandbox/benchmark/theBenchmark.p',fact_evaln__Suc) ).
thf(997,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)],[158]) ).
thf(108,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Com_Ocom_OLocal ) ) @ ( c_Com_OWT @ hAPP ) @ hBOOL )
<=> ( A @ ( c_Com_OWT @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_WT_Oequations_I3_J) ).
thf(792,plain,
! [A: $i,B: $i,C: $i] :
( ( ( A @ ( c_Com_OWT @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_Com_Ocom_OLocal ) ) @ ( c_Com_OWT @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ c_Com_Ocom_OLocal ) ) @ ( c_Com_OWT @ hAPP ) @ hBOOL )
=> ( A @ ( c_Com_OWT @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(143,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/sandbox/benchmark/theBenchmark.p',fact_folding__one__idem_Oidem) ).
thf(938,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)],[143]) ).
thf(59,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Com_Ocom_OWhile ) @ ( c_Com_OWT @ hAPP ) @ hBOOL )
<=> ( A @ ( c_Com_OWT @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_WT_Oequations_I6_J) ).
thf(508,plain,
! [A: $i,B: $i] :
( ( ( A @ ( c_Com_OWT @ hAPP ) @ hBOOL )
=> ( A @ ( B @ c_Com_Ocom_OWhile ) @ ( c_Com_OWT @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ c_Com_Ocom_OWhile ) @ ( c_Com_OWT @ hAPP ) @ hBOOL )
=> ( A @ ( c_Com_OWT @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(66,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i,L: $i] :
( ( A @ ( B @ ( C @ c_Com_Ocom_OCond ) ) @ ( D @ ( E @ ( F @ ( G @ ( H @ ( I @ ( J @ ( K @ ( L @ c_Com_Ocom_Ocom__rec ) ) ) ) ) ) ) ) ) )
= ( A @ ( D @ ( E @ ( F @ ( G @ ( H @ ( I @ ( J @ ( K @ ( L @ c_Com_Ocom_Ocom__rec ) ) ) ) ) ) ) ) ) @ ( B @ ( D @ ( E @ ( F @ ( G @ ( H @ ( I @ ( J @ ( K @ ( L @ c_Com_Ocom_Ocom__rec ) ) ) ) ) ) ) ) ) @ ( A @ ( B @ ( C @ ( G @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Orecs_I5_J) ).
thf(541,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i,L: $i] :
( ( A @ ( B @ ( C @ c_Com_Ocom_OCond ) ) @ ( D @ ( E @ ( F @ ( G @ ( H @ ( I @ ( J @ ( K @ ( L @ c_Com_Ocom_Ocom__rec ) ) ) ) ) ) ) ) ) )
= ( A @ ( D @ ( E @ ( F @ ( G @ ( H @ ( I @ ( J @ ( K @ ( L @ c_Com_Ocom_Ocom__rec ) ) ) ) ) ) ) ) ) @ ( B @ ( D @ ( E @ ( F @ ( G @ ( H @ ( I @ ( J @ ( K @ ( L @ c_Com_Ocom_Ocom__rec ) ) ) ) ) ) ) ) ) @ ( A @ ( B @ ( C @ ( G @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(167,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ c_Com_Ocom_OBODY )
!= ( A @ ( B @ ( C @ c_Com_Ocom_OLocal ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I41_J) ).
thf(1026,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ c_Com_Ocom_OBODY )
!= ( A @ ( B @ ( C @ c_Com_Ocom_OLocal ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(208,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_New__DSequence_Opos__empty @ hAPP ) )
= ( B @ c_Lazy__Sequence_Oempty ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_New__DSequence_Opos__empty__def) ).
thf(1185,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)],[208]) ).
thf(75,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/sandbox/benchmark/theBenchmark.p',fact_pair__box_Oinject) ).
thf(586,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)],[75]) ).
thf(131,axiom,
! [A: $i] : ( A @ ( A @ ( c_Com_Ocom_OSKIP @ c_Natural_Oevalc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc_OSkip) ).
thf(888,plain,
! [A: $i] : ( A @ ( A @ ( c_Com_Ocom_OSKIP @ c_Natural_Oevalc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(25,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( E @ c_Com_Ocom_OWhile ) )
!= ( A @ ( B @ ( C @ c_Com_Ocom_OCond ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I53_J) ).
thf(298,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( E @ c_Com_Ocom_OWhile ) )
!= ( A @ ( B @ ( C @ c_Com_Ocom_OCond ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(150,axiom,
! [A: $i] :
( ( A @ c_Com_Ocom_OBODY @ ( c_Com_OWT @ hAPP ) @ hBOOL )
<=> ? [B: $i] :
( ( A @ ( c_Com_Obody @ hAPP ) )
= ( B @ ( tc_Com_Ocom @ c_Option_Ooption_OSome @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_WT_Oequations_I7_J) ).
thf(965,plain,
! [A: $i] :
( ( ? [B: $i] :
( ( A @ ( c_Com_Obody @ hAPP ) )
= ( B @ ( tc_Com_Ocom @ c_Option_Ooption_OSome @ hAPP ) ) )
=> ( A @ c_Com_Ocom_OBODY @ ( c_Com_OWT @ hAPP ) @ hBOOL ) )
& ( ( A @ c_Com_Ocom_OBODY @ ( c_Com_OWT @ hAPP ) @ hBOOL )
=> ? [B: $i] :
( ( A @ ( c_Com_Obody @ hAPP ) )
= ( B @ ( tc_Com_Ocom @ c_Option_Ooption_OSome @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(79,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/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I7_J) ).
thf(618,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)],[79]) ).
thf(114,axiom,
! [A: $i,B: $i] :
( ( B
!= ( A @ c_Option_Ooption_ONone ) )
=> ~ ! [C: $i] :
( B
!= ( C @ ( A @ c_Option_Ooption_OSome @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_option_Oexhaust) ).
thf(824,plain,
! [A: $i,B: $i] :
( ( B
!= ( A @ c_Option_Ooption_ONone ) )
=> ~ ! [C: $i] :
( B
!= ( C @ ( A @ c_Option_Ooption_OSome @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(20,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( E @ ( F @ c_Com_Ocom_OCond ) ) )
!= ( A @ ( B @ ( C @ c_Com_Ocom_OCall ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I56_J) ).
thf(279,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( D @ ( E @ ( F @ c_Com_Ocom_OCond ) ) )
!= ( A @ ( B @ ( C @ c_Com_Ocom_OCall ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(87,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( c_Com_Ocom_OSKIP @ c_Natural_Oevalc ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc__elim__cases_I1_J) ).
thf(689,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( c_Com_Ocom_OSKIP @ c_Natural_Oevalc ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(198,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i] :
( ( A @ c_Com_Ocom_OBODY @ ( B @ ( C @ ( D @ ( E @ ( F @ ( G @ ( H @ ( I @ ( J @ c_Com_Ocom_Ocom__case ) ) ) ) ) ) ) ) ) )
= ( A @ ( C @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I70_J) ).
thf(1146,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i] :
( ( A @ c_Com_Ocom_OBODY @ ( B @ ( C @ ( D @ ( E @ ( F @ ( G @ ( H @ ( I @ ( J @ c_Com_Ocom_Ocom__case ) ) ) ) ) ) ) ) ) )
= ( A @ ( C @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(46,axiom,
! [A: $i,B: $i,C: $i] :
( c_Com_Ocom_OSKIP
!= ( A @ ( B @ ( C @ c_Com_Ocom_OLocal ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I10_J) ).
thf(430,plain,
! [A: $i,B: $i,C: $i] :
( c_Com_Ocom_OSKIP
!= ( A @ ( B @ ( C @ c_Com_Ocom_OLocal ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(42,axiom,
! [A: $i,B: $i] :
( ( B
!= ( A @ c_Option_Ooption_ONone ) )
<=> ? [C: $i] :
( B
= ( C @ ( A @ c_Option_Ooption_OSome @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__None__eq) ).
thf(402,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( B
= ( C @ ( A @ c_Option_Ooption_OSome @ hAPP ) ) )
=> ( B
!= ( A @ c_Option_Ooption_ONone ) ) )
& ( ( B
!= ( A @ c_Option_Ooption_ONone ) )
=> ? [C: $i] :
( B
= ( C @ ( A @ c_Option_Ooption_OSome @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(96,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( E @ c_Com_Ocom_OSemi ) )
!= ( A @ ( B @ ( C @ c_Com_Ocom_OCall ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I50_J) ).
thf(732,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( E @ c_Com_Ocom_OSemi ) )
!= ( A @ ( B @ ( C @ c_Com_Ocom_OCall ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(194,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( C @ ( D @ ( E @ c_Power_Opower_Opower ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( D @ ( E @ c_Power_Opower_Opower ) ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power_Opower_Opower__Suc) ).
thf(1125,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( C @ ( D @ ( E @ c_Power_Opower_Opower ) ) @ hAPP ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( D @ ( E @ c_Power_Opower_Opower ) ) @ hAPP ) @ hAPP ) @ ( B @ ( C @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(21,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Com_Ocom_OCall ) ) )
!= c_Com_Ocom_OSKIP ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I21_J) ).
thf(283,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Com_Ocom_OCall ) ) )
!= c_Com_Ocom_OSKIP ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(284,plain,
~ ? [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Com_Ocom_OCall ) ) )
= c_Com_Ocom_OSKIP ),
inference(miniscope,[status(thm)],[283]) ).
thf(285,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_Com_Ocom_OCall ) ) )
!= c_Com_Ocom_OSKIP ),
inference(cnf,[status(esa)],[284]) ).
thf(286,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_Com_Ocom_OCall ) ) )
!= c_Com_Ocom_OSKIP ),
inference(lifteq,[status(thm)],[285]) ).
thf(23,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( C @ ( D @ c_Sum__Type_OInl ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Sum__Type_OInl ) @ hAPP ) ) )
=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inl__inject) ).
thf(291,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( C @ ( D @ c_Sum__Type_OInl ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Sum__Type_OInl ) @ hAPP ) ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(27,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/sandbox/benchmark/theBenchmark.p',fact_Pair__inject) ).
thf(313,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)],[27]) ).
thf(190,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( D @ ( E @ ( F @ c_Natural_Oevaln ) ) ) )
=> ( ( A @ ( D @ ( C @ ( B @ c_Natural_Oevaln ) ) ) )
=> ( A @ ( D @ ( E @ ( B @ ( F @ c_Com_Ocom_OSemi ) @ c_Natural_Oevaln ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln_OSemi) ).
thf(1107,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( C @ ( D @ ( E @ ( F @ c_Natural_Oevaln ) ) ) )
=> ( ( A @ ( D @ ( C @ ( B @ c_Natural_Oevaln ) ) ) )
=> ( A @ ( D @ ( E @ ( B @ ( F @ c_Com_Ocom_OSemi ) @ c_Natural_Oevaln ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( E @ ( F @ hAPP ) )
= ( D @ c_Option_Ooption_ONone ) )
=> ( ( E @ ( F @ ( A @ ( B @ ( C @ ( D @ c_Map_Omap__comp ) ) ) ) ) )
= ( C @ c_Option_Ooption_ONone ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__comp__simps_I1_J) ).
thf(236,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( E @ ( F @ hAPP ) )
= ( D @ c_Option_Ooption_ONone ) )
=> ( ( E @ ( F @ ( A @ ( B @ ( C @ ( D @ c_Map_Omap__comp ) ) ) ) ) )
= ( C @ c_Option_Ooption_ONone ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(110,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( E @ hAPP ) @ hBOOL )
=> ( ( B @ ( D @ ( C @ c_Natural_Oevalc ) ) )
=> ( B @ ( D @ ( A @ ( C @ ( E @ c_Com_Ocom_OCond ) ) @ c_Natural_Oevalc ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc_OIfTrue) ).
thf(804,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( E @ hAPP ) @ hBOOL )
=> ( ( B @ ( D @ ( C @ c_Natural_Oevalc ) ) )
=> ( B @ ( D @ ( A @ ( C @ ( E @ c_Com_Ocom_OCond ) ) @ c_Natural_Oevalc ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(36,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Com_Ocom_OSemi ) @ c_Natural_Oevalc ) ) )
=> ~ ! [E: $i] :
( ( E @ ( B @ ( D @ c_Natural_Oevalc ) ) )
=> ~ ( A @ ( E @ ( C @ c_Natural_Oevalc ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc__elim__cases_I4_J) ).
thf(350,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Com_Ocom_OSemi ) @ c_Natural_Oevalc ) ) )
=> ~ ! [E: $i] :
( ( E @ ( B @ ( D @ c_Natural_Oevalc ) ) )
=> ~ ( A @ ( E @ ( C @ c_Natural_Oevalc ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(77,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Com_Ocom_OWhile ) @ c_Natural_Oevalc ) ) )
=> ( ( ( A = B )
=> ( B @ ( D @ hAPP ) @ hBOOL ) )
=> ~ ( ( B @ ( D @ hAPP ) @ hBOOL )
=> ! [E: $i] :
( ( E @ ( B @ ( C @ c_Natural_Oevalc ) ) )
=> ~ ( A @ ( E @ ( C @ ( D @ c_Com_Ocom_OWhile ) @ c_Natural_Oevalc ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc__WHILE__case) ).
thf(604,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Com_Ocom_OWhile ) @ c_Natural_Oevalc ) ) )
=> ( ( ( A = B )
=> ( B @ ( D @ hAPP ) @ hBOOL ) )
=> ~ ( ( B @ ( D @ hAPP ) @ hBOOL )
=> ! [E: $i] :
( ( E @ ( B @ ( C @ c_Natural_Oevalc ) ) )
=> ~ ( A @ ( E @ ( C @ ( D @ c_Com_Ocom_OWhile ) @ c_Natural_Oevalc ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(86,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( B
!= ( C @ ( A @ c_Option_Ooption_OSome @ hAPP ) ) )
<=> ( B
= ( A @ c_Option_Ooption_ONone ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__Some__eq) ).
thf(681,plain,
! [A: $i,B: $i] :
( ( ( B
= ( A @ c_Option_Ooption_ONone ) )
=> ! [C: $i] :
( B
!= ( C @ ( A @ c_Option_Ooption_OSome @ hAPP ) ) ) )
& ( ! [C: $i] :
( B
!= ( C @ ( A @ c_Option_Ooption_OSome @ hAPP ) ) )
=> ( B
= ( A @ c_Option_Ooption_ONone ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(219,plain,
( ( sk7 @ ( v_n @ ( sk6 @ ( v_pn @ ( c_Com_Obody @ hAPP ) @ ( tc_Com_Ocom @ c_Option_Othe @ hAPP ) @ c_Natural_Oevaln ) ) ) )
| sk1 ),
inference(cnfConj,[status(thm)],[213]) ).
thf(164,axiom,
! [A: $i] :
( A
!= ( A @ ( c_Nat_OSuc @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_n__not__Suc__n) ).
thf(1011,plain,
! [A: $i] :
( A
!= ( A @ ( c_Nat_OSuc @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(97,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/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I33_J) ).
thf(736,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)],[97]) ).
thf(156,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ c_Com_Ocom_OBODY )
!= ( A @ ( B @ c_Com_Ocom_OWhile ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I59_J) ).
thf(990,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ c_Com_Ocom_OBODY )
!= ( A @ ( B @ c_Com_Ocom_OWhile ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(227,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ ( G @ sk8 ) ) ) ) ) ) @ ( D @ hAPP ) )
= ( A @ ( F @ c_Option_Ooption_OSome @ hAPP ) ) )
| ( ( B @ ( C @ ( D @ ( E @ ( F @ ( G @ c_Map_Omap__comp ) ) ) ) ) )
!= ( A @ ( F @ c_Option_Ooption_OSome @ hAPP ) ) ) ),
inference(cnfConj,[status(thm)],[225]) ).
thf(230,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ ( G @ sk8 ) ) ) ) ) ) @ ( D @ hAPP ) )
= ( A @ ( F @ c_Option_Ooption_OSome @ hAPP ) ) )
| ( ( B @ ( C @ ( D @ ( E @ ( F @ ( G @ c_Map_Omap__comp ) ) ) ) ) )
!= ( A @ ( F @ c_Option_Ooption_OSome @ hAPP ) ) ) ),
inference(lifteq,[status(thm)],[227]) ).
thf(72,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Com_Ocom_OLocal ) ) )
!= ( A @ ( B @ c_Com_Ocom_OWhile ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I38_J) ).
thf(567,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Com_Ocom_OLocal ) ) )
!= ( A @ ( B @ c_Com_Ocom_OWhile ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(47,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( D @ c_Com_Ocom_OSemi ) )
= ( A @ ( B @ c_Com_Ocom_OSemi ) ) )
<=> ( ( C = A )
& ( D = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I3_J) ).
thf(434,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( C = A )
& ( D = B ) )
=> ( ( C @ ( D @ c_Com_Ocom_OSemi ) )
= ( A @ ( B @ c_Com_Ocom_OSemi ) ) ) )
& ( ( ( C @ ( D @ c_Com_Ocom_OSemi ) )
= ( A @ ( B @ c_Com_Ocom_OSemi ) ) )
=> ( ( C = A )
& ( D = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(17,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Natural_Oevalc ) ) )
=> ( ( A @ ( C @ ( B @ c_Natural_Oevalc ) ) )
=> ( A @ ( D @ ( B @ ( E @ c_Com_Ocom_OSemi ) @ c_Natural_Oevalc ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc_OSemi) ).
thf(271,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Natural_Oevalc ) ) )
=> ( ( A @ ( C @ ( B @ c_Natural_Oevalc ) ) )
=> ( A @ ( D @ ( B @ ( E @ c_Com_Ocom_OSemi ) @ c_Natural_Oevalc ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(132,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_OCond ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I57_J) ).
thf(890,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_OCond ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(52,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Com_Ocom_OCond ) ) @ ( c_Com_OWT @ hAPP ) @ hBOOL )
<=> ( ( A @ ( c_Com_OWT @ hAPP ) @ hBOOL )
& ( B @ ( c_Com_OWT @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_WT_Oequations_I5_J) ).
thf(477,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( A @ ( c_Com_OWT @ hAPP ) @ hBOOL )
& ( B @ ( c_Com_OWT @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ ( C @ c_Com_Ocom_OCond ) ) @ ( c_Com_OWT @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ c_Com_Ocom_OCond ) ) @ ( c_Com_OWT @ hAPP ) @ hBOOL )
=> ( ( A @ ( c_Com_OWT @ hAPP ) @ hBOOL )
& ( B @ ( c_Com_OWT @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(494,plain,
! [B: $i,A: $i] : ( A @ ( B @ c_Com_Ocom_OAss ) @ ( c_Com_OWT @ hAPP ) @ hBOOL ),
inference(cnf,[status(esa)],[493]) ).
thf(321,plain,
~ ? [A: $i,B: $i] :
( ( A @ ( B @ c_Com_Ocom_OAss ) )
= c_Com_Ocom_OSKIP ),
inference(miniscope,[status(thm)],[320]) ).
thf(322,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ c_Com_Ocom_OAss ) )
!= c_Com_Ocom_OSKIP ),
inference(cnf,[status(esa)],[321]) ).
thf(323,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ c_Com_Ocom_OAss ) )
!= c_Com_Ocom_OSKIP ),
inference(lifteq,[status(thm)],[322]) ).
thf(203,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_Com_Ocom_OSemi ) @ c_Natural_Oevaln ) ) ) )
=> ~ ! [F: $i] :
( ( F @ ( B @ ( C @ ( E @ c_Natural_Oevaln ) ) ) )
=> ~ ( A @ ( B @ ( F @ ( D @ c_Natural_Oevaln ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln__elim__cases_I4_J) ).
thf(1162,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_Com_Ocom_OSemi ) @ c_Natural_Oevaln ) ) ) )
=> ~ ! [F: $i] :
( ( F @ ( B @ ( C @ ( E @ c_Natural_Oevaln ) ) ) )
=> ~ ( A @ ( B @ ( F @ ( D @ c_Natural_Oevaln ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(192,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( c_Int_ORep__Integ @ hAPP ) )
= ( A @ ( c_Int_ORep__Integ @ hAPP ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Rep__Integ__inject) ).
thf(1112,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)],[192]) ).
thf(34,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Com_Ocom_OLocal ) ) )
!= c_Com_Ocom_OSKIP ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I11_J) ).
thf(342,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Com_Ocom_OLocal ) ) )
!= c_Com_Ocom_OSKIP ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(343,plain,
~ ? [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Com_Ocom_OLocal ) ) )
= c_Com_Ocom_OSKIP ),
inference(miniscope,[status(thm)],[342]) ).
thf(344,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_Com_Ocom_OLocal ) ) )
!= c_Com_Ocom_OSKIP ),
inference(cnf,[status(esa)],[343]) ).
thf(345,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_Com_Ocom_OLocal ) ) )
!= c_Com_Ocom_OSKIP ),
inference(lifteq,[status(thm)],[344]) ).
thf(69,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Com_Ocom_OAss ) )
!= ( A @ ( B @ c_Com_Ocom_OWhile ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I28_J) ).
thf(552,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Com_Ocom_OAss ) )
!= ( A @ ( B @ c_Com_Ocom_OWhile ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(121,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i] :
( ( A @ ( B @ c_Com_Ocom_OWhile ) @ ( C @ ( D @ ( E @ ( F @ ( G @ ( H @ ( I @ ( J @ ( K @ c_Com_Ocom_Ocom__case ) ) ) ) ) ) ) ) ) )
= ( A @ ( B @ ( E @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I69_J) ).
thf(848,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i] :
( ( A @ ( B @ c_Com_Ocom_OWhile ) @ ( C @ ( D @ ( E @ ( F @ ( G @ ( H @ ( I @ ( J @ ( K @ c_Com_Ocom_Ocom__case ) ) ) ) ) ) ) ) ) )
= ( A @ ( B @ ( E @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(62,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Orotate ) @ hAPP ) @ ( C @ c_List_Orotate1 @ hAPP ) )
= ( A @ ( C @ c_List_Orotate1 @ hAPP ) @ ( B @ ( C @ c_List_Orotate ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rotate1__rotate__swap) ).
thf(520,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_List_Orotate ) @ hAPP ) @ ( C @ c_List_Orotate1 @ hAPP ) )
= ( A @ ( C @ c_List_Orotate1 @ hAPP ) @ ( B @ ( C @ c_List_Orotate ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(199,axiom,
! [A: $i] :
( ( A @ c_Com_Ocom_OBODY @ ( c_Com_OWT @ hAPP ) @ hBOOL )
=> ~ ! [B: $i] :
( ( A @ ( c_Com_Obody @ hAPP ) )
!= ( B @ ( tc_Com_Ocom @ c_Option_Ooption_OSome @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_WTs__elim__cases_I7_J) ).
thf(1149,plain,
! [A: $i] :
( ( A @ c_Com_Ocom_OBODY @ ( c_Com_OWT @ hAPP ) @ hBOOL )
=> ~ ! [B: $i] :
( ( A @ ( c_Com_Obody @ hAPP ) )
!= ( B @ ( tc_Com_Ocom @ c_Option_Ooption_OSome @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(149,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ c_Com_Ocom_OBODY )
!= ( A @ ( B @ c_Com_Ocom_OSemi ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I49_J) ).
thf(961,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ c_Com_Ocom_OBODY )
!= ( A @ ( B @ c_Com_Ocom_OSemi ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(962,plain,
~ ? [A: $i,B: $i,C: $i] :
( ( C @ c_Com_Ocom_OBODY )
= ( A @ ( B @ c_Com_Ocom_OSemi ) ) ),
inference(miniscope,[status(thm)],[961]) ).
thf(963,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ c_Com_Ocom_OBODY )
!= ( A @ ( B @ c_Com_Ocom_OSemi ) ) ),
inference(cnf,[status(esa)],[962]) ).
thf(964,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ c_Com_Ocom_OBODY )
!= ( A @ ( B @ c_Com_Ocom_OSemi ) ) ),
inference(lifteq,[status(thm)],[963]) ).
thf(154,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/sandbox/benchmark/theBenchmark.p',fact_neg__single__def) ).
thf(983,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)],[154]) ).
thf(177,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/sandbox/benchmark/theBenchmark.p',fact_pos__not__random__dseq__def) ).
thf(1066,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)],[177]) ).
thf(165,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/sandbox/benchmark/theBenchmark.p',fact_pair__box_Osimps_I2_J) ).
thf(1015,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)],[165]) ).
thf(80,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ c_Com_Ocom_OCond ) ) @ c_Natural_Oevaln ) ) ) )
<=> ( ( ( A @ ( B @ ( C @ ( D @ c_Natural_Oevaln ) ) ) )
& ~ ( C @ ( F @ hAPP ) @ hBOOL ) )
| ( ( A @ ( B @ ( C @ ( E @ c_Natural_Oevaln ) ) ) )
& ( C @ ( F @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln_Oequations_I6_J) ).
thf(636,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ( ( A @ ( B @ ( C @ ( D @ c_Natural_Oevaln ) ) ) )
& ~ ( C @ ( F @ hAPP ) @ hBOOL ) )
| ( ( A @ ( B @ ( C @ ( E @ c_Natural_Oevaln ) ) ) )
& ( C @ ( F @ hAPP ) @ hBOOL ) ) )
=> ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ c_Com_Ocom_OCond ) ) @ c_Natural_Oevaln ) ) ) ) )
& ( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ c_Com_Ocom_OCond ) ) @ c_Natural_Oevaln ) ) ) )
=> ( ( ( A @ ( B @ ( C @ ( D @ c_Natural_Oevaln ) ) ) )
& ~ ( C @ ( F @ hAPP ) @ hBOOL ) )
| ( ( A @ ( B @ ( C @ ( E @ c_Natural_Oevaln ) ) ) )
& ( C @ ( F @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(171,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( C @ ( D @ c_Nat_Onat_Onat__rec ) ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( D @ c_Nat_Onat_Onat__rec ) ) @ hAPP ) @ ( A @ ( B @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__rec__Suc) ).
thf(1044,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( C @ ( D @ c_Nat_Onat_Onat__rec ) ) @ hAPP ) )
= ( A @ ( B @ ( C @ ( D @ c_Nat_Onat_Onat__rec ) ) @ hAPP ) @ ( A @ ( B @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Com_Ocom_OSemi ) @ ( c_Com_OWT @ hAPP ) @ hBOOL )
=> ~ ( ( B @ ( c_Com_OWT @ hAPP ) @ hBOOL )
=> ~ ( A @ ( c_Com_OWT @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_WTs__elim__cases_I4_J) ).
thf(267,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Com_Ocom_OSemi ) @ ( c_Com_OWT @ hAPP ) @ hBOOL )
=> ~ ( ( B @ ( c_Com_OWT @ hAPP ) @ hBOOL )
=> ~ ( A @ ( c_Com_OWT @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(122,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( B @ ( C @ hAPP ) @ hBOOL )
=> ( B @ ( B @ ( A @ ( C @ c_Com_Ocom_OWhile ) @ c_Natural_Oevalc ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc_OWhileFalse) ).
thf(851,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( B @ ( C @ hAPP ) @ hBOOL )
=> ( B @ ( B @ ( A @ ( C @ c_Com_Ocom_OWhile ) @ c_Natural_Oevalc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(188,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i] :
( ( A @ c_Com_Ocom_OBODY @ ( B @ ( C @ ( D @ ( E @ ( F @ ( G @ ( H @ ( I @ ( J @ c_Com_Ocom_Ocom__rec ) ) ) ) ) ) ) ) ) )
= ( A @ ( C @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Orecs_I7_J) ).
thf(1102,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i] :
( ( A @ c_Com_Ocom_OBODY @ ( B @ ( C @ ( D @ ( E @ ( F @ ( G @ ( H @ ( I @ ( J @ c_Com_Ocom_Ocom__rec ) ) ) ) ) ) ) ) ) )
= ( A @ ( C @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(169,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Com_Ocom_OWhile ) )
!= ( A @ c_Com_Ocom_OBODY ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I58_J) ).
thf(1034,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Com_Ocom_OWhile ) )
!= ( A @ c_Com_Ocom_OBODY ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(204,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ c_Com_Ocom_OBODY )
!= ( A @ ( B @ ( C @ c_Com_Ocom_OCall ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I62_J) ).
thf(1166,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ c_Com_Ocom_OBODY )
!= ( A @ ( B @ ( C @ c_Com_Ocom_OCall ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(140,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Option_Ooption_OSome @ hAPP ) )
!= ( B @ c_Option_Ooption_ONone ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_option_Osimps_I3_J) ).
thf(927,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Option_Ooption_OSome @ hAPP ) )
!= ( B @ c_Option_Ooption_ONone ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(181,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( c_Com_Ocom_OSKIP @ c_Natural_Oevaln ) ) ) )
=> ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln__elim__cases_I1_J) ).
thf(1081,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ ( c_Com_Ocom_OSKIP @ c_Natural_Oevaln ) ) ) )
=> ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(61,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/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I32_J) ).
thf(516,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)],[61]) ).
thf(166,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( c_Nat_OSuc @ hAPP ) )
= ( A @ ( c_Nat_OSuc @ hAPP ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat_Oinject) ).
thf(1018,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)],[166]) ).
thf(99,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i,L: $i] :
( ( A @ ( B @ ( C @ c_Com_Ocom_OLocal ) ) @ ( D @ ( E @ ( F @ ( G @ ( H @ ( I @ ( J @ ( K @ ( L @ c_Com_Ocom_Ocom__case ) ) ) ) ) ) ) ) ) )
= ( A @ ( B @ ( C @ ( I @ hAPP ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I66_J) ).
thf(754,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i,L: $i] :
( ( A @ ( B @ ( C @ c_Com_Ocom_OLocal ) ) @ ( D @ ( E @ ( F @ ( G @ ( H @ ( I @ ( J @ ( K @ ( L @ c_Com_Ocom_Ocom__case ) ) ) ) ) ) ) ) ) )
= ( A @ ( B @ ( C @ ( I @ hAPP ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(207,axiom,
! [A: $i] :
( c_Com_Ocom_OSKIP
!= ( A @ c_Com_Ocom_OBODY ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I18_J) ).
thf(1181,plain,
! [A: $i] :
( c_Com_Ocom_OSKIP
!= ( A @ c_Com_Ocom_OBODY ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(117,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( E @ c_Com_Ocom_OWhile ) )
!= ( A @ ( B @ ( C @ c_Com_Ocom_OCall ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I60_J) ).
thf(836,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( E @ c_Com_Ocom_OWhile ) )
!= ( A @ ( B @ ( C @ c_Com_Ocom_OCall ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(84,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( D @ c_Com_Ocom_OWhile ) )
= ( A @ ( B @ c_Com_Ocom_OWhile ) ) )
<=> ( ( C = A )
& ( D = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I5_J) ).
thf(663,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( C = A )
& ( D = B ) )
=> ( ( C @ ( D @ c_Com_Ocom_OWhile ) )
= ( A @ ( B @ c_Com_Ocom_OWhile ) ) ) )
& ( ( ( C @ ( D @ c_Com_Ocom_OWhile ) )
= ( A @ ( B @ c_Com_Ocom_OWhile ) ) )
=> ( ( C = A )
& ( D = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(161,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Natural_Oevalc ) ) )
=> ? [D: $i] : ( A @ ( D @ ( B @ ( C @ c_Natural_Oevaln ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc__evaln) ).
thf(1003,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Natural_Oevalc ) ) )
=> ? [D: $i] : ( A @ ( D @ ( B @ ( C @ c_Natural_Oevaln ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(24,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
( ( c_Com_Ocom_OSKIP @ ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ ( G @ ( H @ ( I @ c_Com_Ocom_Ocom__rec ) ) ) ) ) ) ) ) ) )
= H ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Orecs_I1_J) ).
thf(295,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
( ( c_Com_Ocom_OSKIP @ ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ ( G @ ( H @ ( I @ c_Com_Ocom_Ocom__rec ) ) ) ) ) ) ) ) ) )
= H ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(126,axiom,
! [A: $i,B: $i] :
( c_Com_Ocom_OSKIP
!= ( A @ ( B @ c_Com_Ocom_OAss ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I8_J) ).
thf(872,plain,
! [A: $i,B: $i] :
( c_Com_Ocom_OSKIP
!= ( A @ ( B @ c_Com_Ocom_OAss ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(91,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ c_Map_Omap__comp ) ) ) ) ) )
= ( E @ c_Option_Ooption_ONone ) )
<=> ( ? [G: $i] :
( ( ( G @ ( C @ hAPP ) )
= ( E @ c_Option_Ooption_ONone ) )
& ( ( A @ ( B @ hAPP ) )
= ( G @ ( F @ c_Option_Ooption_OSome @ hAPP ) ) ) )
| ( ( A @ ( B @ hAPP ) )
= ( F @ c_Option_Ooption_ONone ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__comp__None__iff) ).
thf(707,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ? [G: $i] :
( ( ( G @ ( C @ hAPP ) )
= ( E @ c_Option_Ooption_ONone ) )
& ( ( A @ ( B @ hAPP ) )
= ( G @ ( F @ c_Option_Ooption_OSome @ hAPP ) ) ) )
| ( ( A @ ( B @ hAPP ) )
= ( F @ c_Option_Ooption_ONone ) ) )
=> ( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ c_Map_Omap__comp ) ) ) ) ) )
= ( E @ c_Option_Ooption_ONone ) ) )
& ( ( ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ c_Map_Omap__comp ) ) ) ) ) )
= ( E @ c_Option_Ooption_ONone ) )
=> ( ? [G: $i] :
( ( ( G @ ( C @ hAPP ) )
= ( E @ c_Option_Ooption_ONone ) )
& ( ( A @ ( B @ hAPP ) )
= ( G @ ( F @ c_Option_Ooption_OSome @ hAPP ) ) ) )
| ( ( A @ ( B @ hAPP ) )
= ( F @ c_Option_Ooption_ONone ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(14,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ c_Com_Ocom_OBODY @ ( c_Com_OWT @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( B @ c_Com_Ocom_OCall ) ) @ ( c_Com_OWT @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_WT_OCall) ).
thf(263,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ c_Com_Ocom_OBODY @ ( c_Com_OWT @ hAPP ) @ hBOOL )
=> ( A @ ( C @ ( B @ c_Com_Ocom_OCall ) ) @ ( c_Com_OWT @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(991,plain,
~ ? [A: $i,B: $i,C: $i] :
( ( C @ c_Com_Ocom_OBODY )
= ( A @ ( B @ c_Com_Ocom_OWhile ) ) ),
inference(miniscope,[status(thm)],[990]) ).
thf(992,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ c_Com_Ocom_OBODY )
!= ( A @ ( B @ c_Com_Ocom_OWhile ) ) ),
inference(cnf,[status(esa)],[991]) ).
thf(993,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ c_Com_Ocom_OBODY )
!= ( A @ ( B @ c_Com_Ocom_OWhile ) ) ),
inference(lifteq,[status(thm)],[992]) ).
thf(174,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i] :
( ( F @ ( E @ hAPP ) )
= ( F @ ( B @ ( C @ ( D @ c_Nat_Onat_Onat__rec ) ) @ hAPP ) ) )
=> ( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( E @ hAPP ) )
= ( A @ ( E @ hAPP ) @ ( A @ ( B @ hAPP ) @ hAPP ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_def__nat__rec__Suc) ).
thf(1053,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i] :
( ( F @ ( E @ hAPP ) )
= ( F @ ( B @ ( C @ ( D @ c_Nat_Onat_Onat__rec ) ) @ hAPP ) ) )
=> ( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( E @ hAPP ) )
= ( A @ ( E @ hAPP ) @ ( A @ ( B @ hAPP ) @ hAPP ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(209,axiom,
! [A: $i,B: $i] : ( B @ ( A @ ( B @ ( c_Com_Ocom_OSKIP @ c_Natural_Oevaln ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln_Oequations_I1_J) ).
thf(1188,plain,
! [A: $i,B: $i] : ( B @ ( A @ ( B @ ( c_Com_Ocom_OSKIP @ c_Natural_Oevaln ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(170,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( C @ ( D @ c_Com_Ocom_OBODY @ c_Natural_Oevaln ) ) ) )
<=> ( A @ ( B @ ( C @ ( D @ ( c_Com_Obody @ hAPP ) @ ( tc_Com_Ocom @ c_Option_Othe @ hAPP ) @ c_Natural_Oevaln ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln_Oequations_I9_J) ).
thf(1038,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 @ c_Natural_Oevaln ) ) ) ) )
& ( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( C @ ( D @ c_Com_Ocom_OBODY @ 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)],[170]) ).
thf(58,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Com_Ocom_OCall ) ) @ ( c_Com_OWT @ hAPP ) @ hBOOL )
<=> ( B @ c_Com_Ocom_OBODY @ ( c_Com_OWT @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_WT_Oequations_I8_J) ).
thf(502,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ c_Com_Ocom_OBODY @ ( c_Com_OWT @ hAPP ) @ hBOOL )
=> ( A @ ( B @ ( C @ c_Com_Ocom_OCall ) ) @ ( c_Com_OWT @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ ( C @ c_Com_Ocom_OCall ) ) @ ( c_Com_OWT @ hAPP ) @ hBOOL )
=> ( B @ c_Com_Ocom_OBODY @ ( c_Com_OWT @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(118,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( c_Com_OWT @ hAPP ) @ hBOOL )
=> ( ( B @ ( c_Com_OWT @ hAPP ) @ hBOOL )
=> ( B @ ( C @ ( A @ c_Com_Ocom_OCond ) ) @ ( c_Com_OWT @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_WT_OIf) ).
thf(840,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( c_Com_OWT @ hAPP ) @ hBOOL )
=> ( ( B @ ( c_Com_OWT @ hAPP ) @ hBOOL )
=> ( B @ ( C @ ( A @ c_Com_Ocom_OCond ) ) @ ( c_Com_OWT @ hAPP ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(33,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/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I42_J) ).
thf(338,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)],[33]) ).
thf(67,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_Sum__Type_OInl ) @ hAPP ) )
!= ( A @ ( D @ ( C @ c_Sum__Type_OInr ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inl__not__Inr) ).
thf(544,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_Sum__Type_OInl ) @ hAPP ) )
!= ( A @ ( D @ ( C @ c_Sum__Type_OInr ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(32,axiom,
! [A: $i,B: $i] :
( ( B @ ( c_Com_OWT @ hAPP ) @ hBOOL )
=> ( B @ ( A @ c_Com_Ocom_OWhile ) @ ( c_Com_OWT @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_While) ).
thf(336,plain,
! [A: $i,B: $i] :
( ( B @ ( c_Com_OWT @ hAPP ) @ hBOOL )
=> ( B @ ( A @ c_Com_Ocom_OWhile ) @ ( c_Com_OWT @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(82,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_Sum__Type_OInr ) @ hAPP ) )
!= ( A @ ( D @ ( C @ c_Sum__Type_OInl ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum_Osimps_I4_J) ).
thf(656,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_Sum__Type_OInr ) @ hAPP ) )
!= ( A @ ( D @ ( C @ c_Sum__Type_OInl ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(76,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Com_Ocom_OSemi ) )
!= ( A @ ( B @ c_Com_Ocom_OAss ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I25_J) ).
thf(600,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Com_Ocom_OSemi ) )
!= ( A @ ( B @ c_Com_Ocom_OAss ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(40,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( A @ ( B @ ( C @ ( D @ c_Com_Ocom_OWhile ) @ c_Natural_Oevaln ) ) ) )
<=> ( ( B @ ( D @ hAPP ) @ hBOOL )
=> ? [E: $i] :
( ( B @ ( A @ ( E @ ( C @ ( D @ c_Com_Ocom_OWhile ) @ c_Natural_Oevaln ) ) ) )
& ( E @ ( A @ ( B @ ( C @ c_Natural_Oevaln ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln_Oequations_I7_J) ).
thf(386,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( B @ ( D @ hAPP ) @ hBOOL )
=> ? [E: $i] :
( ( B @ ( A @ ( E @ ( C @ ( D @ c_Com_Ocom_OWhile ) @ c_Natural_Oevaln ) ) ) )
& ( E @ ( A @ ( B @ ( C @ c_Natural_Oevaln ) ) ) ) ) )
=> ( B @ ( A @ ( B @ ( C @ ( D @ c_Com_Ocom_OWhile ) @ c_Natural_Oevaln ) ) ) ) )
& ( ( B @ ( A @ ( B @ ( C @ ( D @ c_Com_Ocom_OWhile ) @ c_Natural_Oevaln ) ) ) )
=> ( ( B @ ( D @ hAPP ) @ hBOOL )
=> ? [E: $i] :
( ( B @ ( A @ ( E @ ( C @ ( D @ c_Com_Ocom_OWhile ) @ c_Natural_Oevaln ) ) ) )
& ( E @ ( A @ ( B @ ( C @ c_Natural_Oevaln ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(163,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Option_Ooption_OSome @ hAPP ) @ ( B @ c_Option_Othe @ hAPP ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_the_Osimps) ).
thf(1008,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Option_Ooption_OSome @ hAPP ) @ ( B @ c_Option_Othe @ hAPP ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(73,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_Com_Ocom_OCond ) ) @ c_Natural_Oevalc ) ) )
<=> ( ( ( A @ ( B @ ( C @ c_Natural_Oevalc ) ) )
& ~ ( B @ ( E @ hAPP ) @ hBOOL ) )
| ( ( A @ ( B @ ( D @ c_Natural_Oevalc ) ) )
& ( B @ ( E @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc_Oequations_I6_J) ).
thf(571,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( ( ( A @ ( B @ ( C @ c_Natural_Oevalc ) ) )
& ~ ( B @ ( E @ hAPP ) @ hBOOL ) )
| ( ( A @ ( B @ ( D @ c_Natural_Oevalc ) ) )
& ( B @ ( E @ hAPP ) @ hBOOL ) ) )
=> ( A @ ( B @ ( C @ ( D @ ( E @ c_Com_Ocom_OCond ) ) @ c_Natural_Oevalc ) ) ) )
& ( ( A @ ( B @ ( C @ ( D @ ( E @ c_Com_Ocom_OCond ) ) @ c_Natural_Oevalc ) ) )
=> ( ( ( A @ ( B @ ( C @ c_Natural_Oevalc ) ) )
& ~ ( B @ ( E @ hAPP ) @ hBOOL ) )
| ( ( A @ ( B @ ( D @ c_Natural_Oevalc ) ) )
& ( B @ ( E @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(127,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i,L: $i] :
( ( A @ ( B @ ( C @ c_Com_Ocom_OCall ) ) @ ( D @ ( E @ ( F @ ( G @ ( H @ ( I @ ( J @ ( K @ ( L @ c_Com_Ocom_Ocom__case ) ) ) ) ) ) ) ) ) )
= ( A @ ( B @ ( C @ ( D @ hAPP ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I71_J) ).
thf(876,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i,L: $i] :
( ( A @ ( B @ ( C @ c_Com_Ocom_OCall ) ) @ ( D @ ( E @ ( F @ ( G @ ( H @ ( I @ ( J @ ( K @ ( L @ c_Com_Ocom_Ocom__case ) ) ) ) ) ) ) ) ) )
= ( A @ ( B @ ( C @ ( D @ hAPP ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(120,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/sandbox/benchmark/theBenchmark.p',fact_pos__empty__def) ).
thf(845,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)],[120]) ).
thf(70,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ c_Option_Ooption_OSome @ hAPP ) )
= ( A @ ( C @ c_Option_Ooption_OSome @ hAPP ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_option_Oinject) ).
thf(556,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B = A )
=> ( ( B @ ( C @ c_Option_Ooption_OSome @ hAPP ) )
= ( A @ ( C @ c_Option_Ooption_OSome @ hAPP ) ) ) )
& ( ( ( B @ ( C @ c_Option_Ooption_OSome @ hAPP ) )
= ( A @ ( C @ c_Option_Ooption_OSome @ hAPP ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(141,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
( ( c_Com_Ocom_OSKIP @ ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ ( G @ ( H @ ( I @ c_Com_Ocom_Ocom__case ) ) ) ) ) ) ) ) ) )
= H ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I64_J) ).
thf(931,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
( ( c_Com_Ocom_OSKIP @ ( A @ ( B @ ( C @ ( D @ ( E @ ( F @ ( G @ ( H @ ( I @ c_Com_Ocom_Ocom__case ) ) ) ) ) ) ) ) ) )
= H ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(201,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Osemiring__1 )
=> ( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( C @ ( D @ c_Nat_Osemiring__1__class_Oof__nat__aux ) ) ) )
= ( A @ ( C @ hAPP ) @ ( B @ ( C @ ( D @ c_Nat_Osemiring__1__class_Oof__nat__aux ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__aux_Osimps_I2_J) ).
thf(1157,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ class_Rings_Osemiring__1 )
=> ( ( A @ ( B @ ( c_Nat_OSuc @ hAPP ) @ ( C @ ( D @ c_Nat_Osemiring__1__class_Oof__nat__aux ) ) ) )
= ( A @ ( C @ hAPP ) @ ( B @ ( C @ ( D @ c_Nat_Osemiring__1__class_Oof__nat__aux ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(56,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Com_Ocom_OCond ) ) )
!= ( A @ ( B @ c_Com_Ocom_OSemi ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I45_J) ).
thf(495,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Com_Ocom_OCond ) ) )
!= ( A @ ( B @ c_Com_Ocom_OSemi ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(39,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( E @ ( F @ c_Com_Ocom_OCond ) ) )
= ( A @ ( B @ ( C @ c_Com_Ocom_OCond ) ) ) )
<=> ( ( D = A )
& ( E = B )
& ( F = C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I4_J) ).
thf(368,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ( D = A )
& ( E = B )
& ( F = C ) )
=> ( ( D @ ( E @ ( F @ c_Com_Ocom_OCond ) ) )
= ( A @ ( B @ ( C @ c_Com_Ocom_OCond ) ) ) ) )
& ( ( ( D @ ( E @ ( F @ c_Com_Ocom_OCond ) ) )
= ( A @ ( B @ ( C @ c_Com_Ocom_OCond ) ) ) )
=> ( ( D = A )
& ( E = B )
& ( F = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(103,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_Com_Ocom_OCond ) ) @ c_Natural_Oevalc ) ) )
=> ( ( ( B @ ( E @ hAPP ) @ hBOOL )
=> ~ ( A @ ( B @ ( D @ c_Natural_Oevalc ) ) ) )
=> ~ ( ~ ( B @ ( E @ hAPP ) @ hBOOL )
=> ~ ( A @ ( B @ ( C @ c_Natural_Oevalc ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc__elim__cases_I5_J) ).
thf(771,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_Com_Ocom_OCond ) ) @ c_Natural_Oevalc ) ) )
=> ( ( ( B @ ( E @ hAPP ) @ hBOOL )
=> ~ ( A @ ( B @ ( D @ c_Natural_Oevalc ) ) ) )
=> ~ ( ~ ( B @ ( E @ hAPP ) @ hBOOL )
=> ~ ( A @ ( B @ ( C @ c_Natural_Oevalc ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(1307,plain,
( ( ( sk4 @ ( sk2 @ v_Q ) )
!= ( sk3 @ ( sk2 @ v_Q ) ) )
| ~ sk1
| ~ $true
| ( ( v_pn @ ( c_Com_Obody @ hAPP ) @ ( tc_Com_Ocom @ c_Option_Othe @ hAPP ) )
!= c_Com_Ocom_OSKIP )
| ~ sk1 ),
inference(paramod_ordered,[status(thm)],[1302,216]) ).
thf(1308,plain,
( ( ( sk4 @ ( sk2 @ v_Q ) )
!= ( sk3 @ ( sk2 @ v_Q ) ) )
| ( ( v_pn @ ( c_Com_Obody @ hAPP ) @ ( tc_Com_Ocom @ c_Option_Othe @ hAPP ) )
!= c_Com_Ocom_OSKIP )
| ~ sk1 ),
inference(simp,[status(thm)],[1307]) ).
thf(1313,plain,
( ( sk4 != sk3 )
| ( sk2 != sk2 )
| ( ( v_pn @ ( c_Com_Obody @ hAPP ) @ ( tc_Com_Ocom @ c_Option_Othe @ hAPP ) )
!= c_Com_Ocom_OSKIP )
| ~ sk1 ),
inference(simp,[status(thm)],[1308]) ).
thf(1316,plain,
( ( sk4 != sk3 )
| ( ( v_pn @ ( c_Com_Obody @ hAPP ) @ ( tc_Com_Ocom @ c_Option_Othe @ hAPP ) )
!= c_Com_Ocom_OSKIP )
| ~ sk1 ),
inference(simp,[status(thm)],[1313]) ).
thf(49,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/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I2_J) ).
thf(450,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)],[49]) ).
thf(90,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( C @ ( D @ c_Sum__Type_OInl ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Sum__Type_OInl ) @ hAPP ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum_Osimps_I1_J) ).
thf(699,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B = A )
=> ( ( B @ ( C @ ( D @ c_Sum__Type_OInl ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Sum__Type_OInl ) @ hAPP ) ) ) )
& ( ( ( B @ ( C @ ( D @ c_Sum__Type_OInl ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Sum__Type_OInl ) @ hAPP ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(145,axiom,
! [A: $i] :
( ( ( A @ ( c_Com_Obody @ hAPP ) )
!= ( tc_Com_Ocom @ c_Option_Ooption_ONone ) )
=> ( A @ c_Com_Ocom_OBODY @ ( c_Com_OWT @ hAPP ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_WT_OBody) ).
thf(946,plain,
! [A: $i] :
( ( ( A @ ( c_Com_Obody @ hAPP ) )
!= ( tc_Com_Ocom @ c_Option_Ooption_ONone ) )
=> ( A @ c_Com_Ocom_OBODY @ ( c_Com_OWT @ hAPP ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(106,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_Sum__Type_OInl ) @ hAPP ) )
!= ( A @ ( D @ ( C @ c_Sum__Type_OInr ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum_Osimps_I3_J) ).
thf(781,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( B @ ( C @ ( D @ c_Sum__Type_OInl ) @ hAPP ) )
!= ( A @ ( D @ ( C @ c_Sum__Type_OInr ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(113,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_Com_Ocom_OCond ) ) @ c_Natural_Oevalc ) ) )
<=> ( ( ( A @ ( B @ ( C @ c_Natural_Oevalc ) ) )
& ~ ( B @ ( E @ hAPP ) @ hBOOL ) )
| ( ( A @ ( B @ ( D @ c_Natural_Oevalc ) ) )
& ( B @ ( E @ hAPP ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc_Oequations_I5_J) ).
thf(813,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( ( ( A @ ( B @ ( C @ c_Natural_Oevalc ) ) )
& ~ ( B @ ( E @ hAPP ) @ hBOOL ) )
| ( ( A @ ( B @ ( D @ c_Natural_Oevalc ) ) )
& ( B @ ( E @ hAPP ) @ hBOOL ) ) )
=> ( A @ ( B @ ( C @ ( D @ ( E @ c_Com_Ocom_OCond ) ) @ c_Natural_Oevalc ) ) ) )
& ( ( A @ ( B @ ( C @ ( D @ ( E @ c_Com_Ocom_OCond ) ) @ c_Natural_Oevalc ) ) )
=> ( ( ( A @ ( B @ ( C @ c_Natural_Oevalc ) ) )
& ~ ( B @ ( E @ hAPP ) @ hBOOL ) )
| ( ( A @ ( B @ ( D @ c_Natural_Oevalc ) ) )
& ( B @ ( E @ hAPP ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(168,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Com_Ocom_OAss ) )
!= ( A @ c_Com_Ocom_OBODY ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I30_J) ).
thf(1030,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Com_Ocom_OAss ) )
!= ( A @ c_Com_Ocom_OBODY ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(135,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( A @ ( B @ ( C @ ( D @ ( E @ c_Com_Ocom_OWhile ) @ c_Natural_Oevaln ) ) ) )
<=> ( ( ? [F: $i] :
( ( A @ ( B @ ( F @ ( D @ ( E @ c_Com_Ocom_OWhile ) @ c_Natural_Oevaln ) ) ) )
& ( F @ ( B @ ( C @ ( D @ c_Natural_Oevaln ) ) ) ) )
& ( C @ ( E @ hAPP ) @ hBOOL ) )
| ( ~ ( C @ ( E @ hAPP ) @ hBOOL )
& ( A = C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln_Oequations_I8_J) ).
thf(899,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( ( ? [F: $i] :
( ( A @ ( B @ ( F @ ( D @ ( E @ c_Com_Ocom_OWhile ) @ c_Natural_Oevaln ) ) ) )
& ( F @ ( B @ ( C @ ( D @ c_Natural_Oevaln ) ) ) ) )
& ( C @ ( E @ hAPP ) @ hBOOL ) )
| ( ~ ( C @ ( E @ hAPP ) @ hBOOL )
& ( A = C ) ) )
=> ( A @ ( B @ ( C @ ( D @ ( E @ c_Com_Ocom_OWhile ) @ c_Natural_Oevaln ) ) ) ) )
& ( ( A @ ( B @ ( C @ ( D @ ( E @ c_Com_Ocom_OWhile ) @ c_Natural_Oevaln ) ) ) )
=> ( ( ? [F: $i] :
( ( A @ ( B @ ( F @ ( D @ ( E @ c_Com_Ocom_OWhile ) @ c_Natural_Oevaln ) ) ) )
& ( F @ ( B @ ( C @ ( D @ c_Natural_Oevaln ) ) ) ) )
& ( C @ ( E @ hAPP ) @ hBOOL ) )
| ( ~ ( C @ ( E @ hAPP ) @ hBOOL )
& ( A = C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(116,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/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I23_J) ).
thf(832,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)],[116]) ).
thf(35,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Com_Ocom_OCond ) ) )
!= ( A @ ( B @ c_Com_Ocom_OWhile ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I52_J) ).
thf(346,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Com_Ocom_OCond ) ) )
!= ( A @ ( B @ c_Com_Ocom_OWhile ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(214,plain,
( ~ ( sk7 @ ( sk5 @ v_Q ) )
| sk1 ),
inference(cnfConj,[status(thm)],[213]) ).
thf(22,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_OCond ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I36_J) ).
thf(287,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_OCond ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(159,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/sandbox/benchmark/theBenchmark.p',fact_rp__inv__image__rp) ).
thf(999,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)],[159]) ).
thf(43,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/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I1_J) ).
thf(410,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)],[43]) ).
thf(71,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( F @ ( D @ c_Sum__Type_OInr ) @ hAPP ) @ ( B @ ( C @ ( D @ ( E @ ( F @ c_Sum__Type_Osum_Osum__case ) ) ) ) @ hAPP ) )
= ( A @ ( B @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum_Osimps_I6_J) ).
thf(564,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( A @ ( F @ ( D @ c_Sum__Type_OInr ) @ hAPP ) @ ( B @ ( C @ ( D @ ( E @ ( F @ c_Sum__Type_Osum_Osum__case ) ) ) ) @ hAPP ) )
= ( A @ ( B @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Com_Ocom_OWhile ) )
!= ( A @ ( B @ c_Com_Ocom_OSemi ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I47_J) ).
thf(239,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( C @ ( D @ c_Com_Ocom_OWhile ) )
!= ( A @ ( B @ c_Com_Ocom_OSemi ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(38,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/sandbox/benchmark/theBenchmark.p',fact_Pair__eq) ).
thf(358,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)],[38]) ).
thf(175,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/sandbox/benchmark/theBenchmark.p',fact_type__definition_ORep__inject) ).
thf(1056,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)],[175]) ).
thf(1031,plain,
~ ? [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Com_Ocom_OAss ) )
= ( A @ c_Com_Ocom_OBODY ) ),
inference(miniscope,[status(thm)],[1030]) ).
thf(1032,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ c_Com_Ocom_OAss ) )
!= ( A @ c_Com_Ocom_OBODY ) ),
inference(cnf,[status(esa)],[1031]) ).
thf(1033,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ c_Com_Ocom_OAss ) )
!= ( A @ c_Com_Ocom_OBODY ) ),
inference(lifteq,[status(thm)],[1032]) ).
thf(115,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Com_Ocom_OCond ) ) )
!= c_Com_Ocom_OSKIP ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I15_J) ).
thf(828,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ ( C @ c_Com_Ocom_OCond ) ) )
!= c_Com_Ocom_OSKIP ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(89,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i] :
( ( A @ ( B @ c_Com_Ocom_OWhile ) @ ( C @ ( D @ ( E @ ( F @ ( G @ ( H @ ( I @ ( J @ ( K @ c_Com_Ocom_Ocom__rec ) ) ) ) ) ) ) ) ) )
= ( A @ ( C @ ( D @ ( E @ ( F @ ( G @ ( H @ ( I @ ( J @ ( K @ c_Com_Ocom_Ocom__rec ) ) ) ) ) ) ) ) ) @ ( A @ ( B @ ( E @ hAPP ) @ hAPP ) @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Orecs_I6_J) ).
thf(696,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i] :
( ( A @ ( B @ c_Com_Ocom_OWhile ) @ ( C @ ( D @ ( E @ ( F @ ( G @ ( H @ ( I @ ( J @ ( K @ c_Com_Ocom_Ocom__rec ) ) ) ) ) ) ) ) ) )
= ( A @ ( C @ ( D @ ( E @ ( F @ ( G @ ( H @ ( I @ ( J @ ( K @ c_Com_Ocom_Ocom__rec ) ) ) ) ) ) ) ) ) @ ( A @ ( B @ ( E @ hAPP ) @ hAPP ) @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(92,axiom,
! [A: $i,B: $i,C: $i] :
( c_Com_Ocom_OSKIP
!= ( A @ ( B @ ( C @ c_Com_Ocom_OCond ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I14_J) ).
thf(720,plain,
! [A: $i,B: $i,C: $i] :
( c_Com_Ocom_OSKIP
!= ( A @ ( B @ ( C @ c_Com_Ocom_OCond ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(134,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( E @ ( F @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ ( E @ ( D @ c_Natural_Oevaln ) ) ) )
=> ( ( A @ ( C @ ( B @ ( D @ ( F @ c_Com_Ocom_OWhile ) @ c_Natural_Oevaln ) ) ) )
=> ( A @ ( C @ ( E @ ( D @ ( F @ c_Com_Ocom_OWhile ) @ c_Natural_Oevaln ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln_OWhileTrue) ).
thf(897,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( E @ ( F @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ ( E @ ( D @ c_Natural_Oevaln ) ) ) )
=> ( ( A @ ( C @ ( B @ ( D @ ( F @ c_Com_Ocom_OWhile ) @ c_Natural_Oevaln ) ) ) )
=> ( A @ ( C @ ( E @ ( D @ ( F @ c_Com_Ocom_OWhile ) @ c_Natural_Oevaln ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(102,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Com_Ocom_OCond ) ) )
!= ( A @ ( B @ c_Com_Ocom_OAss ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I27_J) ).
thf(767,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Com_Ocom_OCond ) ) )
!= ( A @ ( B @ c_Com_Ocom_OAss ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(31,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( E @ c_Com_Ocom_OSemi ) )
!= ( A @ ( B @ ( C @ c_Com_Ocom_OLocal ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I35_J) ).
thf(332,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( D @ ( E @ c_Com_Ocom_OSemi ) )
!= ( A @ ( B @ ( C @ c_Com_Ocom_OLocal ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(721,plain,
~ ? [A: $i,B: $i,C: $i] :
( c_Com_Ocom_OSKIP
= ( A @ ( B @ ( C @ c_Com_Ocom_OCond ) ) ) ),
inference(miniscope,[status(thm)],[720]) ).
thf(722,plain,
! [C: $i,B: $i,A: $i] :
( c_Com_Ocom_OSKIP
!= ( A @ ( B @ ( C @ c_Com_Ocom_OCond ) ) ) ),
inference(cnf,[status(esa)],[721]) ).
thf(723,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ c_Com_Ocom_OCond ) ) )
!= c_Com_Ocom_OSKIP ),
inference(lifteq,[status(thm)],[722]) ).
thf(19,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( E @ ( F @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ ( E @ ( D @ c_Natural_Oevaln ) ) ) )
=> ( B @ ( C @ ( E @ ( D @ ( A @ ( F @ c_Com_Ocom_OCond ) ) @ c_Natural_Oevaln ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln_OIfFalse) ).
thf(277,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( E @ ( F @ hAPP ) @ hBOOL )
=> ( ( B @ ( C @ ( E @ ( D @ c_Natural_Oevaln ) ) ) )
=> ( B @ ( C @ ( E @ ( D @ ( A @ ( F @ c_Com_Ocom_OCond ) ) @ c_Natural_Oevaln ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(193,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Com_Ocom_OBODY @ 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/sandbox/benchmark/theBenchmark.p',fact_evaln__elim__cases_I6_J) ).
thf(1120,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Com_Ocom_OBODY @ 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)],[193]) ).
thf(185,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( C @ ( D @ c_Nat_Onat_Onat__case ) ) ) )
= ( A @ ( B @ hAPP ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__case__Suc) ).
thf(1093,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) @ ( B @ ( C @ ( D @ c_Nat_Onat_Onat__case ) ) ) )
= ( A @ ( B @ hAPP ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(41,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ c_Com_Ocom_OSemi ) @ ( c_Com_OWT @ hAPP ) @ hBOOL )
<=> ( ( A @ ( c_Com_OWT @ hAPP ) @ hBOOL )
& ( B @ ( c_Com_OWT @ hAPP ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_WT_Oequations_I4_J) ).
thf(395,plain,
! [A: $i,B: $i] :
( ( ( ( A @ ( c_Com_OWT @ hAPP ) @ hBOOL )
& ( B @ ( c_Com_OWT @ hAPP ) @ hBOOL ) )
=> ( A @ ( B @ c_Com_Ocom_OSemi ) @ ( c_Com_OWT @ hAPP ) @ hBOOL ) )
& ( ( A @ ( B @ c_Com_Ocom_OSemi ) @ ( c_Com_OWT @ hAPP ) @ hBOOL )
=> ( ( A @ ( c_Com_OWT @ hAPP ) @ hBOOL )
& ( B @ ( c_Com_OWT @ hAPP ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(94,axiom,
! [A: $i,B: $i,C: $i] : ( A @ ( B @ hAPP ) @ ( C @ ( A @ c_Natural_Oupdate ) ) @ ( A @ ( B @ ( C @ c_Com_Ocom_OAss ) @ c_Natural_Oevalc ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc_OAssign) ).
thf(728,plain,
! [A: $i,B: $i,C: $i] : ( A @ ( B @ hAPP ) @ ( C @ ( A @ c_Natural_Oupdate ) ) @ ( A @ ( B @ ( C @ c_Com_Ocom_OAss ) @ c_Natural_Oevalc ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(98,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( A @ ( B @ ( C @ ( D @ c_Com_Ocom_OWhile ) @ c_Natural_Oevalc ) ) )
<=> ( ( ? [E: $i] :
( ( A @ ( E @ ( C @ ( D @ c_Com_Ocom_OWhile ) @ c_Natural_Oevalc ) ) )
& ( E @ ( B @ ( C @ c_Natural_Oevalc ) ) ) )
& ( B @ ( D @ hAPP ) @ hBOOL ) )
| ( ~ ( B @ ( D @ hAPP ) @ hBOOL )
& ( A = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc_Oequations_I8_J) ).
thf(740,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( ? [E: $i] :
( ( A @ ( E @ ( C @ ( D @ c_Com_Ocom_OWhile ) @ c_Natural_Oevalc ) ) )
& ( E @ ( B @ ( C @ c_Natural_Oevalc ) ) ) )
& ( B @ ( D @ hAPP ) @ hBOOL ) )
| ( ~ ( B @ ( D @ hAPP ) @ hBOOL )
& ( A = B ) ) )
=> ( A @ ( B @ ( C @ ( D @ c_Com_Ocom_OWhile ) @ c_Natural_Oevalc ) ) ) )
& ( ( A @ ( B @ ( C @ ( D @ c_Com_Ocom_OWhile ) @ c_Natural_Oevalc ) ) )
=> ( ( ? [E: $i] :
( ( A @ ( E @ ( C @ ( D @ c_Com_Ocom_OWhile ) @ c_Natural_Oevalc ) ) )
& ( E @ ( B @ ( C @ c_Natural_Oevalc ) ) ) )
& ( B @ ( D @ hAPP ) @ hBOOL ) )
| ( ~ ( B @ ( D @ hAPP ) @ hBOOL )
& ( A = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(51,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B @ ( C @ ( D @ c_Sum__Type_OInr ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Sum__Type_OInr ) @ hAPP ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum_Osimps_I2_J) ).
thf(469,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( B = A )
=> ( ( B @ ( C @ ( D @ c_Sum__Type_OInr ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Sum__Type_OInr ) @ hAPP ) ) ) )
& ( ( ( B @ ( C @ ( D @ c_Sum__Type_OInr ) @ hAPP ) )
= ( A @ ( C @ ( D @ c_Sum__Type_OInr ) @ hAPP ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(37,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Com_Ocom_OCall ) ) )
!= ( A @ ( B @ c_Com_Ocom_OWhile ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I61_J) ).
thf(354,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( C @ ( D @ ( E @ c_Com_Ocom_OCall ) ) )
!= ( A @ ( B @ c_Com_Ocom_OWhile ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(1035,plain,
~ ? [A: $i,B: $i,C: $i] :
( ( B @ ( C @ c_Com_Ocom_OWhile ) )
= ( A @ c_Com_Ocom_OBODY ) ),
inference(miniscope,[status(thm)],[1034]) ).
thf(1036,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ c_Com_Ocom_OWhile ) )
!= ( A @ c_Com_Ocom_OBODY ) ),
inference(cnf,[status(esa)],[1035]) ).
thf(1037,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ c_Com_Ocom_OWhile ) )
!= ( A @ c_Com_Ocom_OBODY ) ),
inference(lifteq,[status(thm)],[1036]) ).
thf(183,axiom,
! [A: $i,B: $i] :
( ( ( B @ ( c_Nat_OSuc @ hAPP ) )
= ( A @ ( c_Nat_OSuc @ hAPP ) ) )
=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__inject) ).
thf(1088,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)],[183]) ).
thf(178,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/sandbox/benchmark/theBenchmark.p',fact_prod_Orecs) ).
thf(1069,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)],[178]) ).
thf(228,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ ( D @ ( E @ ( F @ ( G @ c_Map_Omap__comp ) ) ) ) ) )
= ( A @ ( F @ c_Option_Ooption_OSome @ hAPP ) ) )
| ( ( H @ ( D @ hAPP ) )
!= ( A @ ( F @ c_Option_Ooption_OSome @ hAPP ) ) )
| ( ( B @ ( C @ hAPP ) )
!= ( H @ ( G @ c_Option_Ooption_OSome @ hAPP ) ) ) ),
inference(cnfConj,[status(thm)],[225]) ).
thf(231,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ ( D @ ( E @ ( F @ ( G @ c_Map_Omap__comp ) ) ) ) ) )
= ( A @ ( F @ c_Option_Ooption_OSome @ hAPP ) ) )
| ( ( H @ ( D @ hAPP ) )
!= ( A @ ( F @ c_Option_Ooption_OSome @ hAPP ) ) )
| ( ( B @ ( C @ hAPP ) )
!= ( H @ ( G @ c_Option_Ooption_OSome @ hAPP ) ) ) ),
inference(lifteq,[status(thm)],[228]) ).
thf(232,plain,
! [H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ ( D @ ( E @ ( F @ ( G @ c_Map_Omap__comp ) ) ) ) ) )
= ( A @ ( F @ c_Option_Ooption_OSome @ hAPP ) ) )
| ( ( H @ ( D @ hAPP ) )
!= ( A @ ( F @ c_Option_Ooption_OSome @ hAPP ) ) )
| ( ( B @ ( C @ hAPP ) )
!= ( H @ ( G @ c_Option_Ooption_OSome @ hAPP ) ) ) ),
inference(simp,[status(thm)],[231]) ).
thf(1012,plain,
~ ? [A: $i] :
( A
= ( A @ ( c_Nat_OSuc @ hAPP ) ) ),
inference(miniscope,[status(thm)],[1011]) ).
thf(1013,plain,
! [A: $i] :
( A
!= ( A @ ( c_Nat_OSuc @ hAPP ) ) ),
inference(cnf,[status(esa)],[1012]) ).
thf(1014,plain,
! [A: $i] :
( ( A @ ( c_Nat_OSuc @ hAPP ) )
!= A ),
inference(lifteq,[status(thm)],[1013]) ).
thf(9827,plain,
$false,
inference(e,[status(thm)],[809,1190,1105,1237,249,468,777,977,1005,994,247,677,861,1173,523,582,730,217,276,913,538,1001,320,257,973,885,724,785,934,1132,949,853,1087,448,1100,216,924,1302,1109,253,1136,514,806,692,221,956,1072,660,243,428,265,527,920,942,220,1206,233,1153,761,1047,798,1091,302,260,1174,424,1238,957,894,916,879,493,757,842,324,229,484,551,1128,615,1064,980,1096,499,989,857,884,1160,1075,489,212,328,256,1192,1050,1002,779,647,997,792,938,508,541,1170,1026,1185,586,888,298,965,618,824,279,689,1146,430,402,732,1125,286,291,313,1107,236,804,350,604,681,219,1011,736,990,230,567,434,271,890,477,494,323,1162,1112,345,552,848,520,1149,964,983,1066,883,1015,223,986,636,1044,267,851,1102,1034,1166,927,1081,516,342,1018,754,1181,836,663,548,1003,295,872,707,263,993,1053,1188,1038,502,840,338,544,336,656,600,386,1008,571,876,845,556,931,1157,495,368,771,1316,450,1084,699,946,781,961,813,1030,899,832,346,214,287,999,410,273,564,239,358,1056,1033,828,696,720,955,283,897,767,332,723,277,1120,1093,395,728,740,469,354,215,1037,1088,222,1069,232,1014]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWW295+1 : TPTP v9.3.1. Released v5.2.0.
% 0.00/0.06 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.12/0.43 % Computer : n005.cluster.edu
% 0.12/0.43 % Model : x86_64 x86_64
% 0.12/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.43 % Memory : 8046.5625MB
% 0.12/0.43 % OS : Linux 6.8.0-71-generic
% 0.12/0.43 % CPULimit : 300
% 0.12/0.43 % WCLimit : 300
% 0.12/0.43 % DateTime : Sat Sep 26 15:36:16 UTC 2026
% 0.12/0.43 % CPUTime :
% 0.12/0.44 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.66/1.03 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 3.74/2.38 % [INFO] Parsing done (1337ms).
% 3.89/2.41 % [INFO] Running in sequential loop mode.
% 4.45/2.97 % [INFO] eprover registered as external prover.
% 4.45/2.98 % [INFO] Scanning for conjecture ...
% 6.80/4.04 % [INFO] Found a conjecture (or negated_conjecture) and 5204 axioms. Running axiom selection ...
% 9.30/5.43 % [INFO] Axiom selection finished. Selected 209 axioms (removed 4995 axioms).
% 9.87/5.75 % [INFO] Problem is first-order (TPTP FOF).
% 9.87/5.80 % [INFO] Type checking passed.
% 10.10/5.81 % [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 ...
% 62.56/17.07 % External prover 'e' found a proof!
% 62.56/17.07 % [INFO] Killing All external provers ...
% 62.56/17.07 % Time passed: 16466ms (effective reasoning time: 14659ms)
% 62.56/17.07 % 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)>
% 62.56/17.08 % Axioms used in derivation (209): fact_WT_OLocal, fact_com_Osimps_I58_J, fact_While, fact_sum_Osimps_I5_J, fact_com_Osimps_I56_J, fact_evalc__evaln, fact_evalc_Oequations_I8_J, fact_com__det, fact_com_Osimps_I8_J, fact_com_Osimps_I71_J, fact_evalc_OIfFalse, fact_evaln__elim__cases_I5_J, fact_nat__rec__Suc, fact_com_Osimps_I17_J, fact_sum__case__weak__cong, fact_com_Osimps_I50_J, fact_Inr__not__Inl, fact_prod_Orecs, fact_com_Osimps_I22_J, fact_com_Osimps_I31_J, fact_com_Osimps_I37_J, fact_WT_Oequations_I5_J, fact_pair__box_Oinject, fact_com_Osimps_I40_J, fact_WTs__elim__cases_I3_J, fact_com_Osimps_I69_J, fact_evalc__elim__cases_I1_J, fact_com_Osimps_I10_J, fact_option_Osimps_I2_J, fact_com_Osimps_I24_J, fact_com_Osimps_I46_J, fact_evalc__elim__cases_I4_J, fact_evalc_Oequations_I1_J, fact_com_Osimps_I2_J, fact_WTs__elim__cases_I8_J, fact_com_Osimps_I60_J, fact_evaln_OAssign, fact_Projl_Osimps, fact_option_Oexhaust, fact_com_Osimps_I27_J, fact_sum_Osimps_I3_J, fact_neg__single__def, fact_com_Osimps_I59_J, fact_evalc__elim__cases_I6_J, fact_evaln__Suc, fact_com_Orecs_I1_J, fact_split__paired__All, fact_com_Orecs_I4_J, fact_evalc__elim__cases_I2_J, fact_com_Osimps_I62_J, fact_com_Osimps_I14_J, fact_WT_Oequations_I2_J, fact_com_Osimps_I55_J, fact_com_Osimps_I53_J, fact_nat_Oinject, fact_option_Osimps_I3_J, fact_com_Osimps_I3_J, fact_com_Osimps_I20_J, fact_com_Osimps_I5_J, fact_com_Osimps_I66_J, fact_evaln_Oequations_I2_J, fact_evalc_OIfTrue, fact_pos__empty__def, fact_Rep__Integ__inject, fact_com_Osimps_I23_J, fact_WT__bodiesD, fact_com_Osimps_I13_J, fact_com_Osimps_I41_J, fact_WT_Oequations_I7_J, fact_WT_OAssign, fact_com_Orecs_I7_J, fact_evalc_Oequations_I4_J, fact_Inr__inject, fact_WT_OSemi, fact_evaln_OBody, fact_com_Osimps_I30_J, fact_com_Osimps_I57_J, fact_evaln_OWhileFalse, fact_com_Osimps_I47_J, fact_com_Osimps_I63_J, fact_New__DSequence_Oneg__single__def, fact_com_Osimps_I35_J, fact_evaln_Oequations_I7_J, fact_com_Osimps_I18_J, fact_evaln_OSkip, fact_evaln_OIfTrue, fact_evaln_OSemi, fact_sum_Osimps_I6_J, fact_com_Orecs_I2_J, fact_com_Osimps_I12_J, fact_evalc_OSemi, fact_evalc_OSkip, fact_folding__one__idem_Oidem, fact_com_Osimps_I7_J, fact_of__nat__aux_Osimps_I2_J, fact_com_Orecs_I6_J, fact_WTs__elim__cases_I4_J, fact_body__def, fact_com_Osimps_I45_J, fact_com_Osimps_I28_J, fact_com_Orecs_I3_J, fact_pos__single__def, fact_evalc__WHILE__case, fact_rp__inv__image__rp, fact_WT_OBody, fact_com_Osimps_I32_J, fact_pair__box_Orecs, fact_WT_OSkip, fact_not__Some__eq, fact_WT_Oequations_I3_J, fact_com_Osimps_I6_J, fact_WT_Oequations_I4_J, fact_evalc_Oequations_I9_J, fact_com_Osimps_I21_J, fact_not__None__eq, fact_com_Osimps_I26_J, fact_com_Orecs_I8_J, fact_Pair__inject, fact_evaln_OIfFalse, fact_Suc__inject, fact_ext, fact_com_Osimps_I42_J, fact_com_Osimps_I54_J, fact_evaln__WHILE__case, fact_com_Osimps_I33_J, fact_com_Osimps_I67_J, fact_com_Osimps_I48_J, fact_com_Osimps_I68_J, fact_map__comp__None__iff, fact_n__not__Suc__n, fact_com_Osimps_I64_J, fact_evaln_Oequations_I5_J, fact_WTs__elim__cases_I6_J, fact_com_Osimps_I34_J, fact_Inl__inject, fact_WT_Oequations_I8_J, fact_WT_OCall, fact_evaln_Oequations_I6_J, fact_evalc_OBody, fact_com_Osimps_I36_J, fact_WTs__elim__cases_I5_J, fact_evalc_OWhileFalse, fact_com_Orecs_I5_J, fact_com_Osimps_I38_J, fact_map__comp__simps_I1_J, fact_map__comp__simps_I2_J, fact_com_Osimps_I16_J, fact_evaln__elim__cases_I2_J, fact_evalc_OWhileTrue, fact_sum_Osimps_I4_J, fact_New__DSequence_Opos__empty__def, fact_com_Osimps_I11_J, fact_sum_Osimps_I1_J, fact_evaln__elim__cases_I4_J, fact_com_Osimps_I9_J, fact_nat__case__Suc, fact_rotate__Suc, fact_com_Osimps_I44_J, fact_power_Opower_Opower__Suc, fact_evaln_OWhileTrue, fact_map__comp__Some__iff, fact_evalc_Oequations_I5_J, fact_evaln__elim__cases_I6_J, fact_com_Osimps_I29_J, fact_Pair__eq, fact_Projr_Osimps, fact_com_Osimps_I39_J, fact_com_Osimps_I25_J, fact_com_Osimps_I19_J, fact_evalc__elim__cases_I5_J, fact_com_Osimps_I1_J, fact_option_Oinject, fact_sum__case__inject, fact_evaln_Oequations_I4_J, fact_evaln_Oequations_I9_J, fact_com_Osimps_I61_J, fact_WT_Oequations_I1_J, fact_type__definition_ORep__inject, fact_WT_OIf, fact_New__DSequence_Opos__single__def, fact_com_Osimps_I49_J, fact_com_Osimps_I43_J, fact_evalc_Oequations_I2_J, fact_the_Osimps, fact_pair__box_Osimps_I2_J, fact_com_Osimps_I52_J, fact_Suc__n__not__n, fact_pos__not__random__dseq__def, fact_com_Osimps_I15_J, fact_evaln_Oequations_I8_J, fact_com_Osimps_I70_J, fact_sum_Osimps_I2_J, fact_evalc_Oequations_I6_J, fact_WT_Oequations_I6_J, fact_com_Osimps_I4_J, fact_type__definition_ORep__inverse, fact_WTs__elim__cases_I7_J, fact_evalc_OAssign, fact_folding__image__simple__idem_Oidem, fact_com_Osimps_I51_J, fact_eval__eq, fact_com_Osimps_I65_J, fact_evaln__evalc, fact_evalc_Oequations_I7_J, fact_def__nat__rec__Suc, fact_rotate1__rotate__swap, fact_evaln__elim__cases_I1_J, fact_evaln_Oequations_I1_J, fact_Inl__not__Inr
% 62.56/17.08 % No. of inferences in proof: 510
% 62.56/17.08 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 16466 ms resp. 14659 ms w/o parsing
% 55.30/17.35 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 55.30/17.35 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------