TSTP Solution File: SWW508_5 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SWW508_5 : TPTP v8.1.2. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n011.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 12:24:56 EDT 2023
% Result : Theorem 43.00s 16.66s
% Output : Refutation 43.27s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 178
% Syntax : Number of formulae : 310 ( 69 unt; 48 typ; 0 def)
% Number of atoms : 1525 ( 252 equ; 0 cnn)
% Maximal formula atoms : 36 ( 5 avg)
% Number of connectives : 7789 ( 146 ~; 55 |; 99 &;7221 @)
% ( 24 <=>; 244 =>; 0 <=; 0 <~>)
% Maximal formula depth : 27 ( 11 avg)
% Number of types : 9 ( 8 usr)
% Number of type conns : 54 ( 54 >; 0 *; 0 +; 0 <<)
% Number of symbols : 44 ( 42 usr; 14 con; 0-10 aty)
% Number of variables : 986 ( 0 ^; 896 !; 53 ?; 986 :)
% ( 37 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(a_type,type,
a: $tType ).
thf(com_type,type,
com: $tType ).
thf(loc_type,type,
loc: $tType ).
thf(pname_type,type,
pname: $tType ).
thf(state_type,type,
state: $tType ).
thf(vname_type,type,
vname: $tType ).
thf(bool_type,type,
bool: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(cl_Groups_Ominus_type,type,
cl_Groups_Ominus:
!>[TA: $tType] : $o ).
thf(bot_type,type,
bot:
!>[TA: $tType] : $o ).
thf(finite_finite_type,type,
finite_finite:
!>[TA: $tType] : $o ).
thf(combb_type,type,
combb:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( fun @ TC @ TB ) > ( fun @ TA @ TC ) > ( fun @ TA @ TB ) ) ).
thf(combc_type,type,
combc:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( fun @ TC @ ( fun @ TB @ TA ) ) > TB > ( fun @ TC @ TA ) ) ).
thf(combk_type,type,
combk:
!>[TA: $tType,TB: $tType] : ( TB > ( fun @ TA @ TB ) ) ).
thf(combs_type,type,
combs:
!>[TA: $tType,TB: $tType,TC: $tType] : ( ( fun @ TC @ ( fun @ TB @ TA ) ) > ( fun @ TC @ TB ) > ( fun @ TC @ TA ) ) ).
thf(skip_type,type,
skip: com ).
thf(semi_type,type,
semi: com > com > com ).
thf(com_case_type,type,
com_case:
!>[TA: $tType] : ( TA > ( fun @ vname @ ( fun @ ( fun @ state @ nat ) @ TA ) ) > ( fun @ loc @ ( fun @ ( fun @ state @ nat ) @ ( fun @ com @ TA ) ) ) > ( fun @ com @ ( fun @ com @ TA ) ) > ( fun @ ( fun @ state @ bool ) @ ( fun @ com @ ( fun @ com @ TA ) ) ) > ( fun @ ( fun @ state @ bool ) @ ( fun @ com @ TA ) ) > ( fun @ pname @ TA ) > ( fun @ vname @ ( fun @ pname @ ( fun @ ( fun @ state @ nat ) @ TA ) ) ) > com > TA ) ).
thf(finite_finite1_type,type,
finite_finite1:
!>[TA: $tType] : ( ( fun @ TA @ bool ) > $o ) ).
thf(finite_fold1Set_type,type,
finite_fold1Set:
!>[TA: $tType] : ( ( fun @ TA @ ( fun @ TA @ TA ) ) > ( fun @ TA @ bool ) > TA > $o ) ).
thf(finite_fold_graph_type,type,
finite_fold_graph:
!>[TA: $tType,TB: $tType] : ( ( fun @ TB @ ( fun @ TA @ TA ) ) > TA > ( fun @ TB @ bool ) > TA > $o ) ).
thf(finite_folding_one_type,type,
finite_folding_one:
!>[TA: $tType] : ( ( fun @ TA @ ( fun @ TA @ TA ) ) > ( fun @ ( fun @ TA @ bool ) @ TA ) > $o ) ).
thf(minus_minus_type,type,
minus_minus:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(hoare_992312373derivs_type,type,
hoare_992312373derivs:
!>[TA: $tType] : ( ( fun @ ( hoare_28830079triple @ TA ) @ bool ) > ( fun @ ( hoare_28830079triple @ TA ) @ bool ) > $o ) ).
thf(hoare_1841697145triple_type,type,
hoare_1841697145triple:
!>[TA: $tType] : ( ( fun @ TA @ ( fun @ state @ bool ) ) > com > ( fun @ TA @ ( fun @ state @ bool ) ) > ( hoare_28830079triple @ TA ) ) ).
thf(hoare_376461865e_case_type,type,
hoare_376461865e_case:
!>[TA: $tType,TB: $tType] : ( ( fun @ ( fun @ TB @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ TB @ ( fun @ state @ bool ) ) @ TA ) ) ) > ( hoare_28830079triple @ TB ) > TA ) ).
thf(hoare_678420151le_rec_type,type,
hoare_678420151le_rec:
!>[TA: $tType,TB: $tType] : ( ( fun @ ( fun @ TB @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ TB @ ( fun @ state @ bool ) ) @ TA ) ) ) > ( hoare_28830079triple @ TB ) > TA ) ).
thf(bot_bot_type,type,
bot_bot:
!>[TA: $tType] : TA ).
thf(inv_imagep_type,type,
inv_imagep:
!>[TA: $tType,TB: $tType] : ( ( fun @ TB @ ( fun @ TB @ bool ) ) > ( fun @ TA @ TB ) > TA > TA > $o ) ).
thf(collect_type,type,
collect:
!>[TA: $tType] : ( ( fun @ TA @ bool ) > ( fun @ TA @ bool ) ) ).
thf(insert_type,type,
insert:
!>[TA: $tType] : ( TA > ( fun @ TA @ bool ) > ( fun @ TA @ bool ) ) ).
thf(the_elem_type,type,
the_elem:
!>[TA: $tType] : ( ( fun @ TA @ bool ) > TA ) ).
thf(aa_type,type,
aa:
!>[TA: $tType,TB: $tType] : ( ( fun @ TB @ TA ) > TB > TA ) ).
thf(fFalse_type,type,
fFalse: bool ).
thf(fNot_type,type,
fNot: fun @ bool @ bool ).
thf(fTrue_type,type,
fTrue: bool ).
thf(fconj_type,type,
fconj: fun @ bool @ ( fun @ bool @ bool ) ).
thf(fdisj_type,type,
fdisj: fun @ bool @ ( fun @ bool @ bool ) ).
thf(fequal_type,type,
fequal:
!>[TA: $tType] : ( fun @ TA @ ( fun @ TA @ bool ) ) ).
thf(fimplies_type,type,
fimplies: fun @ bool @ ( fun @ bool @ bool ) ).
thf(member_type,type,
member:
!>[TA: $tType] : ( fun @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) ) ).
thf(pp_type,type,
pp: bool > $o ).
thf(g_type,type,
g: fun @ ( hoare_28830079triple @ a ) @ bool ).
thf(p_type,type,
p: a > state > $o ).
thf(p1_type,type,
p1: fun @ a @ ( fun @ state @ bool ) ).
thf(q_type,type,
q: a > state > $o ).
thf(q1_type,type,
q1: fun @ a @ ( fun @ state @ bool ) ).
thf(c_type,type,
c: com ).
thf(70,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ ( fun @ TA @ bool ) @ TA,C: fun @ TA @ ( fun @ TA @ TA )] :
( ( finite_folding_one @ TA @ C @ B )
=> ( ( finite_finite1 @ TA @ A )
=> ( ( A
!= ( bot_bot @ ( fun @ TA @ bool ) ) )
=> ( ! [D: TA,E: TA] : ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ C @ D ) @ E ) ) @ ( insert @ TA @ D @ ( insert @ TA @ E @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ) ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ ( aa @ ( fun @ TA @ bool ) @ TA @ B @ A ) ) @ A ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_folding__one_Oclosed) ).
thf(365,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ ( fun @ TA @ bool ) @ TA,C: fun @ TA @ ( fun @ TA @ TA )] :
( ( finite_folding_one @ TA @ C @ B )
=> ( ( finite_finite1 @ TA @ A )
=> ( ( A
!= ( bot_bot @ ( fun @ TA @ bool ) ) )
=> ( ! [D: TA,E: TA] : ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ C @ D ) @ E ) ) @ ( insert @ TA @ D @ ( insert @ TA @ E @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ) ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ ( aa @ ( fun @ TA @ bool ) @ TA @ B @ A ) ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(64,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: TA] :
( ( insert @ TA @ B @ ( minus_minus @ ( fun @ TA @ bool ) @ A @ ( insert @ TA @ B @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ) )
= ( insert @ TA @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_insert__Diff__single) ).
thf(347,plain,
! [TA: $tType,A: fun @ TA @ bool,B: TA] :
( ( insert @ TA @ B @ ( minus_minus @ ( fun @ TA @ bool ) @ A @ ( insert @ TA @ B @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ) )
= ( insert @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(36,axiom,
! [TA: $tType,TB: $tType,A: TA,B: fun @ TB @ ( fun @ TA @ TA )] : ( finite_fold_graph @ TB @ TA @ B @ A @ ( bot_bot @ ( fun @ TB @ bool ) ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_fold__graph_OemptyI) ).
thf(249,plain,
! [TA: $tType,TB: $tType,A: TA,B: fun @ TB @ ( fun @ TA @ TA )] : ( finite_fold_graph @ TB @ TA @ B @ A @ ( bot_bot @ ( fun @ TB @ bool ) ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(107,axiom,
! [TA: $tType,A: fun @ TA @ ( fun @ state @ bool ),B: fun @ ( hoare_28830079triple @ TA ) @ bool] : ( hoare_992312373derivs @ TA @ B @ ( insert @ ( hoare_28830079triple @ TA ) @ ( hoare_1841697145triple @ TA @ A @ skip @ A ) @ ( bot_bot @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_hoare__derivs_OSkip) ).
thf(518,plain,
! [TA: $tType,A: fun @ TA @ ( fun @ state @ bool ),B: fun @ ( hoare_28830079triple @ TA ) @ bool] : ( hoare_992312373derivs @ TA @ B @ ( insert @ ( hoare_28830079triple @ TA ) @ ( hoare_1841697145triple @ TA @ A @ skip @ A ) @ ( bot_bot @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(92,axiom,
! [TA: $tType,TB: $tType] :
( ( bot @ TA )
=> ( bot @ ( fun @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Orderings_Obot) ).
thf(468,plain,
! [TA: $tType,TB: $tType] :
( ( bot @ TA )
=> ( bot @ ( fun @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(31,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) )
=> ( ( minus_minus @ ( fun @ TA @ bool ) @ ( insert @ TA @ C @ A ) @ B )
= ( minus_minus @ ( fun @ TA @ bool ) @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_insert__Diff1) ).
thf(234,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) )
=> ( ( minus_minus @ ( fun @ TA @ bool ) @ ( insert @ TA @ C @ A ) @ B )
= ( minus_minus @ ( fun @ TA @ bool ) @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(44,axiom,
! [TA: $tType,A: TA] :
( ( the_elem @ TA @ ( insert @ TA @ A @ ( bot_bot @ ( fun @ TA @ bool ) ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_the__elem__eq) ).
thf(276,plain,
! [TA: $tType,A: TA] :
( ( the_elem @ TA @ ( insert @ TA @ A @ ( bot_bot @ ( fun @ TA @ bool ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(54,axiom,
! [TA: $tType,A: TA,B: fun @ TA @ bool,C: fun @ TA @ ( fun @ TA @ TA )] :
( ( finite_fold1Set @ TA @ C @ B @ A )
=> ( B
!= ( bot_bot @ ( fun @ TA @ bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_fold1Set__nonempty) ).
thf(308,plain,
! [TA: $tType,A: TA,B: fun @ TA @ bool,C: fun @ TA @ ( fun @ TA @ TA )] :
( ( finite_fold1Set @ TA @ C @ B @ A )
=> ( B
!= ( bot_bot @ ( fun @ TA @ bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(75,axiom,
! [A: bool] :
( ( pp @ A )
| ( pp @ ( aa @ bool @ bool @ fNot @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fNot_2_1_U) ).
thf(379,plain,
! [A: bool] :
( ( pp @ A )
| ( pp @ ( aa @ bool @ bool @ fNot @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(129,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TA,C: fun @ TB @ ( fun @ TA @ TA )] :
( ( finite_fold_graph @ TB @ TA @ C @ B @ ( bot_bot @ ( fun @ TB @ bool ) ) @ A )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_empty__fold__graphE) ).
thf(597,plain,
! [TA: $tType,TB: $tType,A: TA,B: TA,C: fun @ TB @ ( fun @ TA @ TA )] :
( ( finite_fold_graph @ TB @ TA @ C @ B @ ( bot_bot @ ( fun @ TB @ bool ) ) @ A )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(109,axiom,
! [TA: $tType] : ( finite_finite1 @ TA @ ( bot_bot @ ( fun @ TA @ bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_finite_OemptyI) ).
thf(523,plain,
! [TA: $tType] : ( finite_finite1 @ TA @ ( bot_bot @ ( fun @ TA @ bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(124,axiom,
! [TA: $tType,A: TA,B: fun @ TA @ bool,C: TA] :
( ( ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) )
=> ( C = A ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( insert @ TA @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_insertCI) ).
thf(582,plain,
! [TA: $tType,A: TA,B: fun @ TA @ bool,C: TA] :
( ( ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) )
=> ( C = A ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( insert @ TA @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(77,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( minus_minus @ ( fun @ TA @ bool ) @ B @ A ) ) )
=> ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_DiffD2) ).
thf(384,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( minus_minus @ ( fun @ TA @ bool ) @ B @ A ) ) )
=> ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(113,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: TA] :
( ( insert @ TA @ B @ ( collect @ TA @ A ) )
= ( collect @ TA @ ( combs @ TA @ bool @ bool @ ( combb @ bool @ ( fun @ bool @ bool ) @ TA @ fimplies @ ( combb @ bool @ bool @ TA @ fNot @ ( combc @ TA @ TA @ bool @ ( fequal @ TA ) @ B ) ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_insert__Collect) ).
thf(533,plain,
! [TA: $tType,A: fun @ TA @ bool,B: TA] :
( ( insert @ TA @ B @ ( collect @ TA @ A ) )
= ( collect @ TA @ ( combs @ TA @ bool @ bool @ ( combb @ bool @ ( fun @ bool @ bool ) @ TA @ fimplies @ ( combb @ bool @ bool @ TA @ fNot @ ( combc @ TA @ TA @ bool @ ( fequal @ TA ) @ B ) ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(5,axiom,
! [A: com,B: com] :
( ( semi @ B @ A )
!= skip ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_com_Osimps_I13_J) ).
thf(142,plain,
! [A: com,B: com] :
( ( semi @ B @ A )
!= skip ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(100,axiom,
! [TA: $tType,A: fun @ TA @ bool] :
( ! [B: TA] :
~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) )
=> ( A
= ( bot_bot @ ( fun @ TA @ bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_equals0I) ).
thf(500,plain,
! [TA: $tType,A: fun @ TA @ bool] :
( ! [B: TA] :
~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) )
=> ( A
= ( bot_bot @ ( fun @ TA @ bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(83,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: TA,C: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( insert @ TA @ B @ A ) ) )
=> ( ( C != B )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_insertE) ).
thf(417,plain,
! [TA: $tType,A: fun @ TA @ bool,B: TA,C: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( insert @ TA @ B @ A ) ) )
=> ( ( C != B )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(48,axiom,
! [TA: $tType,A: TA,B: fun @ TA @ bool,C: TA,D: fun @ TA @ ( fun @ TA @ TA )] :
( ( finite_fold_graph @ TA @ TA @ D @ C @ B @ A )
=> ( ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) )
=> ( finite_fold1Set @ TA @ D @ ( insert @ TA @ C @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_fold1Set_Ointros) ).
thf(288,plain,
! [TA: $tType,A: TA,B: fun @ TA @ bool,C: TA,D: fun @ TA @ ( fun @ TA @ TA )] :
( ( finite_fold_graph @ TA @ TA @ D @ C @ B @ A )
=> ( ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) )
=> ( finite_fold1Set @ TA @ D @ ( insert @ TA @ C @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(57,axiom,
! [TA: $tType,A: TA,B: fun @ TA @ bool,C: fun @ ( fun @ TA @ bool ) @ TA,D: fun @ TA @ ( fun @ TA @ TA )] :
( ( finite_folding_one @ TA @ D @ C )
=> ( ( finite_finite1 @ TA @ B )
=> ( ( ( ( minus_minus @ ( fun @ TA @ bool ) @ B @ ( insert @ TA @ A @ ( bot_bot @ ( fun @ TA @ bool ) ) ) )
= ( bot_bot @ ( fun @ TA @ bool ) ) )
=> ( ( aa @ ( fun @ TA @ bool ) @ TA @ C @ ( insert @ TA @ A @ B ) )
= A ) )
& ( ( ( minus_minus @ ( fun @ TA @ bool ) @ B @ ( insert @ TA @ A @ ( bot_bot @ ( fun @ TA @ bool ) ) ) )
!= ( bot_bot @ ( fun @ TA @ bool ) ) )
=> ( ( aa @ ( fun @ TA @ bool ) @ TA @ C @ ( insert @ TA @ A @ B ) )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ D @ A ) @ ( aa @ ( fun @ TA @ bool ) @ TA @ C @ ( minus_minus @ ( fun @ TA @ bool ) @ B @ ( insert @ TA @ A @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_folding__one_Oinsert__remove) ).
thf(320,plain,
! [TA: $tType,A: TA,B: fun @ TA @ bool,C: fun @ ( fun @ TA @ bool ) @ TA,D: fun @ TA @ ( fun @ TA @ TA )] :
( ( finite_folding_one @ TA @ D @ C )
=> ( ( finite_finite1 @ TA @ B )
=> ( ( ( ( minus_minus @ ( fun @ TA @ bool ) @ B @ ( insert @ TA @ A @ ( bot_bot @ ( fun @ TA @ bool ) ) ) )
= ( bot_bot @ ( fun @ TA @ bool ) ) )
=> ( ( aa @ ( fun @ TA @ bool ) @ TA @ C @ ( insert @ TA @ A @ B ) )
= A ) )
& ( ( ( minus_minus @ ( fun @ TA @ bool ) @ B @ ( insert @ TA @ A @ ( bot_bot @ ( fun @ TA @ bool ) ) ) )
!= ( bot_bot @ ( fun @ TA @ bool ) ) )
=> ( ( aa @ ( fun @ TA @ bool ) @ TA @ C @ ( insert @ TA @ A @ B ) )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ D @ A ) @ ( aa @ ( fun @ TA @ bool ) @ TA @ C @ ( minus_minus @ ( fun @ TA @ bool ) @ B @ ( insert @ TA @ A @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(119,axiom,
! [TA: $tType,TB: $tType] :
( ( cl_Groups_Ominus @ TB )
=> ! [A: fun @ TA @ TB,B: fun @ TA @ TB,C: TA] :
( ( aa @ TA @ TB @ ( minus_minus @ ( fun @ TA @ TB ) @ B @ A ) @ C )
= ( minus_minus @ TB @ ( aa @ TA @ TB @ B @ C ) @ ( aa @ TA @ TB @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_fun__diff__def) ).
thf(570,plain,
! [TA: $tType,TB: $tType] :
( ( cl_Groups_Ominus @ TB )
=> ! [A: fun @ TA @ TB,B: fun @ TA @ TB,C: TA] :
( ( aa @ TA @ TB @ ( minus_minus @ ( fun @ TA @ TB ) @ B @ A ) @ C )
= ( minus_minus @ TB @ ( aa @ TA @ TB @ B @ C ) @ ( aa @ TA @ TB @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(125,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) )
=> ( ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ A ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( minus_minus @ ( fun @ TA @ bool ) @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_DiffI) ).
thf(587,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) )
=> ( ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ A ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( minus_minus @ ( fun @ TA @ bool ) @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(62,axiom,
! [TA: $tType,TB: $tType] :
( ( ( finite_finite @ TA )
& ( finite_finite @ TB ) )
=> ( finite_finite @ ( fun @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Finite__Set_Ofinite) ).
thf(344,plain,
! [TA: $tType,TB: $tType] :
( ( ( finite_finite @ TA )
& ( finite_finite @ TB ) )
=> ( finite_finite @ ( fun @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(90,axiom,
! [TA: $tType,A: fun @ TA @ bool] :
( ? [B: TA] : ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) )
<=> ( A
!= ( bot_bot @ ( fun @ TA @ bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_ex__in__conv) ).
thf(460,plain,
! [TA: $tType,A: fun @ TA @ bool] :
( ( ? [B: TA] : ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) )
=> ( A
!= ( bot_bot @ ( fun @ TA @ bool ) ) ) )
& ( ( A
!= ( bot_bot @ ( fun @ TA @ bool ) ) )
=> ? [B: TA] : ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(7,axiom,
! [TA: $tType] :
( ( finite_finite @ TA )
=> ! [A: fun @ TA @ bool] : ( finite_finite1 @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_finite__code) ).
thf(157,plain,
! [TA: $tType] :
( ( finite_finite @ TA )
=> ! [A: fun @ TA @ bool] : ( finite_finite1 @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(16,axiom,
! [TA: $tType,A: fun @ TA @ ( fun @ state @ bool ),B: com,C: fun @ TA @ ( fun @ state @ bool ),D: com,E: fun @ TA @ ( fun @ state @ bool ),F: fun @ ( hoare_28830079triple @ TA ) @ bool] :
( ( hoare_992312373derivs @ TA @ F @ ( insert @ ( hoare_28830079triple @ TA ) @ ( hoare_1841697145triple @ TA @ E @ D @ C ) @ ( bot_bot @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) ) ) )
=> ( ( hoare_992312373derivs @ TA @ F @ ( insert @ ( hoare_28830079triple @ TA ) @ ( hoare_1841697145triple @ TA @ C @ B @ A ) @ ( bot_bot @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) ) ) )
=> ( hoare_992312373derivs @ TA @ F @ ( insert @ ( hoare_28830079triple @ TA ) @ ( hoare_1841697145triple @ TA @ E @ ( semi @ D @ B ) @ A ) @ ( bot_bot @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_Comp) ).
thf(189,plain,
! [TA: $tType,A: fun @ TA @ ( fun @ state @ bool ),B: com,C: fun @ TA @ ( fun @ state @ bool ),D: com,E: fun @ TA @ ( fun @ state @ bool ),F: fun @ ( hoare_28830079triple @ TA ) @ bool] :
( ( hoare_992312373derivs @ TA @ F @ ( insert @ ( hoare_28830079triple @ TA ) @ ( hoare_1841697145triple @ TA @ E @ D @ C ) @ ( bot_bot @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) ) ) )
=> ( ( hoare_992312373derivs @ TA @ F @ ( insert @ ( hoare_28830079triple @ TA ) @ ( hoare_1841697145triple @ TA @ C @ B @ A ) @ ( bot_bot @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) ) ) )
=> ( hoare_992312373derivs @ TA @ F @ ( insert @ ( hoare_28830079triple @ TA ) @ ( hoare_1841697145triple @ TA @ E @ ( semi @ D @ B ) @ A ) @ ( bot_bot @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(58,axiom,
! [TA: $tType,A: fun @ TA @ bool] :
( ( finite_finite1 @ TA @ A )
<=> ( ( A
= ( bot_bot @ ( fun @ TA @ bool ) ) )
| ? [B: fun @ TA @ bool,C: TA] :
( ( A
= ( insert @ TA @ C @ B ) )
& ( finite_finite1 @ TA @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_finite_Osimps) ).
thf(325,plain,
! [TA: $tType,A: fun @ TA @ bool] :
( ( ( finite_finite1 @ TA @ A )
=> ( ( A
= ( bot_bot @ ( fun @ TA @ bool ) ) )
| ? [B: fun @ TA @ bool,C: TA] :
( ( A
= ( insert @ TA @ C @ B ) )
& ( finite_finite1 @ TA @ B ) ) ) )
& ( ( ( A
= ( bot_bot @ ( fun @ TA @ bool ) ) )
| ? [B: fun @ TA @ bool,C: TA] :
( ( A
= ( insert @ TA @ C @ B ) )
& ( finite_finite1 @ TA @ B ) ) )
=> ( finite_finite1 @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(29,axiom,
! [TA: $tType,TB: $tType] :
( ( bot @ TA )
=> ! [A: TB] :
( ( aa @ TB @ TA @ ( bot_bot @ ( fun @ TB @ TA ) ) @ A )
= ( bot_bot @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_bot__apply) ).
thf(228,plain,
! [TA: $tType,TB: $tType] :
( ( bot @ TA )
=> ! [A: TB] :
( ( aa @ TB @ TA @ ( bot_bot @ ( fun @ TB @ TA ) ) @ A )
= ( bot_bot @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(94,axiom,
! [TA: $tType,A: fun @ TA @ bool] :
( ( A
!= ( bot_bot @ ( fun @ TA @ bool ) ) )
<=> ? [B: TA,C: fun @ TA @ bool] :
( ( A
= ( insert @ TA @ B @ C ) )
& ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_nonempty__iff) ).
thf(475,plain,
! [TA: $tType,A: fun @ TA @ bool] :
( ( ( A
!= ( bot_bot @ ( fun @ TA @ bool ) ) )
=> ? [B: TA,C: fun @ TA @ bool] :
( ( A
= ( insert @ TA @ B @ C ) )
& ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ C ) ) ) )
& ( ? [B: TA,C: fun @ TA @ bool] :
( ( A
= ( insert @ TA @ B @ C ) )
& ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ C ) ) )
=> ( A
!= ( bot_bot @ ( fun @ TA @ bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(66,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: TA] :
( ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) )
=> ( ( minus_minus @ ( fun @ TA @ bool ) @ ( insert @ TA @ C @ A ) @ B )
= ( minus_minus @ ( fun @ TA @ bool ) @ A @ B ) ) )
& ( ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) )
=> ( ( minus_minus @ ( fun @ TA @ bool ) @ ( insert @ TA @ C @ A ) @ B )
= ( insert @ TA @ C @ ( minus_minus @ ( fun @ TA @ bool ) @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_insert__Diff__if) ).
thf(353,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: TA] :
( ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) )
=> ( ( minus_minus @ ( fun @ TA @ bool ) @ ( insert @ TA @ C @ A ) @ B )
= ( minus_minus @ ( fun @ TA @ bool ) @ A @ B ) ) )
& ( ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) )
=> ( ( minus_minus @ ( fun @ TA @ bool ) @ ( insert @ TA @ C @ A ) @ B )
= ( insert @ TA @ C @ ( minus_minus @ ( fun @ TA @ bool ) @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(1,conjecture,
! [A: a,B: state] :
( ~ ( p @ A @ B )
| ? [C: fun @ a @ ( fun @ state @ bool ),D: fun @ a @ ( fun @ state @ bool )] :
( ( hoare_992312373derivs @ a @ g @ ( insert @ ( hoare_28830079triple @ a ) @ ( hoare_1841697145triple @ a @ C @ c @ D ) @ ( bot_bot @ ( fun @ ( hoare_28830079triple @ a ) @ bool ) ) ) )
& ! [E: state] :
( ? [F: a] :
( ( pp @ ( aa @ state @ bool @ ( aa @ a @ ( fun @ state @ bool ) @ C @ F ) @ B ) )
& ~ ( pp @ ( aa @ state @ bool @ ( aa @ a @ ( fun @ state @ bool ) @ D @ F ) @ E ) ) )
| ( q @ A @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_2) ).
thf(2,negated_conjecture,
~ ! [A: a,B: state] :
( ~ ( p @ A @ B )
| ? [C: fun @ a @ ( fun @ state @ bool ),D: fun @ a @ ( fun @ state @ bool )] :
( ( hoare_992312373derivs @ a @ g @ ( insert @ ( hoare_28830079triple @ a ) @ ( hoare_1841697145triple @ a @ C @ c @ D ) @ ( bot_bot @ ( fun @ ( hoare_28830079triple @ a ) @ bool ) ) ) )
& ! [E: state] :
( ? [F: a] :
( ( pp @ ( aa @ state @ bool @ ( aa @ a @ ( fun @ state @ bool ) @ C @ F ) @ B ) )
& ~ ( pp @ ( aa @ state @ bool @ ( aa @ a @ ( fun @ state @ bool ) @ D @ F ) @ E ) ) )
| ( q @ A @ E ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(132,plain,
~ ! [A: a,B: state] :
( ~ ( p @ A @ B )
| ? [C: fun @ a @ ( fun @ state @ bool ),D: fun @ a @ ( fun @ state @ bool )] :
( ( hoare_992312373derivs @ a @ g @ ( insert @ ( hoare_28830079triple @ a ) @ ( hoare_1841697145triple @ a @ C @ c @ D ) @ ( bot_bot @ ( fun @ ( hoare_28830079triple @ a ) @ bool ) ) ) )
& ! [E: state] :
( ? [F: a] :
( ( pp @ ( aa @ state @ bool @ ( aa @ a @ ( fun @ state @ bool ) @ C @ F ) @ B ) )
& ~ ( pp @ ( aa @ state @ bool @ ( aa @ a @ ( fun @ state @ bool ) @ D @ F ) @ E ) ) )
| ( q @ A @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(33,axiom,
hoare_992312373derivs @ a @ g @ ( insert @ ( hoare_28830079triple @ a ) @ ( hoare_1841697145triple @ a @ p1 @ c @ q1 ) @ ( bot_bot @ ( fun @ ( hoare_28830079triple @ a ) @ bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(243,plain,
hoare_992312373derivs @ a @ g @ ( insert @ ( hoare_28830079triple @ a ) @ ( hoare_1841697145triple @ a @ p1 @ c @ q1 ) @ ( bot_bot @ ( fun @ ( hoare_28830079triple @ a ) @ bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(55,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( ( insert @ TA @ B @ ( bot_bot @ ( fun @ TA @ bool ) ) )
= ( insert @ TA @ A @ ( bot_bot @ ( fun @ TA @ bool ) ) ) )
=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_singleton__inject) ).
thf(312,plain,
! [TA: $tType,A: TA,B: TA] :
( ( ( insert @ TA @ B @ ( bot_bot @ ( fun @ TA @ bool ) ) )
= ( insert @ TA @ A @ ( bot_bot @ ( fun @ TA @ bool ) ) ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(23,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: TA,C: TA] :
( ( insert @ TA @ C @ ( insert @ TA @ B @ A ) )
= ( insert @ TA @ B @ ( insert @ TA @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_insert__commute) ).
thf(206,plain,
! [TA: $tType,A: fun @ TA @ bool,B: TA,C: TA] :
( ( insert @ TA @ C @ ( insert @ TA @ B @ A ) )
= ( insert @ TA @ B @ ( insert @ TA @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(105,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TC,B: TA,C: fun @ TC @ ( fun @ TA @ TB )] :
( ( aa @ TC @ TB @ ( combc @ TC @ TA @ TB @ C @ B ) @ A )
= ( aa @ TA @ TB @ ( aa @ TC @ ( fun @ TA @ TB ) @ C @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_U) ).
thf(512,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TC,B: TA,C: fun @ TC @ ( fun @ TA @ TB )] :
( ( aa @ TC @ TB @ ( combc @ TC @ TA @ TB @ C @ B ) @ A )
= ( aa @ TA @ TB @ ( aa @ TC @ ( fun @ TA @ TB ) @ C @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(21,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( finite_finite1 @ TA @ B )
=> ( finite_finite1 @ TA @ ( minus_minus @ ( fun @ TA @ bool ) @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_finite__Diff) ).
thf(201,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( finite_finite1 @ TA @ B )
=> ( finite_finite1 @ TA @ ( minus_minus @ ( fun @ TA @ bool ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(76,axiom,
! [TA: $tType,A: TA,B: fun @ TA @ bool,C: fun @ ( fun @ TA @ bool ) @ TA,D: fun @ TA @ ( fun @ TA @ TA )] :
( ( finite_folding_one @ TA @ D @ C )
=> ( ( finite_finite1 @ TA @ B )
=> ( ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ B ) )
=> ( ( B
!= ( bot_bot @ ( fun @ TA @ bool ) ) )
=> ( ( aa @ ( fun @ TA @ bool ) @ TA @ C @ ( insert @ TA @ A @ B ) )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ D @ A ) @ ( aa @ ( fun @ TA @ bool ) @ TA @ C @ B ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_folding__one_Oinsert) ).
thf(381,plain,
! [TA: $tType,A: TA,B: fun @ TA @ bool,C: fun @ ( fun @ TA @ bool ) @ TA,D: fun @ TA @ ( fun @ TA @ TA )] :
( ( finite_folding_one @ TA @ D @ C )
=> ( ( finite_finite1 @ TA @ B )
=> ( ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ B ) )
=> ( ( B
!= ( bot_bot @ ( fun @ TA @ bool ) ) )
=> ( ( aa @ ( fun @ TA @ bool ) @ TA @ C @ ( insert @ TA @ A @ B ) )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ D @ A ) @ ( aa @ ( fun @ TA @ bool ) @ TA @ C @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(26,axiom,
! [TA: $tType,A: TA,B: TA] :
( ~ ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( fequal @ TA ) @ B ) @ A ) )
| ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_1_1_T) ).
thf(220,plain,
! [TA: $tType,A: TA,B: TA] :
( ~ ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( fequal @ TA ) @ B ) @ A ) )
| ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(40,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ ( insert @ TA @ A @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_singleton__iff) ).
thf(260,plain,
! [TA: $tType,A: TA,B: TA] :
( ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ ( insert @ TA @ A @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ) )
=> ( B = A ) )
& ( ( B = A )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ ( insert @ TA @ A @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(80,axiom,
~ ( pp @ fFalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_1_1_U) ).
thf(407,plain,
~ ( pp @ fFalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(19,axiom,
! [A: bool,B: bool] :
( ~ ( pp @ B )
| ~ ( pp @ A )
| ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fconj @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_1_1_U) ).
thf(197,plain,
! [A: bool,B: bool] :
( ~ ( pp @ B )
| ~ ( pp @ A )
| ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fconj @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(47,axiom,
! [TA: $tType,A: TA,B: fun @ ( fun @ TA @ bool ) @ TA,C: fun @ TA @ ( fun @ TA @ TA )] :
( ( finite_folding_one @ TA @ C @ B )
=> ( ( aa @ ( fun @ TA @ bool ) @ TA @ B @ ( insert @ TA @ A @ ( bot_bot @ ( fun @ TA @ bool ) ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_folding__one_Osingleton) ).
thf(285,plain,
! [TA: $tType,A: TA,B: fun @ ( fun @ TA @ bool ) @ TA,C: fun @ TA @ ( fun @ TA @ TA )] :
( ( finite_folding_one @ TA @ C @ B )
=> ( ( aa @ ( fun @ TA @ bool ) @ TA @ B @ ( insert @ TA @ A @ ( bot_bot @ ( fun @ TA @ bool ) ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(79,axiom,
! [TA: $tType,A: TA,B: fun @ TA @ bool] :
( ( B
= ( bot_bot @ ( fun @ TA @ bool ) ) )
=> ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_equals0D) ).
thf(403,plain,
! [TA: $tType,A: TA,B: fun @ TA @ bool] :
( ( B
= ( bot_bot @ ( fun @ TA @ bool ) ) )
=> ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(84,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: TA,C: fun @ TA @ bool] :
( ( minus_minus @ ( fun @ TA @ bool ) @ C @ ( insert @ TA @ B @ A ) )
= ( minus_minus @ ( fun @ TA @ bool ) @ ( minus_minus @ ( fun @ TA @ bool ) @ C @ ( insert @ TA @ B @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_Diff__insert2) ).
thf(420,plain,
! [TA: $tType,A: fun @ TA @ bool,B: TA,C: fun @ TA @ bool] :
( ( minus_minus @ ( fun @ TA @ bool ) @ C @ ( insert @ TA @ B @ A ) )
= ( minus_minus @ ( fun @ TA @ bool ) @ ( minus_minus @ ( fun @ TA @ bool ) @ C @ ( insert @ TA @ B @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(39,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) )
=> ~ ! [C: fun @ TA @ bool] :
( ( A
= ( insert @ TA @ B @ C ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_Set_Oset__insert) ).
thf(256,plain,
! [TA: $tType,A: fun @ TA @ bool,B: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) )
=> ~ ! [C: fun @ TA @ bool] :
( ( A
= ( insert @ TA @ B @ C ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(28,axiom,
! [A: a,B: state] :
( ( p @ A @ B )
=> ! [C: state] :
( ! [D: a] :
( ( pp @ ( aa @ state @ bool @ ( aa @ a @ ( fun @ state @ bool ) @ p1 @ D ) @ B ) )
=> ( pp @ ( aa @ state @ bool @ ( aa @ a @ ( fun @ state @ bool ) @ q1 @ D ) @ C ) ) )
=> ( q @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
thf(225,plain,
! [A: a,B: state] :
( ( p @ A @ B )
=> ! [C: state] :
( ! [D: a] :
( ( pp @ ( aa @ state @ bool @ ( aa @ a @ ( fun @ state @ bool ) @ p1 @ D ) @ B ) )
=> ( pp @ ( aa @ state @ bool @ ( aa @ a @ ( fun @ state @ bool ) @ q1 @ D ) @ C ) ) )
=> ( q @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(60,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: TA] : ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ ( insert @ TA @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_insertI1) ).
thf(339,plain,
! [TA: $tType,A: fun @ TA @ bool,B: TA] : ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ ( insert @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(106,axiom,
! [TA: $tType,TB: $tType,A: TB,B: TA] :
( ( aa @ TB @ TA @ ( combk @ TA @ TB @ B ) @ A )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBK_1_1_U) ).
thf(515,plain,
! [TA: $tType,TB: $tType,A: TB,B: TA] :
( ( aa @ TB @ TA @ ( combk @ TA @ TB @ B ) @ A )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(12,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( minus_minus @ ( fun @ TA @ bool ) @ B @ A ) ) )
<=> ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) )
& ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_Diff__iff) ).
thf(173,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: TA] :
( ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( minus_minus @ ( fun @ TA @ bool ) @ B @ A ) ) )
=> ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) )
& ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ A ) ) ) )
& ( ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) )
& ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ A ) ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( minus_minus @ ( fun @ TA @ bool ) @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(72,axiom,
! [TA: $tType,A: fun @ TA @ bool] :
( ( minus_minus @ ( fun @ TA @ bool ) @ ( bot_bot @ ( fun @ TA @ bool ) ) @ A )
= ( bot_bot @ ( fun @ TA @ bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_empty__Diff) ).
thf(371,plain,
! [TA: $tType,A: fun @ TA @ bool] :
( ( minus_minus @ ( fun @ TA @ bool ) @ ( bot_bot @ ( fun @ TA @ bool ) ) @ A )
= ( bot_bot @ ( fun @ TA @ bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(101,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: TA] :
( ( insert @ TA @ B @ A )
!= ( bot_bot @ ( fun @ TA @ bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_insert__not__empty) ).
thf(503,plain,
! [TA: $tType,A: fun @ TA @ bool,B: TA] :
( ( insert @ TA @ B @ A )
!= ( bot_bot @ ( fun @ TA @ bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(32,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: TA] :
( ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) )
=> ( ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ A ) )
=> ( ( ( insert @ TA @ C @ B )
= ( insert @ TA @ C @ A ) )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_insert__ident) ).
thf(237,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: TA] :
( ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) )
=> ( ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ A ) )
=> ( ( ( ( insert @ TA @ C @ B )
= ( insert @ TA @ C @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( insert @ TA @ C @ B )
= ( insert @ TA @ C @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(34,axiom,
! [A: bool,B: bool] :
( ~ ( pp @ B )
| ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fdisj @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fdisj_1_1_U) ).
thf(244,plain,
! [A: bool,B: bool] :
( ~ ( pp @ B )
| ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fdisj @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(41,axiom,
! [TA: $tType,A: fun @ TA @ bool] :
( ! [B: TA] :
~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) )
<=> ( A
= ( bot_bot @ ( fun @ TA @ bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_all__not__in__conv) ).
thf(266,plain,
! [TA: $tType,A: fun @ TA @ bool] :
( ( ! [B: TA] :
~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) )
=> ( A
= ( bot_bot @ ( fun @ TA @ bool ) ) ) )
& ( ( A
= ( bot_bot @ ( fun @ TA @ bool ) ) )
=> ! [B: TA] :
~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(68,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ ( insert @ TA @ A @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ) )
=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_singletonE) ).
thf(360,plain,
! [TA: $tType,A: TA,B: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ ( insert @ TA @ A @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(116,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: TA,C: fun @ TA @ bool,D: TA] :
( ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ D ) @ C ) )
=> ( ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) )
=> ( ( ( insert @ TA @ D @ C )
= ( insert @ TA @ B @ A ) )
<=> ( ( ( D = B )
=> ( C = A ) )
& ( ( D != B )
=> ? [E: fun @ TA @ bool] :
( ( C
= ( insert @ TA @ B @ E ) )
& ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ E ) )
& ( A
= ( insert @ TA @ D @ E ) )
& ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ D ) @ E ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_insert__eq__iff) ).
thf(541,plain,
! [TA: $tType,A: fun @ TA @ bool,B: TA,C: fun @ TA @ bool,D: TA] :
( ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ D ) @ C ) )
=> ( ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) )
=> ( ( ( ( insert @ TA @ D @ C )
= ( insert @ TA @ B @ A ) )
=> ( ( ( D = B )
=> ( C = A ) )
& ( ( D != B )
=> ? [E: fun @ TA @ bool] :
( ( C
= ( insert @ TA @ B @ E ) )
& ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ E ) )
& ( A
= ( insert @ TA @ D @ E ) )
& ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ D ) @ E ) ) ) ) ) )
& ( ( ( ( D = B )
=> ( C = A ) )
& ( ( D != B )
=> ? [E: fun @ TA @ bool] :
( ( C
= ( insert @ TA @ B @ E ) )
& ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ E ) )
& ( A
= ( insert @ TA @ D @ E ) )
& ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ D ) @ E ) ) ) ) )
=> ( ( insert @ TA @ D @ C )
= ( insert @ TA @ B @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(112,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: TA] :
( ( finite_finite1 @ TA @ ( insert @ TA @ B @ A ) )
<=> ( finite_finite1 @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_finite__insert) ).
thf(530,plain,
! [TA: $tType,A: fun @ TA @ bool,B: TA] :
( ( ( finite_finite1 @ TA @ ( insert @ TA @ B @ A ) )
=> ( finite_finite1 @ TA @ A ) )
& ( ( finite_finite1 @ TA @ A )
=> ( finite_finite1 @ TA @ ( insert @ TA @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(51,axiom,
! [A: bool,B: bool] :
( ~ ( pp @ B )
| ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fimplies @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fimplies_2_1_U) ).
thf(298,plain,
! [A: bool,B: bool] :
( ~ ( pp @ B )
| ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fimplies @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(10,axiom,
! [TA: $tType] :
( ( finite_finite @ TA )
=> ! [A: fun @ TA @ bool] : ( finite_finite1 @ TA @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_finite) ).
thf(166,plain,
! [TA: $tType] :
( ( finite_finite @ TA )
=> ! [A: fun @ TA @ bool] : ( finite_finite1 @ TA @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(45,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( B != A )
| ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( fequal @ TA ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_T) ).
thf(279,plain,
! [TA: $tType,A: TA,B: TA] :
( ( B != A )
| ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( fequal @ TA ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(120,axiom,
! [TA: $tType,A: TA,B: fun @ TA @ bool,C: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( insert @ TA @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_insertI2) ).
thf(573,plain,
! [TA: $tType,A: TA,B: fun @ TA @ bool,C: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( insert @ TA @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(14,axiom,
! [TA: $tType,A: TA,B: TA,C: fun @ TA @ ( fun @ TA @ TA )] :
( ( finite_fold1Set @ TA @ C @ ( insert @ TA @ B @ ( bot_bot @ ( fun @ TA @ bool ) ) ) @ A )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_fold1Set__sing) ).
thf(180,plain,
! [TA: $tType,A: TA,B: TA,C: fun @ TA @ ( fun @ TA @ TA )] :
( ( ( finite_fold1Set @ TA @ C @ ( insert @ TA @ B @ ( bot_bot @ ( fun @ TA @ bool ) ) ) @ A )
=> ( B = A ) )
& ( ( B = A )
=> ( finite_fold1Set @ TA @ C @ ( insert @ TA @ B @ ( bot_bot @ ( fun @ TA @ bool ) ) ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(85,axiom,
! [TA: $tType,A: TA,B: TA,C: TA,D: TA] :
( ( ( insert @ TA @ D @ ( insert @ TA @ C @ ( bot_bot @ ( fun @ TA @ bool ) ) ) )
= ( insert @ TA @ B @ ( insert @ TA @ A @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ) )
<=> ( ( ( D = B )
& ( C = A ) )
| ( ( D = A )
& ( C = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_doubleton__eq__iff) ).
thf(423,plain,
! [TA: $tType,A: TA,B: TA,C: TA,D: TA] :
( ( ( ( insert @ TA @ D @ ( insert @ TA @ C @ ( bot_bot @ ( fun @ TA @ bool ) ) ) )
= ( insert @ TA @ B @ ( insert @ TA @ A @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ) )
=> ( ( ( D = B )
& ( C = A ) )
| ( ( D = A )
& ( C = B ) ) ) )
& ( ( ( ( D = B )
& ( C = A ) )
| ( ( D = A )
& ( C = B ) ) )
=> ( ( insert @ TA @ D @ ( insert @ TA @ C @ ( bot_bot @ ( fun @ TA @ bool ) ) ) )
= ( insert @ TA @ B @ ( insert @ TA @ A @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(17,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) )
=> ( ( insert @ TA @ B @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_insert__absorb) ).
thf(191,plain,
! [TA: $tType,A: fun @ TA @ bool,B: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) )
=> ( ( insert @ TA @ B @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(122,axiom,
! [TA: $tType] :
( ( bot_bot @ ( fun @ TA @ bool ) )
= ( collect @ TA @ ( combk @ bool @ TA @ fFalse ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_empty__def) ).
thf(577,plain,
! [TA: $tType] :
( ( bot_bot @ ( fun @ TA @ bool ) )
= ( collect @ TA @ ( combk @ bool @ TA @ fFalse ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(50,axiom,
! [TA: $tType,A: TA,B: fun @ TA @ bool,C: TA] :
( ( pp @ ( aa @ TA @ bool @ ( insert @ TA @ C @ B ) @ A ) )
<=> ( ( C = A )
| ( pp @ ( aa @ TA @ bool @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_insert__code) ).
thf(291,plain,
! [TA: $tType,A: TA,B: fun @ TA @ bool,C: TA] :
( ( ( pp @ ( aa @ TA @ bool @ ( insert @ TA @ C @ B ) @ A ) )
=> ( ( C = A )
| ( pp @ ( aa @ TA @ bool @ B @ A ) ) ) )
& ( ( ( C = A )
| ( pp @ ( aa @ TA @ bool @ B @ A ) ) )
=> ( pp @ ( aa @ TA @ bool @ ( insert @ TA @ C @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(87,axiom,
! [TA: $tType,A: TA,B: fun @ TA @ bool,C: fun @ TA @ ( fun @ TA @ TA )] :
( ( finite_fold1Set @ TA @ C @ B @ A )
<=> ? [D: TA,E: fun @ TA @ bool,F: TA] :
( ( B
= ( insert @ TA @ D @ E ) )
& ( A = F )
& ( finite_fold_graph @ TA @ TA @ C @ D @ E @ F )
& ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ D ) @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_fold1Set_Osimps) ).
thf(445,plain,
! [TA: $tType,A: TA,B: fun @ TA @ bool,C: fun @ TA @ ( fun @ TA @ TA )] :
( ( ( finite_fold1Set @ TA @ C @ B @ A )
=> ? [D: TA,E: fun @ TA @ bool,F: TA] :
( ( B
= ( insert @ TA @ D @ E ) )
& ( A = F )
& ( finite_fold_graph @ TA @ TA @ C @ D @ E @ F )
& ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ D ) @ E ) ) ) )
& ( ? [D: TA,E: fun @ TA @ bool,F: TA] :
( ( B
= ( insert @ TA @ D @ E ) )
& ( A = F )
& ( finite_fold_graph @ TA @ TA @ C @ D @ E @ F )
& ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ D ) @ E ) ) )
=> ( finite_fold1Set @ TA @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(91,axiom,
! [TA: $tType,A: fun @ ( hoare_28830079triple @ TA ) @ bool] : ( hoare_992312373derivs @ TA @ A @ ( bot_bot @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_empty) ).
thf(466,plain,
! [TA: $tType,A: fun @ ( hoare_28830079triple @ TA ) @ bool] : ( hoare_992312373derivs @ TA @ A @ ( bot_bot @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(65,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: fun @ TA @ TB,C: fun @ TB @ TC] :
( ( aa @ TA @ TC @ ( combb @ TB @ TC @ TA @ C @ B ) @ A )
= ( aa @ TB @ TC @ C @ ( aa @ TA @ TB @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_U) ).
thf(350,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: fun @ TA @ TB,C: fun @ TB @ TC] :
( ( aa @ TA @ TC @ ( combb @ TB @ TC @ TA @ C @ B ) @ A )
= ( aa @ TB @ TC @ C @ ( aa @ TA @ TB @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(8,axiom,
! [TA: $tType,A: fun @ vname @ ( fun @ pname @ ( fun @ ( fun @ state @ nat ) @ TA ) ),B: fun @ pname @ TA,C: fun @ ( fun @ state @ bool ) @ ( fun @ com @ TA ),D: fun @ ( fun @ state @ bool ) @ ( fun @ com @ ( fun @ com @ TA ) ),E: fun @ com @ ( fun @ com @ TA ),F: fun @ loc @ ( fun @ ( fun @ state @ nat ) @ ( fun @ com @ TA ) ),G: fun @ vname @ ( fun @ ( fun @ state @ nat ) @ TA ),H: TA] :
( ( com_case @ TA @ H @ G @ F @ E @ D @ C @ B @ A @ skip )
= H ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_com_Osimps_I64_J) ).
thf(159,plain,
! [TA: $tType,A: fun @ vname @ ( fun @ pname @ ( fun @ ( fun @ state @ nat ) @ TA ) ),B: fun @ pname @ TA,C: fun @ ( fun @ state @ bool ) @ ( fun @ com @ TA ),D: fun @ ( fun @ state @ bool ) @ ( fun @ com @ ( fun @ com @ TA ) ),E: fun @ com @ ( fun @ com @ TA ),F: fun @ loc @ ( fun @ ( fun @ state @ nat ) @ ( fun @ com @ TA ) ),G: fun @ vname @ ( fun @ ( fun @ state @ nat ) @ TA ),H: TA] :
( ( com_case @ TA @ H @ G @ F @ E @ D @ C @ B @ A @ skip )
= H ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(43,axiom,
! [TA: $tType,A: TA] :
~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_empty__iff) ).
thf(274,plain,
! [TA: $tType,A: TA] :
~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(74,axiom,
! [TA: $tType,A: fun @ ( hoare_28830079triple @ TA ) @ bool,B: hoare_28830079triple @ TA,C: fun @ ( hoare_28830079triple @ TA ) @ bool] :
( ( hoare_992312373derivs @ TA @ C @ ( insert @ ( hoare_28830079triple @ TA ) @ B @ ( bot_bot @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) ) ) )
=> ( ( hoare_992312373derivs @ TA @ C @ A )
=> ( hoare_992312373derivs @ TA @ C @ ( insert @ ( hoare_28830079triple @ TA ) @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_hoare__derivs_Oinsert) ).
thf(377,plain,
! [TA: $tType,A: fun @ ( hoare_28830079triple @ TA ) @ bool,B: hoare_28830079triple @ TA,C: fun @ ( hoare_28830079triple @ TA ) @ bool] :
( ( hoare_992312373derivs @ TA @ C @ ( insert @ ( hoare_28830079triple @ TA ) @ B @ ( bot_bot @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) ) ) )
=> ( ( hoare_992312373derivs @ TA @ C @ A )
=> ( hoare_992312373derivs @ TA @ C @ ( insert @ ( hoare_28830079triple @ TA ) @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(118,axiom,
! [TA: $tType,A: fun @ TA @ ( fun @ TA @ TA ),B: fun @ TA @ bool] :
( ( finite_finite1 @ TA @ B )
=> ( ( B
!= ( bot_bot @ ( fun @ TA @ bool ) ) )
=> ? [C: TA] : ( finite_fold1Set @ TA @ A @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_finite__nonempty__imp__fold1Set) ).
thf(567,plain,
! [TA: $tType,A: fun @ TA @ ( fun @ TA @ TA ),B: fun @ TA @ bool] :
( ( finite_finite1 @ TA @ B )
=> ( ( B
!= ( bot_bot @ ( fun @ TA @ bool ) ) )
=> ? [C: TA] : ( finite_fold1Set @ TA @ A @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(103,axiom,
pp @ fTrue,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_pp_2_1_U) ).
thf(509,plain,
pp @ fTrue,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(53,axiom,
! [TA: $tType,A: TA,B: fun @ TA @ bool,C: fun @ ( fun @ TA @ bool ) @ TA,D: fun @ TA @ ( fun @ TA @ TA )] :
( ( finite_folding_one @ TA @ D @ C )
=> ( ( finite_finite1 @ TA @ B )
=> ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ B ) )
=> ( ( ( ( minus_minus @ ( fun @ TA @ bool ) @ B @ ( insert @ TA @ A @ ( bot_bot @ ( fun @ TA @ bool ) ) ) )
= ( bot_bot @ ( fun @ TA @ bool ) ) )
=> ( ( aa @ ( fun @ TA @ bool ) @ TA @ C @ B )
= A ) )
& ( ( ( minus_minus @ ( fun @ TA @ bool ) @ B @ ( insert @ TA @ A @ ( bot_bot @ ( fun @ TA @ bool ) ) ) )
!= ( bot_bot @ ( fun @ TA @ bool ) ) )
=> ( ( aa @ ( fun @ TA @ bool ) @ TA @ C @ B )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ D @ A ) @ ( aa @ ( fun @ TA @ bool ) @ TA @ C @ ( minus_minus @ ( fun @ TA @ bool ) @ B @ ( insert @ TA @ A @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_folding__one_Oremove) ).
thf(303,plain,
! [TA: $tType,A: TA,B: fun @ TA @ bool,C: fun @ ( fun @ TA @ bool ) @ TA,D: fun @ TA @ ( fun @ TA @ TA )] :
( ( finite_folding_one @ TA @ D @ C )
=> ( ( finite_finite1 @ TA @ B )
=> ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ B ) )
=> ( ( ( ( minus_minus @ ( fun @ TA @ bool ) @ B @ ( insert @ TA @ A @ ( bot_bot @ ( fun @ TA @ bool ) ) ) )
= ( bot_bot @ ( fun @ TA @ bool ) ) )
=> ( ( aa @ ( fun @ TA @ bool ) @ TA @ C @ B )
= A ) )
& ( ( ( minus_minus @ ( fun @ TA @ bool ) @ B @ ( insert @ TA @ A @ ( bot_bot @ ( fun @ TA @ bool ) ) ) )
!= ( bot_bot @ ( fun @ TA @ bool ) ) )
=> ( ( aa @ ( fun @ TA @ bool ) @ TA @ C @ B )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ D @ A ) @ ( aa @ ( fun @ TA @ bool ) @ TA @ C @ ( minus_minus @ ( fun @ TA @ bool ) @ B @ ( insert @ TA @ A @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(98,axiom,
! [TA: $tType,TB: $tType] :
( ( bot @ TA )
=> ! [A: TB] :
( ( aa @ TB @ TA @ ( bot_bot @ ( fun @ TB @ TA ) ) @ A )
= ( bot_bot @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_bot__fun__def) ).
thf(494,plain,
! [TA: $tType,TB: $tType] :
( ( bot @ TA )
=> ! [A: TB] :
( ( aa @ TB @ TA @ ( bot_bot @ ( fun @ TB @ TA ) ) @ A )
= ( bot_bot @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(128,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: TA] :
( ( bot_bot @ ( fun @ TA @ bool ) )
!= ( insert @ TA @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_empty__not__insert) ).
thf(594,plain,
! [TA: $tType,A: fun @ TA @ bool,B: TA] :
( ( bot_bot @ ( fun @ TA @ bool ) )
!= ( insert @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(95,axiom,
! [TA: $tType,A: fun @ TA @ ( fun @ state @ bool ),B: com,C: fun @ ( hoare_28830079triple @ TA ) @ bool,D: fun @ TA @ ( fun @ state @ bool )] :
( ! [E: TA,F: state] :
( ( pp @ ( aa @ state @ bool @ ( aa @ TA @ ( fun @ state @ bool ) @ D @ E ) @ F ) )
=> ? [G: fun @ TA @ ( fun @ state @ bool ),H: fun @ TA @ ( fun @ state @ bool )] :
( ( hoare_992312373derivs @ TA @ C @ ( insert @ ( hoare_28830079triple @ TA ) @ ( hoare_1841697145triple @ TA @ G @ B @ H ) @ ( bot_bot @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) ) ) )
& ! [I: state] :
( ! [J: TA] :
( ( pp @ ( aa @ state @ bool @ ( aa @ TA @ ( fun @ state @ bool ) @ G @ J ) @ F ) )
=> ( pp @ ( aa @ state @ bool @ ( aa @ TA @ ( fun @ state @ bool ) @ H @ J ) @ I ) ) )
=> ( pp @ ( aa @ state @ bool @ ( aa @ TA @ ( fun @ state @ bool ) @ A @ E ) @ I ) ) ) ) )
=> ( hoare_992312373derivs @ TA @ C @ ( insert @ ( hoare_28830079triple @ TA ) @ ( hoare_1841697145triple @ TA @ D @ B @ A ) @ ( bot_bot @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_conseq) ).
thf(483,plain,
! [TA: $tType,A: fun @ TA @ ( fun @ state @ bool ),B: com,C: fun @ ( hoare_28830079triple @ TA ) @ bool,D: fun @ TA @ ( fun @ state @ bool )] :
( ! [E: TA,F: state] :
( ( pp @ ( aa @ state @ bool @ ( aa @ TA @ ( fun @ state @ bool ) @ D @ E ) @ F ) )
=> ? [G: fun @ TA @ ( fun @ state @ bool ),H: fun @ TA @ ( fun @ state @ bool )] :
( ( hoare_992312373derivs @ TA @ C @ ( insert @ ( hoare_28830079triple @ TA ) @ ( hoare_1841697145triple @ TA @ G @ B @ H ) @ ( bot_bot @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) ) ) )
& ! [I: state] :
( ! [J: TA] :
( ( pp @ ( aa @ state @ bool @ ( aa @ TA @ ( fun @ state @ bool ) @ G @ J ) @ F ) )
=> ( pp @ ( aa @ state @ bool @ ( aa @ TA @ ( fun @ state @ bool ) @ H @ J ) @ I ) ) )
=> ( pp @ ( aa @ state @ bool @ ( aa @ TA @ ( fun @ state @ bool ) @ A @ E ) @ I ) ) ) ) )
=> ( hoare_992312373derivs @ TA @ C @ ( insert @ ( hoare_28830079triple @ TA ) @ ( hoare_1841697145triple @ TA @ D @ B @ A ) @ ( bot_bot @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(108,axiom,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: fun @ TA @ TB,C: fun @ TA @ ( fun @ TB @ TC )] :
( ( aa @ TA @ TC @ ( combs @ TA @ TB @ TC @ C @ B ) @ A )
= ( aa @ TB @ TC @ ( aa @ TA @ ( fun @ TB @ TC ) @ C @ A ) @ ( aa @ TA @ TB @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBS_1_1_U) ).
thf(520,plain,
! [TA: $tType,TB: $tType,TC: $tType,A: TA,B: fun @ TA @ TB,C: fun @ TA @ ( fun @ TB @ TC )] :
( ( aa @ TA @ TC @ ( combs @ TA @ TB @ TC @ C @ B ) @ A )
= ( aa @ TB @ TC @ ( aa @ TA @ ( fun @ TB @ TC ) @ C @ A ) @ ( aa @ TA @ TB @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(37,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) )
=> ( ( insert @ TA @ B @ ( minus_minus @ ( fun @ TA @ bool ) @ A @ ( insert @ TA @ B @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_insert__Diff) ).
thf(251,plain,
! [TA: $tType,A: fun @ TA @ bool,B: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) )
=> ( ( insert @ TA @ B @ ( minus_minus @ ( fun @ TA @ bool ) @ A @ ( insert @ TA @ B @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(88,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: TA,C: fun @ TA @ bool] :
( ( minus_minus @ ( fun @ TA @ bool ) @ C @ ( insert @ TA @ B @ A ) )
= ( minus_minus @ ( fun @ TA @ bool ) @ ( minus_minus @ ( fun @ TA @ bool ) @ C @ A ) @ ( insert @ TA @ B @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_Diff__insert) ).
thf(455,plain,
! [TA: $tType,A: fun @ TA @ bool,B: TA,C: fun @ TA @ bool] :
( ( minus_minus @ ( fun @ TA @ bool ) @ C @ ( insert @ TA @ B @ A ) )
= ( minus_minus @ ( fun @ TA @ bool ) @ ( minus_minus @ ( fun @ TA @ bool ) @ C @ A ) @ ( insert @ TA @ B @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(27,axiom,
! [A: bool,B: bool] :
( ~ ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fconj @ B ) @ A ) )
| ( pp @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_2_1_U) ).
thf(223,plain,
! [A: bool,B: bool] :
( ~ ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fconj @ B ) @ A ) )
| ( pp @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(86,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: TA,C: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( insert @ TA @ B @ A ) ) )
<=> ( ( C = B )
| ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_insert__iff) ).
thf(438,plain,
! [TA: $tType,A: fun @ TA @ bool,B: TA,C: TA] :
( ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( insert @ TA @ B @ A ) ) )
=> ( ( C = B )
| ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ A ) ) ) )
& ( ( ( C = B )
| ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ A ) ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( insert @ TA @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(97,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) )
=> ? [C: fun @ TA @ bool] :
( ( A
= ( insert @ TA @ B @ C ) )
& ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_mk__disjoint__insert) ).
thf(490,plain,
! [TA: $tType,A: fun @ TA @ bool,B: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) )
=> ? [C: fun @ TA @ bool] :
( ( A
= ( insert @ TA @ B @ C ) )
& ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(126,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( minus_minus @ ( fun @ TA @ bool ) @ ( minus_minus @ ( fun @ TA @ bool ) @ B @ A ) @ A )
= ( minus_minus @ ( fun @ TA @ bool ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_Diff__idemp) ).
thf(589,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( minus_minus @ ( fun @ TA @ bool ) @ ( minus_minus @ ( fun @ TA @ bool ) @ B @ A ) @ A )
= ( minus_minus @ ( fun @ TA @ bool ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(9,axiom,
! [A: com,B: com] :
( skip
!= ( semi @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_com_Osimps_I12_J) ).
thf(162,plain,
! [A: com,B: com] :
( skip
!= ( semi @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(73,axiom,
! [TA: $tType,TB: $tType] :
( ( cl_Groups_Ominus @ TB )
=> ! [A: TA,B: fun @ TA @ TB,C: fun @ TA @ TB] :
( ( aa @ TA @ TB @ ( minus_minus @ ( fun @ TA @ TB ) @ C @ B ) @ A )
= ( minus_minus @ TB @ ( aa @ TA @ TB @ C @ A ) @ ( aa @ TA @ TB @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_minus__apply) ).
thf(374,plain,
! [TA: $tType,TB: $tType] :
( ( cl_Groups_Ominus @ TB )
=> ! [A: TA,B: fun @ TA @ TB,C: fun @ TA @ TB] :
( ( aa @ TA @ TB @ ( minus_minus @ ( fun @ TA @ TB ) @ C @ B ) @ A )
= ( minus_minus @ TB @ ( aa @ TA @ TB @ C @ A ) @ ( aa @ TA @ TB @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(89,axiom,
! [A: bool,B: bool] :
( ( pp @ B )
| ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fimplies @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fimplies_1_1_U) ).
thf(458,plain,
! [A: bool,B: bool] :
( ( pp @ B )
| ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fimplies @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(18,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TA,C: fun @ TA @ TB,D: fun @ TB @ ( fun @ TB @ bool )] :
( ( inv_imagep @ TB @ TA @ D @ C @ B @ A )
<=> ( pp @ ( aa @ TB @ bool @ ( aa @ TB @ ( fun @ TB @ bool ) @ D @ ( aa @ TA @ TB @ C @ B ) ) @ ( aa @ TA @ TB @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_in__inv__imagep) ).
thf(194,plain,
! [TA: $tType,TB: $tType,A: TA,B: TA,C: fun @ TA @ TB,D: fun @ TB @ ( fun @ TB @ bool )] :
( ( ( inv_imagep @ TB @ TA @ D @ C @ B @ A )
=> ( pp @ ( aa @ TB @ bool @ ( aa @ TB @ ( fun @ TB @ bool ) @ D @ ( aa @ TA @ TB @ C @ B ) ) @ ( aa @ TA @ TB @ C @ A ) ) ) )
& ( ( pp @ ( aa @ TB @ bool @ ( aa @ TB @ ( fun @ TB @ bool ) @ D @ ( aa @ TA @ TB @ C @ B ) ) @ ( aa @ TA @ TB @ C @ A ) ) )
=> ( inv_imagep @ TB @ TA @ D @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(24,axiom,
cl_Groups_Ominus @ bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Groups_Ominus) ).
thf(209,plain,
cl_Groups_Ominus @ bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(96,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: TA] :
( ( insert @ TA @ B @ A )
= ( collect @ TA @ ( combs @ TA @ bool @ bool @ ( combb @ bool @ ( fun @ bool @ bool ) @ TA @ fdisj @ ( combc @ TA @ TA @ bool @ ( fequal @ TA ) @ B ) ) @ ( combc @ TA @ ( fun @ TA @ bool ) @ bool @ ( member @ TA ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_insert__compr) ).
thf(487,plain,
! [TA: $tType,A: fun @ TA @ bool,B: TA] :
( ( insert @ TA @ B @ A )
= ( collect @ TA @ ( combs @ TA @ bool @ bool @ ( combb @ bool @ ( fun @ bool @ bool ) @ TA @ fdisj @ ( combc @ TA @ TA @ bool @ ( fequal @ TA ) @ B ) ) @ ( combc @ TA @ ( fun @ TA @ bool ) @ bool @ ( member @ TA ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(110,axiom,
! [TA: $tType,A: fun @ TA @ bool] :
( ( minus_minus @ ( fun @ TA @ bool ) @ A @ A )
= ( bot_bot @ ( fun @ TA @ bool ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_Diff__cancel) ).
thf(525,plain,
! [TA: $tType,A: fun @ TA @ bool] :
( ( minus_minus @ ( fun @ TA @ bool ) @ A @ A )
= ( bot_bot @ ( fun @ TA @ bool ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(123,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( minus_minus @ ( fun @ TA @ bool ) @ B @ A ) ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_DiffD1) ).
thf(580,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( minus_minus @ ( fun @ TA @ bool ) @ B @ A ) ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(82,axiom,
! [TA: $tType,A: hoare_28830079triple @ TA] :
~ ! [B: fun @ TA @ ( fun @ state @ bool ),C: com,D: fun @ TA @ ( fun @ state @ bool )] :
( A
!= ( hoare_1841697145triple @ TA @ B @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_triple_Oexhaust) ).
thf(414,plain,
! [TA: $tType,A: hoare_28830079triple @ TA] :
~ ! [B: fun @ TA @ ( fun @ state @ bool ),C: com,D: fun @ TA @ ( fun @ state @ bool )] :
( A
!= ( hoare_1841697145triple @ TA @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(81,axiom,
! [TA: $tType,A: TA,B: fun @ TA @ bool,C: TA,D: fun @ TA @ ( fun @ TA @ TA )] :
( ( finite_fold1Set @ TA @ D @ ( insert @ TA @ C @ B ) @ A )
=> ~ ! [E: TA,F: fun @ TA @ bool] :
( ( ( insert @ TA @ C @ B )
= ( insert @ TA @ E @ F ) )
=> ( ( finite_fold_graph @ TA @ TA @ D @ E @ F @ A )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ E ) @ F ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_insert__fold1SetE) ).
thf(409,plain,
! [TA: $tType,A: TA,B: fun @ TA @ bool,C: TA,D: fun @ TA @ ( fun @ TA @ TA )] :
( ( finite_fold1Set @ TA @ D @ ( insert @ TA @ C @ B ) @ A )
=> ~ ! [E: TA,F: fun @ TA @ bool] :
( ( ( insert @ TA @ C @ B )
= ( insert @ TA @ E @ F ) )
=> ( ( finite_fold_graph @ TA @ TA @ D @ E @ F @ A )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ E ) @ F ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(20,axiom,
! [A: bool] :
( ~ ( pp @ ( aa @ bool @ bool @ fNot @ A ) )
| ~ ( pp @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fNot_1_1_U) ).
thf(199,plain,
! [A: bool] :
( ~ ( pp @ ( aa @ bool @ bool @ fNot @ A ) )
| ~ ( pp @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(13,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) )
<=> ( pp @ ( aa @ TA @ bool @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_mem__def) ).
thf(177,plain,
! [TA: $tType,A: fun @ TA @ bool,B: TA] :
( ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) )
=> ( pp @ ( aa @ TA @ bool @ A @ B ) ) )
& ( ( pp @ ( aa @ TA @ bool @ A @ B ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(93,axiom,
! [TA: $tType,A: fun @ ( fun @ TA @ bool ) @ bool,B: fun @ TA @ bool] :
( ( finite_finite1 @ TA @ B )
=> ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ A @ B ) )
=> ( ! [C: TA,D: fun @ TA @ bool] :
( ( finite_finite1 @ TA @ D )
=> ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ D ) )
=> ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ A @ D ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ A @ ( minus_minus @ ( fun @ TA @ bool ) @ D @ ( insert @ TA @ C @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ A @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_finite__empty__induct) ).
thf(470,plain,
! [TA: $tType,A: fun @ ( fun @ TA @ bool ) @ bool,B: fun @ TA @ bool] :
( ( finite_finite1 @ TA @ B )
=> ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ A @ B ) )
=> ( ! [C: TA,D: fun @ TA @ bool] :
( ( finite_finite1 @ TA @ D )
=> ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ D ) )
=> ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ A @ D ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ A @ ( minus_minus @ ( fun @ TA @ bool ) @ D @ ( insert @ TA @ C @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ) ) ) ) ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ A @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(59,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( minus_minus @ ( fun @ TA @ bool ) @ B @ A ) ) )
=> ~ ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_DiffE) ).
thf(336,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool,C: TA] :
( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ ( minus_minus @ ( fun @ TA @ bool ) @ B @ A ) ) )
=> ~ ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ B ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(130,axiom,
! [TA: $tType,TB: $tType,A: fun @ TA @ ( fun @ state @ bool ),B: com,C: fun @ TA @ ( fun @ state @ bool ),D: fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ TB ) )] :
( ( hoare_376461865e_case @ TA @ TB @ D @ ( hoare_1841697145triple @ TA @ C @ B @ A ) )
= ( aa @ ( fun @ TA @ ( fun @ state @ bool ) ) @ TB @ ( aa @ com @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ TB ) @ ( aa @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ TB ) ) @ D @ C ) @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_triple_Osimps_I2_J) ).
thf(600,plain,
! [TA: $tType,TB: $tType,A: fun @ TA @ ( fun @ state @ bool ),B: com,C: fun @ TA @ ( fun @ state @ bool ),D: fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ TB ) )] :
( ( hoare_376461865e_case @ TA @ TB @ D @ ( hoare_1841697145triple @ TA @ C @ B @ A ) )
= ( aa @ ( fun @ TA @ ( fun @ state @ bool ) ) @ TB @ ( aa @ com @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ TB ) @ ( aa @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ TB ) ) @ D @ C ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(78,axiom,
! [TA: $tType,TB: $tType,A: TA,B: fun @ TB @ bool,C: TA,D: fun @ TB @ ( fun @ TA @ TA )] :
( ( finite_fold_graph @ TB @ TA @ D @ C @ B @ A )
<=> ( ( ( B
= ( bot_bot @ ( fun @ TB @ bool ) ) )
& ( A = C ) )
| ? [E: TB,F: fun @ TB @ bool,G: TA] :
( ( B
= ( insert @ TB @ E @ F ) )
& ( A
= ( aa @ TA @ TA @ ( aa @ TB @ ( fun @ TA @ TA ) @ D @ E ) @ G ) )
& ~ ( pp @ ( aa @ ( fun @ TB @ bool ) @ bool @ ( aa @ TB @ ( fun @ ( fun @ TB @ bool ) @ bool ) @ ( member @ TB ) @ E ) @ F ) )
& ( finite_fold_graph @ TB @ TA @ D @ C @ F @ G ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_fold__graph_Osimps) ).
thf(386,plain,
! [TA: $tType,TB: $tType,A: TA,B: fun @ TB @ bool,C: TA,D: fun @ TB @ ( fun @ TA @ TA )] :
( ( ( finite_fold_graph @ TB @ TA @ D @ C @ B @ A )
=> ( ( ( B
= ( bot_bot @ ( fun @ TB @ bool ) ) )
& ( A = C ) )
| ? [E: TB,F: fun @ TB @ bool,G: TA] :
( ( B
= ( insert @ TB @ E @ F ) )
& ( A
= ( aa @ TA @ TA @ ( aa @ TB @ ( fun @ TA @ TA ) @ D @ E ) @ G ) )
& ~ ( pp @ ( aa @ ( fun @ TB @ bool ) @ bool @ ( aa @ TB @ ( fun @ ( fun @ TB @ bool ) @ bool ) @ ( member @ TB ) @ E ) @ F ) )
& ( finite_fold_graph @ TB @ TA @ D @ C @ F @ G ) ) ) )
& ( ( ( ( B
= ( bot_bot @ ( fun @ TB @ bool ) ) )
& ( A = C ) )
| ? [E: TB,F: fun @ TB @ bool,G: TA] :
( ( B
= ( insert @ TB @ E @ F ) )
& ( A
= ( aa @ TA @ TA @ ( aa @ TB @ ( fun @ TA @ TA ) @ D @ E ) @ G ) )
& ~ ( pp @ ( aa @ ( fun @ TB @ bool ) @ bool @ ( aa @ TB @ ( fun @ ( fun @ TB @ bool ) @ bool ) @ ( member @ TB ) @ E ) @ F ) )
& ( finite_fold_graph @ TB @ TA @ D @ C @ F @ G ) ) )
=> ( finite_fold_graph @ TB @ TA @ D @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(99,axiom,
! [TA: $tType,A: TA] :
( ( pp @ ( aa @ TA @ bool @ ( bot_bot @ ( fun @ TA @ bool ) ) @ A ) )
<=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_bot__empty__eq) ).
thf(497,plain,
! [TA: $tType,A: TA] :
( ( ( pp @ ( aa @ TA @ bool @ ( bot_bot @ ( fun @ TA @ bool ) ) @ A ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ) )
& ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ ( bot_bot @ ( fun @ TA @ bool ) ) ) )
=> ( pp @ ( aa @ TA @ bool @ ( bot_bot @ ( fun @ TA @ bool ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(30,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: TA,C: fun @ TA @ bool] :
( ( finite_finite1 @ TA @ ( minus_minus @ ( fun @ TA @ bool ) @ C @ ( insert @ TA @ B @ A ) ) )
<=> ( finite_finite1 @ TA @ ( minus_minus @ ( fun @ TA @ bool ) @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_finite__Diff__insert) ).
thf(231,plain,
! [TA: $tType,A: fun @ TA @ bool,B: TA,C: fun @ TA @ bool] :
( ( ( finite_finite1 @ TA @ ( minus_minus @ ( fun @ TA @ bool ) @ C @ ( insert @ TA @ B @ A ) ) )
=> ( finite_finite1 @ TA @ ( minus_minus @ ( fun @ TA @ bool ) @ C @ A ) ) )
& ( ( finite_finite1 @ TA @ ( minus_minus @ ( fun @ TA @ bool ) @ C @ A ) )
=> ( finite_finite1 @ TA @ ( minus_minus @ ( fun @ TA @ bool ) @ C @ ( insert @ TA @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(69,axiom,
! [TA: $tType,A: TA,B: fun @ TA @ bool] :
( ( finite_finite1 @ TA @ B )
=> ( finite_finite1 @ TA @ ( insert @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_finite_OinsertI) ).
thf(363,plain,
! [TA: $tType,A: TA,B: fun @ TA @ bool] :
( ( finite_finite1 @ TA @ B )
=> ( finite_finite1 @ TA @ ( insert @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(115,axiom,
! [TA: $tType,A: fun @ ( hoare_28830079triple @ TA ) @ bool,B: fun @ ( hoare_28830079triple @ TA ) @ bool,C: fun @ ( hoare_28830079triple @ TA ) @ bool] :
( ( hoare_992312373derivs @ TA @ C @ B )
=> ( ( hoare_992312373derivs @ TA @ A @ C )
=> ( hoare_992312373derivs @ TA @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_cut) ).
thf(539,plain,
! [TA: $tType,A: fun @ ( hoare_28830079triple @ TA ) @ bool,B: fun @ ( hoare_28830079triple @ TA ) @ bool,C: fun @ ( hoare_28830079triple @ TA ) @ bool] :
( ( hoare_992312373derivs @ TA @ C @ B )
=> ( ( hoare_992312373derivs @ TA @ A @ C )
=> ( hoare_992312373derivs @ TA @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(22,axiom,
! [TA: $tType,A: fun @ TA @ bool] :
( ( minus_minus @ ( fun @ TA @ bool ) @ A @ ( bot_bot @ ( fun @ TA @ bool ) ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_Diff__empty) ).
thf(203,plain,
! [TA: $tType,A: fun @ TA @ bool] :
( ( minus_minus @ ( fun @ TA @ bool ) @ A @ ( bot_bot @ ( fun @ TA @ bool ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(71,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: TA] :
( ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) )
=> ( ( minus_minus @ ( fun @ TA @ bool ) @ ( insert @ TA @ B @ A ) @ ( insert @ TA @ B @ ( bot_bot @ ( fun @ TA @ bool ) ) ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_Diff__insert__absorb) ).
thf(368,plain,
! [TA: $tType,A: fun @ TA @ bool,B: TA] :
( ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ B ) @ A ) )
=> ( ( minus_minus @ ( fun @ TA @ bool ) @ ( insert @ TA @ B @ A ) @ ( insert @ TA @ B @ ( bot_bot @ ( fun @ TA @ bool ) ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(15,axiom,
! [A: bool,B: bool] :
( ~ ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fconj @ B ) @ A ) )
| ( pp @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_3_1_U) ).
thf(186,plain,
! [A: bool,B: bool] :
( ~ ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fconj @ B ) @ A ) )
| ( pp @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(4,axiom,
! [A: bool] :
( ( A = fTrue )
| ( A = fFalse ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fFalse_1_1_T) ).
thf(139,plain,
! [A: bool] :
( ( A = fTrue )
| ( A = fFalse ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(49,axiom,
finite_finite @ bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Finite__Set_Ofinite) ).
thf(290,plain,
finite_finite @ bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(35,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( finite_finite1 @ TA @ B )
=> ( ( finite_finite1 @ TA @ ( minus_minus @ ( fun @ TA @ bool ) @ A @ B ) )
<=> ( finite_finite1 @ TA @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_finite__Diff2) ).
thf(246,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( finite_finite1 @ TA @ B )
=> ( ( ( finite_finite1 @ TA @ ( minus_minus @ ( fun @ TA @ bool ) @ A @ B ) )
=> ( finite_finite1 @ TA @ A ) )
& ( ( finite_finite1 @ TA @ A )
=> ( finite_finite1 @ TA @ ( minus_minus @ ( fun @ TA @ bool ) @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(104,axiom,
! [TA: $tType,A: TA,B: fun @ TA @ ( fun @ TA @ TA )] :
~ ( finite_fold1Set @ TA @ B @ ( bot_bot @ ( fun @ TA @ bool ) ) @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_empty__fold1SetE) ).
thf(510,plain,
! [TA: $tType,A: TA,B: fun @ TA @ ( fun @ TA @ TA )] :
~ ( finite_fold1Set @ TA @ B @ ( bot_bot @ ( fun @ TA @ bool ) ) @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(42,axiom,
! [A: bool,B: bool] :
( ~ ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fimplies @ B ) @ A ) )
| ~ ( pp @ B )
| ( pp @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fimplies_3_1_U) ).
thf(272,plain,
! [A: bool,B: bool] :
( ~ ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fimplies @ B ) @ A ) )
| ~ ( pp @ B )
| ( pp @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(63,axiom,
bot @ bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Obot) ).
thf(346,plain,
bot @ bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(114,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( minus_minus @ ( fun @ TA @ bool ) @ B @ A )
= ( collect @ TA @ ( combs @ TA @ bool @ bool @ ( combb @ bool @ ( fun @ bool @ bool ) @ TA @ fconj @ ( combc @ TA @ ( fun @ TA @ bool ) @ bool @ ( member @ TA ) @ B ) ) @ ( combb @ bool @ bool @ TA @ fNot @ ( combc @ TA @ ( fun @ TA @ bool ) @ bool @ ( member @ TA ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_set__diff__eq) ).
thf(536,plain,
! [TA: $tType,A: fun @ TA @ bool,B: fun @ TA @ bool] :
( ( minus_minus @ ( fun @ TA @ bool ) @ B @ A )
= ( collect @ TA @ ( combs @ TA @ bool @ bool @ ( combb @ bool @ ( fun @ bool @ bool ) @ TA @ fconj @ ( combc @ TA @ ( fun @ TA @ bool ) @ bool @ ( member @ TA ) @ B ) ) @ ( combb @ bool @ bool @ TA @ fNot @ ( combc @ TA @ ( fun @ TA @ bool ) @ bool @ ( member @ TA ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(52,axiom,
! [TA: $tType,TB: $tType,A: fun @ TA @ ( fun @ state @ bool ),B: com,C: fun @ TA @ ( fun @ state @ bool ),D: fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ TB ) )] :
( ( hoare_678420151le_rec @ TA @ TB @ D @ ( hoare_1841697145triple @ TA @ C @ B @ A ) )
= ( aa @ ( fun @ TA @ ( fun @ state @ bool ) ) @ TB @ ( aa @ com @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ TB ) @ ( aa @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ TB ) ) @ D @ C ) @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_triple_Orecs) ).
thf(300,plain,
! [TA: $tType,TB: $tType,A: fun @ TA @ ( fun @ state @ bool ),B: com,C: fun @ TA @ ( fun @ state @ bool ),D: fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ TB ) )] :
( ( hoare_678420151le_rec @ TA @ TB @ D @ ( hoare_1841697145triple @ TA @ C @ B @ A ) )
= ( aa @ ( fun @ TA @ ( fun @ state @ bool ) ) @ TB @ ( aa @ com @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ TB ) @ ( aa @ ( fun @ TA @ ( fun @ state @ bool ) ) @ ( fun @ com @ ( fun @ ( fun @ TA @ ( fun @ state @ bool ) ) @ TB ) ) @ D @ C ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(56,axiom,
! [TA: $tType,A: fun @ TA @ bool] :
( ( ( bot_bot @ ( fun @ TA @ bool ) )
= ( collect @ TA @ A ) )
<=> ! [B: TA] :
~ ( pp @ ( aa @ TA @ bool @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_empty__Collect__eq) ).
thf(315,plain,
! [TA: $tType,A: fun @ TA @ bool] :
( ( ( ( bot_bot @ ( fun @ TA @ bool ) )
= ( collect @ TA @ A ) )
=> ! [B: TA] :
~ ( pp @ ( aa @ TA @ bool @ A @ B ) ) )
& ( ! [B: TA] :
~ ( pp @ ( aa @ TA @ bool @ A @ B ) )
=> ( ( bot_bot @ ( fun @ TA @ bool ) )
= ( collect @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(11,axiom,
! [TA: $tType,A: fun @ ( fun @ TA @ bool ) @ bool,B: fun @ TA @ bool] :
( ( finite_finite1 @ TA @ B )
=> ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ A @ ( bot_bot @ ( fun @ TA @ bool ) ) ) )
=> ( ! [C: TA,D: fun @ TA @ bool] :
( ( finite_finite1 @ TA @ D )
=> ( ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ D ) )
=> ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ A @ D ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ A @ ( insert @ TA @ C @ D ) ) ) ) ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_99_finite__induct) ).
thf(168,plain,
! [TA: $tType,A: fun @ ( fun @ TA @ bool ) @ bool,B: fun @ TA @ bool] :
( ( finite_finite1 @ TA @ B )
=> ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ A @ ( bot_bot @ ( fun @ TA @ bool ) ) ) )
=> ( ! [C: TA,D: fun @ TA @ bool] :
( ( finite_finite1 @ TA @ D )
=> ( ~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ C ) @ D ) )
=> ( ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ A @ D ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ A @ ( insert @ TA @ C @ D ) ) ) ) ) )
=> ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(6,axiom,
! [A: com,B: com,C: com,D: com] :
( ( ( semi @ D @ C )
= ( semi @ B @ A ) )
<=> ( ( D = B )
& ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_com_Osimps_I3_J) ).
thf(146,plain,
! [A: com,B: com,C: com,D: com] :
( ( ( ( semi @ D @ C )
= ( semi @ B @ A ) )
=> ( ( D = B )
& ( C = A ) ) )
& ( ( ( D = B )
& ( C = A ) )
=> ( ( semi @ D @ C )
= ( semi @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(131,axiom,
! [TA: $tType,A: fun @ TA @ bool] :
( ( ( collect @ TA @ A )
= ( bot_bot @ ( fun @ TA @ bool ) ) )
<=> ! [B: TA] :
~ ( pp @ ( aa @ TA @ bool @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_Collect__empty__eq) ).
thf(603,plain,
! [TA: $tType,A: fun @ TA @ bool] :
( ( ( ( collect @ TA @ A )
= ( bot_bot @ ( fun @ TA @ bool ) ) )
=> ! [B: TA] :
~ ( pp @ ( aa @ TA @ bool @ A @ B ) ) )
& ( ! [B: TA] :
~ ( pp @ ( aa @ TA @ bool @ A @ B ) )
=> ( ( collect @ TA @ A )
= ( bot_bot @ ( fun @ TA @ bool ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(117,axiom,
! [TA: $tType,TB: $tType,A: fun @ TA @ TB,B: fun @ TA @ TB] :
( ! [C: TA] :
( ( aa @ TA @ TB @ B @ C )
= ( aa @ TA @ TB @ A @ C ) )
=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_ext) ).
thf(564,plain,
! [TA: $tType,TB: $tType,A: fun @ TA @ TB,B: fun @ TA @ TB] :
( ! [C: TA] :
( ( aa @ TA @ TB @ B @ C )
= ( aa @ TA @ TB @ A @ C ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(25,axiom,
! [TA: $tType,A: fun @ TA @ ( fun @ state @ bool ),B: com,C: fun @ TA @ ( fun @ state @ bool ),D: fun @ TA @ ( fun @ state @ bool ),E: com,F: fun @ TA @ ( fun @ state @ bool )] :
( ( ( hoare_1841697145triple @ TA @ F @ E @ D )
= ( hoare_1841697145triple @ TA @ C @ B @ A ) )
<=> ( ( F = C )
& ( E = B )
& ( D = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_triple_Oinject) ).
thf(210,plain,
! [TA: $tType,A: fun @ TA @ ( fun @ state @ bool ),B: com,C: fun @ TA @ ( fun @ state @ bool ),D: fun @ TA @ ( fun @ state @ bool ),E: com,F: fun @ TA @ ( fun @ state @ bool )] :
( ( ( ( hoare_1841697145triple @ TA @ F @ E @ D )
= ( hoare_1841697145triple @ TA @ C @ B @ A ) )
=> ( ( F = C )
& ( E = B )
& ( D = A ) ) )
& ( ( ( F = C )
& ( E = B )
& ( D = A ) )
=> ( ( hoare_1841697145triple @ TA @ F @ E @ D )
= ( hoare_1841697145triple @ TA @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(3,axiom,
! [TA: $tType,A: fun @ TA @ bool] :
( ( collect @ TA @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_Collect__def) ).
thf(136,plain,
! [TA: $tType,A: fun @ TA @ bool] :
( ( collect @ TA @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(61,axiom,
! [TA: $tType,A: com,B: com,C: fun @ vname @ ( fun @ pname @ ( fun @ ( fun @ state @ nat ) @ TA ) ),D: fun @ pname @ TA,E: fun @ ( fun @ state @ bool ) @ ( fun @ com @ TA ),F: fun @ ( fun @ state @ bool ) @ ( fun @ com @ ( fun @ com @ TA ) ),G: fun @ com @ ( fun @ com @ TA ),H: fun @ loc @ ( fun @ ( fun @ state @ nat ) @ ( fun @ com @ TA ) ),I: fun @ vname @ ( fun @ ( fun @ state @ nat ) @ TA ),J: TA] :
( ( com_case @ TA @ J @ I @ H @ G @ F @ E @ D @ C @ ( semi @ B @ A ) )
= ( aa @ com @ TA @ ( aa @ com @ ( fun @ com @ TA ) @ G @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_com_Osimps_I67_J) ).
thf(341,plain,
! [TA: $tType,A: com,B: com,C: fun @ vname @ ( fun @ pname @ ( fun @ ( fun @ state @ nat ) @ TA ) ),D: fun @ pname @ TA,E: fun @ ( fun @ state @ bool ) @ ( fun @ com @ TA ),F: fun @ ( fun @ state @ bool ) @ ( fun @ com @ ( fun @ com @ TA ) ),G: fun @ com @ ( fun @ com @ TA ),H: fun @ loc @ ( fun @ ( fun @ state @ nat ) @ ( fun @ com @ TA ) ),I: fun @ vname @ ( fun @ ( fun @ state @ nat ) @ TA ),J: TA] :
( ( com_case @ TA @ J @ I @ H @ G @ F @ E @ D @ C @ ( semi @ B @ A ) )
= ( aa @ com @ TA @ ( aa @ com @ ( fun @ com @ TA ) @ G @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(102,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: TA] :
( ( insert @ TA @ B @ ( insert @ TA @ B @ A ) )
= ( insert @ TA @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_insert__absorb2) ).
thf(506,plain,
! [TA: $tType,A: fun @ TA @ bool,B: TA] :
( ( insert @ TA @ B @ ( insert @ TA @ B @ A ) )
= ( insert @ TA @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(67,axiom,
! [A: bool,B: bool] :
( ~ ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fdisj @ B ) @ A ) )
| ( pp @ B )
| ( pp @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fdisj_3_1_U) ).
thf(358,plain,
! [A: bool,B: bool] :
( ~ ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fdisj @ B ) @ A ) )
| ( pp @ B )
| ( pp @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(46,axiom,
! [TA: $tType,TB: $tType] :
( ( cl_Groups_Ominus @ TA )
=> ( cl_Groups_Ominus @ ( fun @ TB @ TA ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Groups_Ominus) ).
thf(283,plain,
! [TA: $tType,TB: $tType] :
( ( cl_Groups_Ominus @ TA )
=> ( cl_Groups_Ominus @ ( fun @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(121,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TA,C: fun @ TB @ ( fun @ TA @ TA ),D: fun @ TB @ bool,E: TB] :
( ~ ( pp @ ( aa @ ( fun @ TB @ bool ) @ bool @ ( aa @ TB @ ( fun @ ( fun @ TB @ bool ) @ bool ) @ ( member @ TB ) @ E ) @ D ) )
=> ( ( finite_fold_graph @ TB @ TA @ C @ B @ D @ A )
=> ( finite_fold_graph @ TB @ TA @ C @ B @ ( insert @ TB @ E @ D ) @ ( aa @ TA @ TA @ ( aa @ TB @ ( fun @ TA @ TA ) @ C @ E ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_fold__graph_OinsertI) ).
thf(575,plain,
! [TA: $tType,TB: $tType,A: TA,B: TA,C: fun @ TB @ ( fun @ TA @ TA ),D: fun @ TB @ bool,E: TB] :
( ~ ( pp @ ( aa @ ( fun @ TB @ bool ) @ bool @ ( aa @ TB @ ( fun @ ( fun @ TB @ bool ) @ bool ) @ ( member @ TB ) @ E ) @ D ) )
=> ( ( finite_fold_graph @ TB @ TA @ C @ B @ D @ A )
=> ( finite_fold_graph @ TB @ TA @ C @ B @ ( insert @ TB @ E @ D ) @ ( aa @ TA @ TA @ ( aa @ TB @ ( fun @ TA @ TA ) @ C @ E ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(111,axiom,
~ ( pp @ fFalse ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fFalse_1_1_U) ).
thf(528,plain,
~ ( pp @ fFalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(38,axiom,
! [A: bool,B: bool] :
( ~ ( pp @ B )
| ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fdisj @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fdisj_2_1_U) ).
thf(254,plain,
! [A: bool,B: bool] :
( ~ ( pp @ B )
| ( pp @ ( aa @ bool @ bool @ ( aa @ bool @ ( fun @ bool @ bool ) @ fdisj @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(127,axiom,
! [TA: $tType,A: TA] :
~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_emptyE) ).
thf(592,plain,
! [TA: $tType,A: TA] :
~ ( pp @ ( aa @ ( fun @ TA @ bool ) @ bool @ ( aa @ TA @ ( fun @ ( fun @ TA @ bool ) @ bool ) @ ( member @ TA ) @ A ) @ ( bot_bot @ ( fun @ TA @ bool ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(608,plain,
$false,
inference(cvc4,[status(thm)],[365,347,249,518,468,234,276,308,379,597,523,582,384,533,142,500,417,288,320,570,587,344,460,157,189,325,228,475,353,132,243,312,206,512,201,381,220,260,407,197,285,403,420,256,225,339,515,173,371,503,237,244,266,360,541,530,298,166,279,573,180,423,191,577,291,445,466,350,159,274,377,567,509,303,494,594,483,520,251,455,223,438,490,589,162,374,458,194,209,487,525,580,414,409,199,177,470,336,600,386,497,231,363,539,203,368,186,139,290,246,510,272,346,536,300,315,168,146,603,564,210,136,341,506,358,283,575,528,254,592]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SWW508_5 : TPTP v8.1.2. Released v6.0.0.
% 0.07/0.16 % Command : run_Leo-III %s %d
% 0.17/0.38 % Computer : n011.cluster.edu
% 0.17/0.38 % Model : x86_64 x86_64
% 0.17/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.38 % Memory : 8042.1875MB
% 0.17/0.38 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.38 % CPULimit : 300
% 0.17/0.38 % WCLimit : 300
% 0.17/0.38 % DateTime : Thu May 18 22:27:19 EDT 2023
% 0.17/0.38 % CPUTime :
% 0.95/0.88 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.57/1.12 % [INFO] Parsing done (236ms).
% 1.57/1.14 % [INFO] Running in sequential loop mode.
% 2.31/1.36 % [INFO] eprover registered as external prover.
% 2.31/1.37 % [INFO] cvc4 registered as external prover.
% 2.31/1.37 % [INFO] Scanning for conjecture ...
% 2.76/1.51 % [INFO] Found a conjecture and 129 axioms. Running axiom selection ...
% 2.86/1.63 % [INFO] Axiom selection finished. Selected 129 axioms (removed 0 axioms).
% 3.89/1.81 % [INFO] Problem is typed first-order (TPTP TFF).
% 4.03/1.82 % [INFO] Type checking passed.
% 4.03/1.83 % [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 ...
% 4.66/2.02 % [INFO] [Domain constraints] Detected constraint on bool
% 4.66/2.02 % [INFO] [Domain constraints] dom(bool) ⊆ {fTrue,fFalse}
% 43.00/16.66 % External prover 'cvc4' found a proof!
% 43.00/16.66 % [INFO] Killing All external provers ...
% 43.00/16.66 % Time passed: 16120ms (effective reasoning time: 15518ms)
% 43.00/16.66 % 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)>
% 43.00/16.66 % Axioms used in derivation (129): help_fimplies_2_1_U, fact_48_fold1Set__sing, arity_HOL_Obool___Finite__Set_Ofinite, fact_86_finite_OemptyI, fact_32_insert__not__empty, fact_7_insertCI, help_COMBS_1_1_U, fact_4_insert__absorb2, fact_92_finite, fact_58_DiffI, fact_70_empty__fold__graphE, fact_88_finite__insert, help_fconj_3_1_U, fact_80_fold1Set_Osimps, arity_fun___Orderings_Obot, fact_12_emptyE, fact_66_DiffD2, fact_30_doubleton__eq__iff, fact_23_insert__code, fact_64_insert__Diff__if, fact_3_hoare__derivs_Oinsert, fact_35_bot__fun__def, fact_20_insertI2, arity_HOL_Obool___Groups_Ominus, fact_98_finite_Osimps, fact_68_set__diff__eq, fact_27_insertI1, fact_61_empty__Diff, fact_21_insert__eq__iff, fact_73_Diff__insert__absorb, help_fNot_2_1_U, fact_53_fold1Set_Ointros, fact_11_Collect__empty__eq, fact_5_insert__iff, fact_41_com_Osimps_I3_J, fact_16_equals0D, fact_1_empty, fact_29_singletonE, fact_6_insertE, fact_14_triple_Osimps_I2_J, help_fNot_1_1_U, fact_71_fold__graph_OinsertI, help_fFalse_1_1_T, fact_13_triple_Orecs, fact_2_cut, fact_38_triple_Oexhaust, fact_59_Diff__idemp, fact_0_triple_Oinject, help_COMBB_1_1_U, fact_19_insert__absorb, help_fdisj_1_1_U, fact_15_empty__not__insert, fact_62_Diff__cancel, fact_25_insert__Collect, fact_95_folding__one_Oclosed, fact_55_in__inv__imagep, help_fconj_2_1_U, fact_40_mk__disjoint__insert, fact_10_empty__iff, fact_44_equals0I, fact_49_com_Osimps_I64_J, fact_65_insert__Diff1, fact_22_insert__ident, fact_26_insert__compr, fact_81_fun__diff__def, fact_8_all__not__in__conv, help_fequal_1_1_T, fact_60_Diff__iff, fact_93_folding__one_Oinsert, fact_18_empty__def, fact_67_DiffD1, fact_79_insert__fold1SetE, fact_24_insert__commute, arity_fun___Finite__Set_Ofinite, fact_76_mem__def, fact_52_com_Osimps_I67_J, fact_31_singleton__iff, help_fdisj_2_1_U, help_COMBK_1_1_U, fact_46_nonempty__iff, fact_85_finite__code, fact_34_bot__apply, fact_33_the__elem__eq, fact_83_fold__graph_Osimps, fact_47_bot__empty__eq, help_COMBC_1_1_U, arity_HOL_Obool___Orderings_Obot, conj_1, help_fequal_2_1_T, help_fconj_1_1_U, help_fdisj_3_1_U, fact_84_folding__one_Oremove, fact_78_Diff__insert, fact_89_finite__Diff, fact_99_finite__induct, help_fFalse_1_1_U, fact_50_fold1Set__nonempty, fact_9_empty__Collect__eq, fact_63_Diff__empty, fact_77_Collect__def, fact_45_conseq, fact_51_empty__fold1SetE, help_pp_1_1_U, fact_42_com_Osimps_I13_J, fact_36_hoare__derivs_OSkip, fact_97_finite__nonempty__imp__fold1Set, fact_54_folding__one_Osingleton, fact_91_finite__Diff2, help_fimplies_1_1_U, fact_96_finite__empty__induct, fact_43_com_Osimps_I12_J, fact_57_DiffE, fact_56_insert__Diff__single, fact_17_ex__in__conv, fact_75_ext, fact_39_Set_Oset__insert, fact_28_singleton__inject, help_fimplies_3_1_U, conj_0, fact_69_fold__graph_OemptyI, help_pp_2_1_U, fact_94_folding__one_Oinsert__remove, fact_72_insert__Diff, fact_74_Diff__insert2, arity_fun___Groups_Ominus, fact_82_minus__apply, fact_37_Comp, fact_90_finite__Diff__insert, fact_87_finite_OinsertI
% 43.00/16.66 % No. of inferences in proof: 262
% 43.00/16.66 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 16120 ms resp. 15518 ms w/o parsing
% 43.27/16.79 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 43.27/16.80 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------