TSTP Solution File: SWW504_5 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SWW504_5 : TPTP v8.1.2. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n007.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 12:24:55 EDT 2023
% Result : Theorem 14.49s 6.79s
% Output : Refutation 15.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 193
% Syntax : Number of formulae : 335 ( 130 unt; 53 typ; 0 def)
% Number of atoms : 1148 ( 235 equ; 0 cnn)
% Maximal formula atoms : 34 ( 4 avg)
% Number of connectives : 4103 ( 88 ~; 11 |; 45 &;3705 @)
% ( 28 <=>; 226 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 6 avg)
% Number of types : 9 ( 8 usr)
% Number of type conns : 34 ( 34 >; 0 *; 0 +; 0 <<)
% Number of symbols : 51 ( 49 usr; 10 con; 0-5 aty)
% Number of variables : 591 ( 0 ^; 537 !; 15 ?; 591 :)
% ( 39 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
thf(com_type,type,
com: $tType ).
thf(state_type,type,
state: $tType ).
thf(bool_type,type,
bool: $tType ).
thf(int_type,type,
int: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(char_type,type,
char: $tType ).
thf(literal_type,type,
literal: $tType ).
thf(nibble_type,type,
nibble: $tType ).
thf(enum_type,type,
enum:
!>[TA: $tType] : $o ).
thf(cl_HOL_Oequal_type,type,
cl_HOL_Oequal:
!>[TA: $tType] : $o ).
thf(one_type,type,
one:
!>[TA: $tType] : $o ).
thf(zero_type,type,
zero:
!>[TA: $tType] : $o ).
thf(sgn_if_type,type,
sgn_if:
!>[TA: $tType] : $o ).
thf(group_add_type,type,
group_add:
!>[TA: $tType] : $o ).
thf(semiring_1_type,type,
semiring_1:
!>[TA: $tType] : $o ).
thf(zero_neq_one_type,type,
zero_neq_one:
!>[TA: $tType] : $o ).
thf(semiring_char_0_type,type,
semiring_char_0:
!>[TA: $tType] : $o ).
thf(linordered_idom_type,type,
linordered_idom:
!>[TA: $tType] : $o ).
thf(linordered_semidom_type,type,
linordered_semidom:
!>[TA: $tType] : $o ).
thf(linord219039673up_add_type,type,
linord219039673up_add:
!>[TA: $tType] : $o ).
thf(one_one_type,type,
one_one:
!>[TA: $tType] : TA ).
thf(semigroup_type,type,
semigroup:
!>[TA: $tType] : ( ( fun @ TA @ ( fun @ TA @ TA ) ) > $o ) ).
thf(sgn_sgn_type,type,
sgn_sgn:
!>[TA: $tType] : ( TA > TA ) ).
thf(uminus_uminus_type,type,
uminus_uminus:
!>[TA: $tType] : ( TA > TA ) ).
thf(zero_zero_type,type,
zero_zero:
!>[TA: $tType] : TA ).
thf(bool_size_type,type,
bool_size: bool > nat ).
thf(equal_equal_type,type,
equal_equal:
!>[TA: $tType] : ( fun @ TA @ ( fun @ TA @ bool ) ) ).
thf(induct_false_type,type,
induct_false: $o ).
thf(induct_true_type,type,
induct_true: $o ).
thf(hoare_689268419triple_type,type,
hoare_689268419triple:
!>[TA: $tType] : ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ TA ) ) @ bool ) @ ( hoare_28830079triple @ TA ) ) ).
thf(hoare_334633230triple_type,type,
hoare_334633230triple:
!>[TA: $tType] : ( fun @ ( hoare_28830079triple @ TA ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ TA ) ) @ bool ) ) ).
thf(hoare_531836380gleton_type,type,
hoare_531836380gleton: $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(hoare_711253694ep_set_type,type,
hoare_711253694ep_set:
!>[TA: $tType] : ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ TA ) ) @ bool ) @ bool ) ).
thf(hoare_47506394e_size_type,type,
hoare_47506394e_size:
!>[TA: $tType] : ( ( fun @ TA @ nat ) > ( hoare_28830079triple @ TA ) > nat ) ).
thf(nat_size_type,type,
nat_size: nat > nat ).
thf(semiring_1_of_nat_type,type,
semiring_1_of_nat:
!>[TA: $tType] : ( nat > TA ) ).
thf(size_size_type,type,
size_size:
!>[TA: $tType] : ( TA > nat ) ).
thf(ord_less_type,type,
ord_less:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(collect_type,type,
collect:
!>[TA: $tType] : ( ( fun @ TA @ bool ) > ( fun @ TA @ bool ) ) ).
thf(char1_type,type,
char1: nibble > nibble > char ).
thf(char_case_type,type,
char_case:
!>[TA: $tType] : ( ( fun @ nibble @ ( fun @ nibble @ TA ) ) > char > TA ) ).
thf(char_rec_type,type,
char_rec:
!>[TA: $tType] : ( ( fun @ nibble @ ( fun @ nibble @ TA ) ) > char > TA ) ).
thf(char_size_type,type,
char_size: char > nat ).
thf(type_definition_type,type,
type_definition:
!>[TA: $tType,TB: $tType] : ( ( fun @ TB @ TA ) > ( fun @ TA @ TB ) > ( fun @ TA @ bool ) > $o ) ).
thf(aa_type,type,
aa:
!>[TA: $tType,TB: $tType] : ( ( fun @ TB @ TA ) > TB > TA ) ).
thf(fFalse_type,type,
fFalse: bool ).
thf(fTrue_type,type,
fTrue: bool ).
thf(fequal_type,type,
fequal:
!>[TA: $tType] : ( fun @ TA @ ( fun @ TA @ bool ) ) ).
thf(member_type,type,
member:
!>[TA: $tType] : ( TA > ( fun @ TA @ bool ) > $o ) ).
thf(pp_type,type,
pp: bool > $o ).
thf(16,axiom,
! [TA: $tType,A: fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ TA ) ) @ bool ) @ bool,B: fun @ ( node @ ( sum_sum @ com @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ TA ) ) @ bool] :
( ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ TA ) ) @ bool ) @ B @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ TA ) ) @ bool ) @ ( hoare_711253694ep_set @ TA ) ) )
=> ( ! [C: hoare_28830079triple @ TA] : ( pp @ ( aa @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ TA ) ) @ bool ) @ bool @ A @ ( aa @ ( hoare_28830079triple @ TA ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ TA ) ) @ bool ) @ ( hoare_334633230triple @ TA ) @ C ) ) )
=> ( pp @ ( aa @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ TA ) ) @ bool ) @ bool @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_Rep__triple__induct) ).
thf(202,plain,
! [TA: $tType,A: fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ TA ) ) @ bool ) @ bool,B: fun @ ( node @ ( sum_sum @ com @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ TA ) ) @ bool] :
( ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ TA ) ) @ bool ) @ B @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ TA ) ) @ bool ) @ ( hoare_711253694ep_set @ TA ) ) )
=> ( ! [C: hoare_28830079triple @ TA] : ( pp @ ( aa @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ TA ) ) @ bool ) @ bool @ A @ ( aa @ ( hoare_28830079triple @ TA ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ TA ) ) @ bool ) @ ( hoare_334633230triple @ TA ) @ C ) ) )
=> ( pp @ ( aa @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ TA ) ) @ bool ) @ bool @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(108,axiom,
linord219039673up_add @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Olinordered__ab__group__add) ).
thf(525,plain,
linord219039673up_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(65,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_less__not__refl) ).
thf(365,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(32,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TA,C: fun @ TA @ bool,D: fun @ TA @ TB,E: fun @ TB @ TA] :
( ( type_definition @ TB @ TA @ E @ D @ C )
=> ( ( member @ TA @ B @ C )
=> ( ( member @ TA @ A @ C )
=> ( ( ( aa @ TA @ TB @ D @ B )
= ( aa @ TA @ TB @ D @ A ) )
<=> ( B = A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_type__definition_OAbs__inject) ).
thf(249,plain,
! [TA: $tType,TB: $tType,A: TA,B: TA,C: fun @ TA @ bool,D: fun @ TA @ TB,E: fun @ TB @ TA] :
( ( type_definition @ TB @ TA @ E @ D @ C )
=> ( ( member @ TA @ B @ C )
=> ( ( member @ TA @ A @ C )
=> ( ( ( ( aa @ TA @ TB @ D @ B )
= ( aa @ TA @ TB @ D @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( aa @ TA @ TB @ D @ B )
= ( aa @ TA @ TB @ D @ A ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(103,axiom,
enum @ char,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_String_Ochar___Enum_Oenum) ).
thf(518,plain,
enum @ char,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(92,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: nat,B: nat] :
( ( ord_less @ nat @ B @ A )
=> ( ord_less @ TA @ ( semiring_1_of_nat @ TA @ B ) @ ( semiring_1_of_nat @ TA @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_less__imp__of__nat__less) ).
thf(468,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: nat,B: nat] :
( ( ord_less @ nat @ B @ A )
=> ( ord_less @ TA @ ( semiring_1_of_nat @ TA @ B ) @ ( semiring_1_of_nat @ TA @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(27,axiom,
induct_true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_induct__trueI) ).
thf(234,plain,
induct_true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(135,axiom,
pp @ fTrue,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fTrue_1_1_U) ).
thf(555,plain,
pp @ fTrue,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(62,axiom,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
<=> ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_neq0__conv) ).
thf(352,plain,
! [A: nat] :
( ( ( A
!= ( zero_zero @ nat ) )
=> ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) )
& ( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
=> ( A
!= ( zero_zero @ nat ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(69,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ B @ A )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_less__not__refl2) ).
thf(384,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ B @ A )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(116,axiom,
zero @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ozero) ).
thf(533,plain,
zero @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(132,axiom,
! [TA: $tType] : ( cl_HOL_Oequal @ ( hoare_28830079triple @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Hoare__Mirabelle__vtrypsmcwp_Otriple___HOL_Oequal) ).
thf(550,plain,
! [TA: $tType] : ( cl_HOL_Oequal @ ( hoare_28830079triple @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(1,conjecture,
! [A: state] :
? [B: state] : B != A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
thf(2,negated_conjecture,
~ ! [A: state] :
? [B: state] : B != A,
inference(neg_conjecture,[status(cth)],[1]) ).
thf(142,plain,
~ ! [A: state] :
? [B: state] : B != A,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(58,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: TA] :
( ( ord_less @ TA @ ( sgn_sgn @ TA @ A ) @ ( zero_zero @ TA ) )
<=> ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_sgn__less) ).
thf(340,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: TA] :
( ( ( ord_less @ TA @ ( sgn_sgn @ TA @ A ) @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) )
& ( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
=> ( ord_less @ TA @ ( sgn_sgn @ TA @ A ) @ ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(121,axiom,
zero_neq_one @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ozero__neq__one) ).
thf(538,plain,
zero_neq_one @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(7,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/sandbox2/benchmark/theBenchmark.p',fact_4_triple_Orecs) ).
thf(174,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)],[7]) ).
thf(44,axiom,
( ( size_size @ bool @ fFalse )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_bool_Osize_I4_J) ).
thf(288,plain,
( ( size_size @ bool @ fFalse )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(49,axiom,
! [A: nibble,B: nibble] :
( ( char_size @ ( char1 @ B @ A ) )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_char_Osize_I1_J) ).
thf(301,plain,
! [A: nibble,B: nibble] :
( ( char_size @ ( char1 @ B @ A ) )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(125,axiom,
cl_HOL_Oequal @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___HOL_Oequal) ).
thf(542,plain,
cl_HOL_Oequal @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(88,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ ( one_one @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_zero__less__one) ).
thf(460,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ ( one_one @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(137,axiom,
~ ( pp @ fFalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fFalse_1_1_U) ).
thf(559,plain,
~ ( pp @ fFalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(76,axiom,
! [A: nat,B: fun @ nat @ bool] :
( ( pp @ ( aa @ nat @ bool @ B @ ( zero_zero @ nat ) ) )
=> ( ! [C: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ C )
=> ( ~ ( pp @ ( aa @ nat @ bool @ B @ C ) )
=> ? [D: nat] :
( ( ord_less @ nat @ D @ C )
& ~ ( pp @ ( aa @ nat @ bool @ B @ D ) ) ) ) )
=> ( pp @ ( aa @ nat @ bool @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_infinite__descent0) ).
thf(416,plain,
! [A: nat,B: fun @ nat @ bool] :
( ( pp @ ( aa @ nat @ bool @ B @ ( zero_zero @ nat ) ) )
=> ( ! [C: nat] :
( ( ord_less @ nat @ ( zero_zero @ nat ) @ C )
=> ( ~ ( pp @ ( aa @ nat @ bool @ B @ C ) )
=> ? [D: nat] :
( ( ord_less @ nat @ D @ C )
& ~ ( pp @ ( aa @ nat @ bool @ B @ D ) ) ) ) )
=> ( pp @ ( aa @ nat @ bool @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(4,axiom,
! [TA: $tType,A: hoare_28830079triple @ TA,B: hoare_28830079triple @ TA] :
( ( pp @ ( aa @ ( hoare_28830079triple @ TA ) @ bool @ ( aa @ ( hoare_28830079triple @ TA ) @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ ( equal_equal @ ( hoare_28830079triple @ TA ) ) @ B ) @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_equal__triple__def) ).
thf(152,plain,
! [TA: $tType,A: hoare_28830079triple @ TA,B: hoare_28830079triple @ TA] :
( ( ( pp @ ( aa @ ( hoare_28830079triple @ TA ) @ bool @ ( aa @ ( hoare_28830079triple @ TA ) @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ ( equal_equal @ ( hoare_28830079triple @ TA ) ) @ B ) @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( pp @ ( aa @ ( hoare_28830079triple @ TA ) @ bool @ ( aa @ ( hoare_28830079triple @ TA ) @ ( fun @ ( hoare_28830079triple @ TA ) @ bool ) @ ( equal_equal @ ( hoare_28830079triple @ TA ) ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(20,axiom,
! [TA: $tType,A: hoare_28830079triple @ TA,B: fun @ ( hoare_28830079triple @ TA ) @ bool] :
( ! [C: fun @ ( node @ ( sum_sum @ com @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ TA ) ) @ bool] :
( ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ TA ) ) @ bool ) @ C @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ TA ) ) @ bool ) @ ( hoare_711253694ep_set @ TA ) ) )
=> ( pp @ ( aa @ ( hoare_28830079triple @ TA ) @ bool @ B @ ( aa @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ TA ) ) @ bool ) @ ( hoare_28830079triple @ TA ) @ ( hoare_689268419triple @ TA ) @ C ) ) ) )
=> ( pp @ ( aa @ ( hoare_28830079triple @ TA ) @ bool @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_Abs__triple__induct) ).
thf(216,plain,
! [TA: $tType,A: hoare_28830079triple @ TA,B: fun @ ( hoare_28830079triple @ TA ) @ bool] :
( ! [C: fun @ ( node @ ( sum_sum @ com @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ TA ) ) @ bool] :
( ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ TA ) ) @ bool ) @ C @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ TA ) ) @ bool ) @ ( hoare_711253694ep_set @ TA ) ) )
=> ( pp @ ( aa @ ( hoare_28830079triple @ TA ) @ bool @ B @ ( aa @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ TA ) ) @ bool ) @ ( hoare_28830079triple @ TA ) @ ( hoare_689268419triple @ TA ) @ C ) ) ) )
=> ( pp @ ( aa @ ( hoare_28830079triple @ TA ) @ bool @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(94,axiom,
! [A: nat] :
( ( ord_less @ int @ ( zero_zero @ int ) @ ( semiring_1_of_nat @ int @ A ) )
<=> ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_zero__less__int__conv) ).
thf(475,plain,
! [A: nat] :
( ( ( ord_less @ int @ ( zero_zero @ int ) @ ( semiring_1_of_nat @ int @ A ) )
=> ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) )
& ( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
=> ( ord_less @ int @ ( zero_zero @ int ) @ ( semiring_1_of_nat @ int @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(6,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/sandbox2/benchmark/theBenchmark.p',fact_3_triple_Oinject) ).
thf(164,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)],[6]) ).
thf(53,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: TA] :
( ( sgn_sgn @ TA @ ( sgn_sgn @ TA @ A ) )
= ( sgn_sgn @ TA @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_sgn__sgn) ).
thf(321,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: TA] :
( ( sgn_sgn @ TA @ ( sgn_sgn @ TA @ A ) )
= ( sgn_sgn @ TA @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(96,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA] :
( ( ( uminus_uminus @ TA @ B )
= ( uminus_uminus @ TA @ A ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_neg__equal__iff__equal) ).
thf(485,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA,B: TA] :
( ( ( ( uminus_uminus @ TA @ B )
= ( uminus_uminus @ TA @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( uminus_uminus @ TA @ B )
= ( uminus_uminus @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(95,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: TA] :
( ( ( sgn_sgn @ TA @ A )
= ( uminus_uminus @ TA @ ( one_one @ TA ) ) )
<=> ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_sgn__1__neg) ).
thf(480,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: TA] :
( ( ( ( sgn_sgn @ TA @ A )
= ( uminus_uminus @ TA @ ( one_one @ TA ) ) )
=> ( ord_less @ TA @ A @ ( zero_zero @ TA ) ) )
& ( ( ord_less @ TA @ A @ ( zero_zero @ TA ) )
=> ( ( sgn_sgn @ TA @ A )
= ( uminus_uminus @ TA @ ( one_one @ TA ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(46,axiom,
! [A: bool] :
( ( size_size @ bool @ A )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_size__bool) ).
thf(293,plain,
! [A: bool] :
( ( size_size @ bool @ A )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(87,axiom,
! [TA: $tType] :
( ( one @ TA )
=> ! [A: TA] :
( ( ( one_one @ TA )
= A )
<=> ( A
= ( one_one @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_one__reorient) ).
thf(453,plain,
! [TA: $tType] :
( ( one @ TA )
=> ! [A: TA] :
( ( ( ( one_one @ TA )
= A )
=> ( A
= ( one_one @ TA ) ) )
& ( ( A
= ( one_one @ TA ) )
=> ( ( one_one @ TA )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(35,axiom,
! [TA: $tType,TB: $tType,A: fun @ TA @ bool,B: TA,C: fun @ TA @ bool,D: fun @ TA @ TB,E: fun @ TB @ TA] :
( ( type_definition @ TB @ TA @ E @ D @ C )
=> ( ( member @ TA @ B @ C )
=> ( ! [F: TB] : ( pp @ ( aa @ TA @ bool @ A @ ( aa @ TB @ TA @ E @ F ) ) )
=> ( pp @ ( aa @ TA @ bool @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_type__definition_ORep__induct) ).
thf(265,plain,
! [TA: $tType,TB: $tType,A: fun @ TA @ bool,B: TA,C: fun @ TA @ bool,D: fun @ TA @ TB,E: fun @ TB @ TA] :
( ( type_definition @ TB @ TA @ E @ D @ C )
=> ( ( member @ TA @ B @ C )
=> ( ! [F: TB] : ( pp @ ( aa @ TA @ bool @ A @ ( aa @ TB @ TA @ E @ F ) ) )
=> ( pp @ ( aa @ TA @ bool @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(110,axiom,
linordered_idom @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__idom) ).
thf(527,plain,
linordered_idom @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(51,axiom,
! [A: nibble,B: nibble,C: nibble,D: nibble] :
( ( ( char1 @ D @ C )
= ( char1 @ B @ A ) )
<=> ( ( D = B )
& ( C = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_char_Oinject) ).
thf(307,plain,
! [A: nibble,B: nibble,C: nibble,D: nibble] :
( ( ( ( char1 @ D @ C )
= ( char1 @ B @ A ) )
=> ( ( D = B )
& ( C = A ) ) )
& ( ( ( D = B )
& ( C = A ) )
=> ( ( char1 @ D @ C )
= ( char1 @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(26,axiom,
induct_true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_induct__true__def) ).
thf(233,plain,
induct_true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(129,axiom,
! [TA: $tType,TB: $tType] : ( cl_HOL_Oequal @ ( sum_sum @ TB @ TA ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_sum___HOL_Oequal) ).
thf(546,plain,
! [TA: $tType,TB: $tType] : ( cl_HOL_Oequal @ ( sum_sum @ TB @ TA ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(68,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_less__irrefl__nat) ).
thf(381,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(117,axiom,
one @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oone) ).
thf(534,plain,
one @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(37,axiom,
! [TA: $tType,TB: $tType,A: TB,B: fun @ TA @ bool,C: fun @ TA @ TB,D: fun @ TB @ TA] :
( ( type_definition @ TB @ TA @ D @ C @ B )
=> ~ ! [E: TA] :
( ( A
= ( aa @ TA @ TB @ C @ E ) )
=> ~ ( member @ TA @ E @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_type__definition_OAbs__cases) ).
thf(270,plain,
! [TA: $tType,TB: $tType,A: TB,B: fun @ TA @ bool,C: fun @ TA @ TB,D: fun @ TB @ TA] :
( ( type_definition @ TB @ TA @ D @ C @ B )
=> ~ ! [E: TA] :
( ( A
= ( aa @ TA @ TB @ C @ E ) )
=> ~ ( member @ TA @ E @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(112,axiom,
zero_neq_one @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ozero__neq__one) ).
thf(529,plain,
zero_neq_one @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(56,axiom,
! [TA: $tType,A: nibble,B: nibble,C: fun @ nibble @ ( fun @ nibble @ TA )] :
( ( char_case @ TA @ C @ ( char1 @ B @ A ) )
= ( aa @ nibble @ TA @ ( aa @ nibble @ ( fun @ nibble @ TA ) @ C @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_char_Osimps_I2_J) ).
thf(334,plain,
! [TA: $tType,A: nibble,B: nibble,C: fun @ nibble @ ( fun @ nibble @ TA )] :
( ( char_case @ TA @ C @ ( char1 @ B @ A ) )
= ( aa @ nibble @ TA @ ( aa @ nibble @ ( fun @ nibble @ TA ) @ C @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(61,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: TA,B: TA] :
( ( B != A )
=> ( ~ ( ord_less @ TA @ B @ A )
=> ( ord_less @ TA @ A @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_linorder__neqE__linordered__idom) ).
thf(349,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: TA,B: TA] :
( ( B != A )
=> ( ~ ( ord_less @ TA @ B @ A )
=> ( ord_less @ TA @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(138,axiom,
! [A: bool] :
( ( A = fTrue )
| ( A = fFalse ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fFalse_1_1_T) ).
thf(561,plain,
! [A: bool] :
( ( A = fTrue )
| ( A = fFalse ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(71,axiom,
! [A: fun @ nat @ ( fun @ nat @ bool ),B: nat,C: nat] :
( ( ( ord_less @ nat @ C @ B )
=> ( pp @ ( aa @ nat @ bool @ ( aa @ nat @ ( fun @ nat @ bool ) @ A @ B ) @ C ) ) )
=> ( ( ( C = B )
=> ( pp @ ( aa @ nat @ bool @ ( aa @ nat @ ( fun @ nat @ bool ) @ A @ B ) @ C ) ) )
=> ( ( ( ord_less @ nat @ B @ C )
=> ( pp @ ( aa @ nat @ bool @ ( aa @ nat @ ( fun @ nat @ bool ) @ A @ B ) @ C ) ) )
=> ( pp @ ( aa @ nat @ bool @ ( aa @ nat @ ( fun @ nat @ bool ) @ A @ B ) @ C ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_nat__less__cases) ).
thf(392,plain,
! [A: fun @ nat @ ( fun @ nat @ bool ),B: nat,C: nat] :
( ( ( ord_less @ nat @ C @ B )
=> ( pp @ ( aa @ nat @ bool @ ( aa @ nat @ ( fun @ nat @ bool ) @ A @ B ) @ C ) ) )
=> ( ( ( C = B )
=> ( pp @ ( aa @ nat @ bool @ ( aa @ nat @ ( fun @ nat @ bool ) @ A @ B ) @ C ) ) )
=> ( ( ( ord_less @ nat @ B @ C )
=> ( pp @ ( aa @ nat @ bool @ ( aa @ nat @ ( fun @ nat @ bool ) @ A @ B ) @ C ) ) )
=> ( pp @ ( aa @ nat @ bool @ ( aa @ nat @ ( fun @ nat @ bool ) @ A @ B ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(80,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( sgn_sgn @ TA @ A )
= ( one_one @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_sgn__pos) ).
thf(429,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( sgn_sgn @ TA @ A )
= ( one_one @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(14,axiom,
! [TA: $tType,A: hoare_28830079triple @ TA] :
( ( aa @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ TA ) ) @ bool ) @ ( hoare_28830079triple @ TA ) @ ( hoare_689268419triple @ TA ) @ ( aa @ ( hoare_28830079triple @ TA ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ TA ) ) @ bool ) @ ( hoare_334633230triple @ TA ) @ A ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_Rep__triple__inverse) ).
thf(197,plain,
! [TA: $tType,A: hoare_28830079triple @ TA] :
( ( aa @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ TA ) ) @ bool ) @ ( hoare_28830079triple @ TA ) @ ( hoare_689268419triple @ TA ) @ ( aa @ ( hoare_28830079triple @ TA ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ TA ) ) @ bool ) @ ( hoare_334633230triple @ TA ) @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(106,axiom,
! [TA: $tType,TB: $tType] :
( ( ( cl_HOL_Oequal @ TA )
& ( enum @ TB ) )
=> ( cl_HOL_Oequal @ ( fun @ TB @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun___HOL_Oequal) ).
thf(522,plain,
! [TA: $tType,TB: $tType] :
( ( ( cl_HOL_Oequal @ TA )
& ( enum @ TB ) )
=> ( cl_HOL_Oequal @ ( fun @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(54,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: TA] :
( ( ( sgn_sgn @ TA @ A )
= ( zero_zero @ TA ) )
<=> ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_sgn__0__0) ).
thf(324,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: TA] :
( ( ( ( sgn_sgn @ TA @ A )
= ( zero_zero @ TA ) )
=> ( A
= ( zero_zero @ TA ) ) )
& ( ( A
= ( zero_zero @ TA ) )
=> ( ( sgn_sgn @ TA @ A )
= ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(104,axiom,
enum @ bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL_Obool___Enum_Oenum) ).
thf(519,plain,
enum @ bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(12,axiom,
! [TA: $tType] :
( ( cl_HOL_Oequal @ TA )
=> ! [A: TA,B: TA] :
( ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( equal_equal @ TA ) @ B ) @ A ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_equal__eq) ).
thf(188,plain,
! [TA: $tType] :
( ( cl_HOL_Oequal @ TA )
=> ! [A: TA,B: TA] :
( ( ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( equal_equal @ TA ) @ B ) @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( equal_equal @ TA ) @ B ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(70,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ B @ A )
=> ( B != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_less__not__refl3) ).
thf(388,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ B @ A )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(77,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/sandbox2/benchmark/theBenchmark.p',fact_74_ext) ).
thf(420,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)],[77]) ).
thf(23,axiom,
~ induct_false,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_induct__false__def) ).
thf(225,plain,
~ induct_false,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(134,axiom,
pp @ fTrue,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_2_1_U) ).
thf(554,plain,
pp @ fTrue,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(120,axiom,
semiring_char_0 @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Nat_Osemiring__char__0) ).
thf(537,plain,
semiring_char_0 @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(109,axiom,
linordered_semidom @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__semidom) ).
thf(526,plain,
linordered_semidom @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(101,axiom,
enum @ nibble,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_String_Onibble___Enum_Oenum) ).
thf(515,plain,
enum @ nibble,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(99,axiom,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( A
= ( uminus_uminus @ TA @ A ) )
<=> ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_equal__neg__zero) ).
thf(503,plain,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ( A
= ( uminus_uminus @ TA @ A ) )
=> ( A
= ( zero_zero @ TA ) ) )
& ( ( A
= ( zero_zero @ TA ) )
=> ( A
= ( uminus_uminus @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(124,axiom,
one @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oone) ).
thf(541,plain,
one @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(113,axiom,
semiring_1 @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Osemiring__1) ).
thf(530,plain,
semiring_1 @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(59,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: TA] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( sgn_sgn @ TA @ A ) )
<=> ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_sgn__greater) ).
thf(343,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: TA] :
( ( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( sgn_sgn @ TA @ A ) )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) )
& ( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ ( sgn_sgn @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(29,axiom,
! [TA: $tType,TB: $tType,A: TA,B: fun @ TB @ bool,C: fun @ TB @ TA,D: fun @ TA @ TB] :
( ( type_definition @ TA @ TB @ D @ C @ B )
=> ( ( aa @ TB @ TA @ C @ ( aa @ TA @ TB @ D @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_type__definition_ORep__inverse) ).
thf(237,plain,
! [TA: $tType,TB: $tType,A: TA,B: fun @ TB @ bool,C: fun @ TB @ TA,D: fun @ TA @ TB] :
( ( type_definition @ TA @ TB @ D @ C @ B )
=> ( ( aa @ TB @ TA @ C @ ( aa @ TA @ TB @ D @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(48,axiom,
! [A: nibble,B: nibble] :
( ( size_size @ char @ ( char1 @ B @ A ) )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_char_Osize_I2_J) ).
thf(298,plain,
! [A: nibble,B: nibble] :
( ( size_size @ char @ ( char1 @ B @ A ) )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(40,axiom,
( ( bool_size @ fTrue )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_bool_Osize_I1_J) ).
thf(279,plain,
( ( bool_size @ fTrue )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(84,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: nat,B: nat] :
( ( ord_less @ TA @ ( semiring_1_of_nat @ TA @ B ) @ ( semiring_1_of_nat @ TA @ A ) )
<=> ( ord_less @ nat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_of__nat__less__iff) ).
thf(444,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: nat,B: nat] :
( ( ( ord_less @ TA @ ( semiring_1_of_nat @ TA @ B ) @ ( semiring_1_of_nat @ TA @ A ) )
=> ( ord_less @ nat @ B @ A ) )
& ( ( ord_less @ nat @ B @ A )
=> ( ord_less @ TA @ ( semiring_1_of_nat @ TA @ B ) @ ( semiring_1_of_nat @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(9,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/sandbox2/benchmark/theBenchmark.p',fact_6_triple_Oexhaust) ).
thf(180,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)],[9]) ).
thf(47,axiom,
( ( size_size @ nat @ ( zero_zero @ nat ) )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_nat_Osize_I3_J) ).
thf(296,plain,
( ( size_size @ nat @ ( zero_zero @ nat ) )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(78,axiom,
! [TA: $tType,A: fun @ TA @ bool,B: TA] :
( ( member @ TA @ B @ A )
<=> ( pp @ ( aa @ TA @ bool @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_mem__def) ).
thf(423,plain,
! [TA: $tType,A: fun @ TA @ bool,B: TA] :
( ( ( member @ TA @ B @ A )
=> ( pp @ ( aa @ TA @ bool @ A @ B ) ) )
& ( ( pp @ ( aa @ TA @ bool @ A @ B ) )
=> ( member @ TA @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(72,axiom,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
=> ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_gr0I) ).
thf(402,plain,
! [A: nat] :
( ( A
!= ( zero_zero @ nat ) )
=> ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(43,axiom,
( ( size_size @ bool @ fTrue )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_bool_Osize_I3_J) ).
thf(286,plain,
( ( size_size @ bool @ fTrue )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(128,axiom,
cl_HOL_Oequal @ char,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_String_Ochar___HOL_Oequal) ).
thf(545,plain,
cl_HOL_Oequal @ char,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(75,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: nat] :
( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( semiring_1_of_nat @ TA @ A ) )
<=> ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_of__nat__0__less__iff) ).
thf(413,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: nat] :
( ( ( ord_less @ TA @ ( zero_zero @ TA ) @ ( semiring_1_of_nat @ TA @ A ) )
=> ( ord_less @ nat @ ( zero_zero @ nat ) @ A ) )
& ( ( ord_less @ nat @ ( zero_zero @ nat ) @ A )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ ( semiring_1_of_nat @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(41,axiom,
( ( nat_size @ ( zero_zero @ nat ) )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_nat_Osize_I1_J) ).
thf(281,plain,
( ( nat_size @ ( zero_zero @ nat ) )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(17,axiom,
! [TA: $tType,A: fun @ ( node @ ( sum_sum @ com @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ TA ) ) @ bool] :
( ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ TA ) ) @ bool ) @ A @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ TA ) ) @ bool ) @ ( hoare_711253694ep_set @ TA ) ) )
=> ~ ! [B: hoare_28830079triple @ TA] :
( A
!= ( aa @ ( hoare_28830079triple @ TA ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ TA ) ) @ bool ) @ ( hoare_334633230triple @ TA ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_Rep__triple__cases) ).
thf(204,plain,
! [TA: $tType,A: fun @ ( node @ ( sum_sum @ com @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ TA ) ) @ bool] :
( ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ TA ) ) @ bool ) @ A @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ TA ) ) @ bool ) @ ( hoare_711253694ep_set @ TA ) ) )
=> ~ ! [B: hoare_28830079triple @ TA] :
( A
!= ( aa @ ( hoare_28830079triple @ TA ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ TA ) ) @ bool ) @ ( hoare_334633230triple @ TA ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(91,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: nat,B: nat] :
( ( ord_less @ TA @ ( semiring_1_of_nat @ TA @ B ) @ ( semiring_1_of_nat @ TA @ A ) )
=> ( ord_less @ nat @ B @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_of__nat__less__imp__less) ).
thf(466,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: nat,B: nat] :
( ( ord_less @ TA @ ( semiring_1_of_nat @ TA @ B ) @ ( semiring_1_of_nat @ TA @ A ) )
=> ( ord_less @ nat @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(123,axiom,
zero @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ozero) ).
thf(540,plain,
zero @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(21,axiom,
! [TA: $tType,A: hoare_28830079triple @ TA] :
~ ! [B: fun @ ( node @ ( sum_sum @ com @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ TA ) ) @ bool] :
( ( A
= ( aa @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ TA ) ) @ bool ) @ ( hoare_28830079triple @ TA ) @ ( hoare_689268419triple @ TA ) @ B ) )
=> ~ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ TA ) ) @ bool ) @ B @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ TA ) ) @ bool ) @ ( hoare_711253694ep_set @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_Abs__triple__cases) ).
thf(219,plain,
! [TA: $tType,A: hoare_28830079triple @ TA] :
~ ! [B: fun @ ( node @ ( sum_sum @ com @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ TA ) ) @ bool] :
( ( A
= ( aa @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ TA ) ) @ bool ) @ ( hoare_28830079triple @ TA ) @ ( hoare_689268419triple @ TA ) @ B ) )
=> ~ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ TA ) ) @ bool ) @ B @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ TA ) ) @ bool ) @ ( hoare_711253694ep_set @ TA ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(38,axiom,
! [A: char] :
( ( char_size @ A )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_char__size) ).
thf(274,plain,
! [A: char] :
( ( char_size @ A )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(25,axiom,
! [TA: $tType,A: fun @ TA @ ( fun @ state @ bool ),B: com,C: fun @ TA @ ( fun @ state @ bool )] :
( ( size_size @ ( hoare_28830079triple @ TA ) @ ( hoare_1841697145triple @ TA @ C @ B @ A ) )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_triple_Osize_I2_J) ).
thf(230,plain,
! [TA: $tType,A: fun @ TA @ ( fun @ state @ bool ),B: com,C: fun @ TA @ ( fun @ state @ bool )] :
( ( size_size @ ( hoare_28830079triple @ TA ) @ ( hoare_1841697145triple @ TA @ C @ B @ A ) )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(52,axiom,
! [A: nat] :
( ( size_size @ nat @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_nat__size) ).
thf(318,plain,
! [A: nat] :
( ( size_size @ nat @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(100,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= ( uminus_uminus @ TA @ A ) )
<=> ( ( zero_zero @ TA )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_neg__0__equal__iff__equal) ).
thf(509,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA] :
( ( ( ( zero_zero @ TA )
= ( uminus_uminus @ TA @ A ) )
=> ( ( zero_zero @ TA )
= A ) )
& ( ( ( zero_zero @ TA )
= A )
=> ( ( zero_zero @ TA )
= ( uminus_uminus @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(64,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_less__zeroE) ).
thf(362,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(140,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/sandbox2/benchmark/theBenchmark.p',help_fequal_2_1_T) ).
thf(567,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)],[140]) ).
thf(133,axiom,
~ ( pp @ fFalse ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_1_1_U) ).
thf(552,plain,
~ ( pp @ fFalse ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(118,axiom,
cl_HOL_Oequal @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___HOL_Oequal) ).
thf(535,plain,
cl_HOL_Oequal @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(19,axiom,
! [TA: $tType,A: fun @ ( node @ ( sum_sum @ com @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ TA ) ) @ bool] :
( ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ TA ) ) @ bool ) @ A @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ TA ) ) @ bool ) @ ( hoare_711253694ep_set @ TA ) ) )
=> ( ( aa @ ( hoare_28830079triple @ TA ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ TA ) ) @ bool ) @ ( hoare_334633230triple @ TA ) @ ( aa @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ TA ) ) @ bool ) @ ( hoare_28830079triple @ TA ) @ ( hoare_689268419triple @ TA ) @ A ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_Abs__triple__inverse) ).
thf(213,plain,
! [TA: $tType,A: fun @ ( node @ ( sum_sum @ com @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ TA ) ) @ bool] :
( ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ TA ) ) @ bool ) @ A @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ TA ) ) @ bool ) @ ( hoare_711253694ep_set @ TA ) ) )
=> ( ( aa @ ( hoare_28830079triple @ TA ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ TA ) ) @ bool ) @ ( hoare_334633230triple @ TA ) @ ( aa @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ TA ) ) @ bool ) @ ( hoare_28830079triple @ TA ) @ ( hoare_689268419triple @ TA ) @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(105,axiom,
! [TA: $tType,TB: $tType] :
( ( ( enum @ TA )
& ( enum @ TB ) )
=> ( enum @ ( fun @ TB @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun___Enum_Oenum) ).
thf(520,plain,
! [TA: $tType,TB: $tType] :
( ( ( enum @ TA )
& ( enum @ TB ) )
=> ( enum @ ( fun @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(30,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TA,C: fun @ TB @ bool,D: fun @ TB @ TA,E: fun @ TA @ TB] :
( ( type_definition @ TA @ TB @ E @ D @ C )
=> ( ( ( aa @ TA @ TB @ E @ B )
= ( aa @ TA @ TB @ E @ A ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_type__definition_ORep__inject) ).
thf(240,plain,
! [TA: $tType,TB: $tType,A: TA,B: TA,C: fun @ TB @ bool,D: fun @ TB @ TA,E: fun @ TA @ TB] :
( ( type_definition @ TA @ TB @ E @ D @ C )
=> ( ( ( ( aa @ TA @ TB @ E @ B )
= ( aa @ TA @ TB @ E @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( aa @ TA @ TB @ E @ B )
= ( aa @ TA @ TB @ E @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(55,axiom,
! [A: char] :
~ ! [B: nibble,C: nibble] :
( A
!= ( char1 @ B @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_char_Oexhaust) ).
thf(330,plain,
! [A: char] :
~ ! [B: nibble,C: nibble] :
( A
!= ( char1 @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(89,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ~ ( ord_less @ TA @ ( one_one @ TA ) @ ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_not__one__less__zero) ).
thf(462,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ~ ( ord_less @ TA @ ( one_one @ TA ) @ ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(22,axiom,
! [TA: $tType] : ( type_definition @ ( hoare_28830079triple @ TA ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ TA ) ) @ bool ) @ ( hoare_334633230triple @ TA ) @ ( hoare_689268419triple @ TA ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ TA ) ) @ bool ) @ ( hoare_711253694ep_set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_type__definition__triple) ).
thf(223,plain,
! [TA: $tType] : ( type_definition @ ( hoare_28830079triple @ TA ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ TA ) ) @ bool ) @ ( hoare_334633230triple @ TA ) @ ( hoare_689268419triple @ TA ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ TA ) ) @ bool ) @ ( hoare_711253694ep_set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(36,axiom,
! [TA: $tType,TB: $tType,A: TA,B: fun @ TA @ bool,C: fun @ TB @ bool,D: fun @ TB @ TA,E: fun @ TA @ TB] :
( ( type_definition @ TA @ TB @ E @ D @ C )
=> ( ! [F: TB] :
( ( member @ TB @ F @ C )
=> ( pp @ ( aa @ TA @ bool @ B @ ( aa @ TB @ TA @ D @ F ) ) ) )
=> ( pp @ ( aa @ TA @ bool @ B @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_type__definition_OAbs__induct) ).
thf(267,plain,
! [TA: $tType,TB: $tType,A: TA,B: fun @ TA @ bool,C: fun @ TB @ bool,D: fun @ TB @ TA,E: fun @ TA @ TB] :
( ( type_definition @ TA @ TB @ E @ D @ C )
=> ( ! [F: TB] :
( ( member @ TB @ F @ C )
=> ( pp @ ( aa @ TA @ bool @ B @ ( aa @ TB @ TA @ D @ F ) ) ) )
=> ( pp @ ( aa @ TA @ bool @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(82,axiom,
! [TA: $tType] :
( ( semiring_1 @ TA )
=> ( ( semiring_1_of_nat @ TA @ ( one_one @ nat ) )
= ( one_one @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_of__nat__1) ).
thf(438,plain,
! [TA: $tType] :
( ( semiring_1 @ TA )
=> ( ( semiring_1_of_nat @ TA @ ( one_one @ nat ) )
= ( one_one @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(79,axiom,
! [TA: $tType,A: fun @ TA @ bool] :
( ( collect @ TA @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_Collect__def) ).
thf(426,plain,
! [TA: $tType,A: fun @ TA @ bool] :
( ( collect @ TA @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(114,axiom,
group_add @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ogroup__add) ).
thf(531,plain,
group_add @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(130,axiom,
cl_HOL_Oequal @ nibble,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_String_Onibble___HOL_Oequal) ).
thf(548,plain,
cl_HOL_Oequal @ nibble,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(33,axiom,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: TA] :
( ( ( zero_zero @ TA )
= A )
<=> ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_zero__reorient) ).
thf(255,plain,
! [TA: $tType] :
( ( zero @ TA )
=> ! [A: TA] :
( ( ( ( zero_zero @ TA )
= A )
=> ( A
= ( zero_zero @ TA ) ) )
& ( ( A
= ( zero_zero @ TA ) )
=> ( ( zero_zero @ TA )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(102,axiom,
! [TA: $tType,TB: $tType] :
( ( ( enum @ TA )
& ( enum @ TB ) )
=> ( enum @ ( sum_sum @ TB @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_sum___Enum_Oenum) ).
thf(516,plain,
! [TA: $tType,TB: $tType] :
( ( ( enum @ TA )
& ( enum @ TB ) )
=> ( enum @ ( sum_sum @ TB @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(13,axiom,
! [TA: $tType] :
( ( cl_HOL_Oequal @ TA )
=> ( ( fequal @ TA )
= ( equal_equal @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_eq__equal) ).
thf(194,plain,
! [TA: $tType] :
( ( cl_HOL_Oequal @ TA )
=> ( ( fequal @ TA )
= ( equal_equal @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(8,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/sandbox2/benchmark/theBenchmark.p',fact_5_triple_Osimps_I2_J) ).
thf(177,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)],[8]) ).
thf(83,axiom,
! [TA: $tType] :
( ( semiring_1 @ TA )
=> ( ( semiring_1_of_nat @ TA @ ( zero_zero @ nat ) )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_of__nat__0) ).
thf(441,plain,
! [TA: $tType] :
( ( semiring_1 @ TA )
=> ( ( semiring_1_of_nat @ TA @ ( zero_zero @ nat ) )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(93,axiom,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: TA] :
( ( ( sgn_sgn @ TA @ A )
= ( one_one @ TA ) )
<=> ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_sgn__1__pos) ).
thf(470,plain,
! [TA: $tType] :
( ( linordered_idom @ TA )
=> ! [A: TA] :
( ( ( ( sgn_sgn @ TA @ A )
= ( one_one @ TA ) )
=> ( ord_less @ TA @ ( zero_zero @ TA ) @ A ) )
& ( ( ord_less @ TA @ ( zero_zero @ TA ) @ A )
=> ( ( sgn_sgn @ TA @ A )
= ( one_one @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(63,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_less__nat__zero__code) ).
thf(359,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(127,axiom,
cl_HOL_Oequal @ state,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Com_Ostate___HOL_Oequal) ).
thf(544,plain,
cl_HOL_Oequal @ state,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(141,axiom,
? [A: state,B: state] : A != B,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(571,plain,
? [A: state,B: state] : A != B,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(98,axiom,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA] :
( ( ( uminus_uminus @ TA @ A )
= ( zero_zero @ TA ) )
<=> ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_neg__equal__0__iff__equal) ).
thf(497,plain,
! [TA: $tType] :
( ( group_add @ TA )
=> ! [A: TA] :
( ( ( ( uminus_uminus @ TA @ A )
= ( zero_zero @ TA ) )
=> ( A
= ( zero_zero @ TA ) ) )
& ( ( A
= ( zero_zero @ TA ) )
=> ( ( uminus_uminus @ TA @ A )
= ( zero_zero @ TA ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(86,axiom,
! [TA: $tType] :
( ( zero_neq_one @ TA )
=> ( ( one_one @ TA )
!= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_one__neq__zero) ).
thf(450,plain,
! [TA: $tType] :
( ( zero_neq_one @ TA )
=> ( ( one_one @ TA )
!= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(136,axiom,
! [A: bool] :
( ( A = fTrue )
| ( A = fFalse ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fTrue_1_1_T) ).
thf(556,plain,
! [A: bool] :
( ( A = fTrue )
| ( A = fFalse ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(122,axiom,
semiring_1 @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Osemiring__1) ).
thf(539,plain,
semiring_1 @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(107,axiom,
cl_HOL_Oequal @ com,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Com_Ocom___HOL_Oequal) ).
thf(524,plain,
cl_HOL_Oequal @ com,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(66,axiom,
! [A: nat,B: nat] :
( ( B != A )
<=> ( ( ord_less @ nat @ B @ A )
| ( ord_less @ nat @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_nat__neq__iff) ).
thf(368,plain,
! [A: nat,B: nat] :
( ( ( B != A )
=> ( ( ord_less @ nat @ B @ A )
| ( ord_less @ nat @ A @ B ) ) )
& ( ( ( ord_less @ nat @ B @ A )
| ( ord_less @ nat @ A @ B ) )
=> ( B != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(50,axiom,
! [TA: $tType] :
( ( sgn_if @ TA )
=> ( ( sgn_sgn @ TA @ ( zero_zero @ TA ) )
= ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_sgn0) ).
thf(304,plain,
! [TA: $tType] :
( ( sgn_if @ TA )
=> ( ( sgn_sgn @ TA @ ( zero_zero @ TA ) )
= ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(5,axiom,
! [TA: $tType,A: hoare_28830079triple @ TA,B: hoare_28830079triple @ TA] :
( ( ( aa @ ( hoare_28830079triple @ TA ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ TA ) ) @ bool ) @ ( hoare_334633230triple @ TA ) @ B )
= ( aa @ ( hoare_28830079triple @ TA ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ TA ) ) @ bool ) @ ( hoare_334633230triple @ TA ) @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_Rep__triple__inject) ).
thf(158,plain,
! [TA: $tType,A: hoare_28830079triple @ TA,B: hoare_28830079triple @ TA] :
( ( ( ( aa @ ( hoare_28830079triple @ TA ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ TA ) ) @ bool ) @ ( hoare_334633230triple @ TA ) @ B )
= ( aa @ ( hoare_28830079triple @ TA ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ TA ) ) @ bool ) @ ( hoare_334633230triple @ TA ) @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( aa @ ( hoare_28830079triple @ TA ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ TA ) ) @ bool ) @ ( hoare_334633230triple @ TA ) @ B )
= ( aa @ ( hoare_28830079triple @ TA ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ TA ) ) @ bool ) @ ( hoare_334633230triple @ TA ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(11,axiom,
! [TA: $tType] :
( ( cl_HOL_Oequal @ TA )
=> ! [A: TA] : ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( equal_equal @ TA ) @ A ) @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_equal__refl) ).
thf(186,plain,
! [TA: $tType] :
( ( cl_HOL_Oequal @ TA )
=> ! [A: TA] : ( pp @ ( aa @ TA @ bool @ ( aa @ TA @ ( fun @ TA @ bool ) @ ( equal_equal @ TA ) @ A ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(18,axiom,
! [TA: $tType,A: fun @ ( node @ ( sum_sum @ com @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ TA ) ) @ bool,B: fun @ ( node @ ( sum_sum @ com @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ TA ) ) @ bool] :
( ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ TA ) ) @ bool ) @ B @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ TA ) ) @ bool ) @ ( hoare_711253694ep_set @ TA ) ) )
=> ( ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ TA ) ) @ bool ) @ A @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ TA ) ) @ bool ) @ ( hoare_711253694ep_set @ TA ) ) )
=> ( ( ( aa @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ TA ) ) @ bool ) @ ( hoare_28830079triple @ TA ) @ ( hoare_689268419triple @ TA ) @ B )
= ( aa @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ TA ) ) @ bool ) @ ( hoare_28830079triple @ TA ) @ ( hoare_689268419triple @ TA ) @ A ) )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_Abs__triple__inject) ).
thf(207,plain,
! [TA: $tType,A: fun @ ( node @ ( sum_sum @ com @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ TA ) ) @ bool,B: fun @ ( node @ ( sum_sum @ com @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ TA ) ) @ bool] :
( ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ TA ) ) @ bool ) @ B @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ TA ) ) @ bool ) @ ( hoare_711253694ep_set @ TA ) ) )
=> ( ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ TA ) ) @ bool ) @ A @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ TA ) ) @ bool ) @ ( hoare_711253694ep_set @ TA ) ) )
=> ( ( ( ( aa @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ TA ) ) @ bool ) @ ( hoare_28830079triple @ TA ) @ ( hoare_689268419triple @ TA ) @ B )
= ( aa @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ TA ) ) @ bool ) @ ( hoare_28830079triple @ TA ) @ ( hoare_689268419triple @ TA ) @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( aa @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ TA ) ) @ bool ) @ ( hoare_28830079triple @ TA ) @ ( hoare_689268419triple @ TA ) @ B )
= ( aa @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ TA ) ) @ bool ) @ ( hoare_28830079triple @ TA ) @ ( hoare_689268419triple @ TA ) @ A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(60,axiom,
! [TA: $tType,A: TA,B: TA,C: TA,D: fun @ TA @ ( fun @ TA @ TA )] :
( ( semigroup @ TA @ D )
=> ( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ D @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ D @ C ) @ B ) ) @ A )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ D @ C ) @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ D @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_semigroup_Oassoc) ).
thf(346,plain,
! [TA: $tType,A: TA,B: TA,C: TA,D: fun @ TA @ ( fun @ TA @ TA )] :
( ( semigroup @ TA @ D )
=> ( ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ D @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ D @ C ) @ B ) ) @ A )
= ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ D @ C ) @ ( aa @ TA @ TA @ ( aa @ TA @ ( fun @ TA @ TA ) @ D @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(131,axiom,
cl_HOL_Oequal @ literal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_String_Oliteral___HOL_Oequal) ).
thf(549,plain,
cl_HOL_Oequal @ literal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(119,axiom,
linordered_semidom @ nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Olinordered__semidom) ).
thf(536,plain,
linordered_semidom @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(45,axiom,
! [A: literal] :
( ( size_size @ literal @ A )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_size__literal__def) ).
thf(290,plain,
! [A: literal] :
( ( size_size @ literal @ A )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(67,axiom,
! [A: nat,B: nat] :
( ( B != A )
=> ( ~ ( ord_less @ nat @ B @ A )
=> ( ord_less @ nat @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_linorder__neqE__nat) ).
thf(378,plain,
! [A: nat,B: nat] :
( ( B != A )
=> ( ~ ( ord_less @ nat @ B @ A )
=> ( ord_less @ nat @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(28,axiom,
! [TA: $tType,TB: $tType,A: TB,B: fun @ TA @ bool,C: fun @ TA @ TB,D: fun @ TB @ TA] :
( ( type_definition @ TB @ TA @ D @ C @ B )
=> ( member @ TA @ ( aa @ TB @ TA @ D @ A ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_type__definition_ORep) ).
thf(235,plain,
! [TA: $tType,TB: $tType,A: TB,B: fun @ TA @ bool,C: fun @ TA @ TB,D: fun @ TB @ TA] :
( ( type_definition @ TB @ TA @ D @ C @ B )
=> ( member @ TA @ ( aa @ TB @ TA @ D @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(31,axiom,
! [TA: $tType,TB: $tType,A: TA,B: fun @ TA @ bool,C: fun @ TA @ TB,D: fun @ TB @ TA] :
( ( type_definition @ TB @ TA @ D @ C @ B )
=> ( ( member @ TA @ A @ B )
=> ( ( aa @ TB @ TA @ D @ ( aa @ TA @ TB @ C @ A ) )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_type__definition_OAbs__inverse) ).
thf(246,plain,
! [TA: $tType,TB: $tType,A: TA,B: fun @ TA @ bool,C: fun @ TA @ TB,D: fun @ TB @ TA] :
( ( type_definition @ TB @ TA @ D @ C @ B )
=> ( ( member @ TA @ A @ B )
=> ( ( aa @ TB @ TA @ D @ ( aa @ TA @ TB @ C @ A ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(85,axiom,
! [TA: $tType] :
( ( zero_neq_one @ TA )
=> ( ( zero_zero @ TA )
!= ( one_one @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_zero__neq__one) ).
thf(447,plain,
! [TA: $tType] :
( ( zero_neq_one @ TA )
=> ( ( zero_zero @ TA )
!= ( one_one @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(81,axiom,
! [TA: $tType] :
( ( semiring_char_0 @ TA )
=> ! [A: nat,B: nat] :
( ( ( semiring_1_of_nat @ TA @ B )
= ( semiring_1_of_nat @ TA @ A ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_of__nat__eq__iff) ).
thf(432,plain,
! [TA: $tType] :
( ( semiring_char_0 @ TA )
=> ! [A: nat,B: nat] :
( ( ( ( semiring_1_of_nat @ TA @ B )
= ( semiring_1_of_nat @ TA @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( semiring_1_of_nat @ TA @ B )
= ( semiring_1_of_nat @ TA @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(74,axiom,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_not__less0) ).
thf(410,plain,
! [A: nat] :
~ ( ord_less @ nat @ A @ ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(34,axiom,
! [TA: $tType,TB: $tType,A: TB,B: fun @ TB @ bool,C: fun @ TB @ TA,D: fun @ TA @ TB] :
( ( type_definition @ TA @ TB @ D @ C @ B )
=> ( ( member @ TB @ A @ B )
=> ~ ! [E: TA] :
( A
!= ( aa @ TA @ TB @ D @ E ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_type__definition_ORep__cases) ).
thf(262,plain,
! [TA: $tType,TB: $tType,A: TB,B: fun @ TB @ bool,C: fun @ TB @ TA,D: fun @ TA @ TB] :
( ( type_definition @ TA @ TB @ D @ C @ B )
=> ( ( member @ TB @ A @ B )
=> ~ ! [E: TA] :
( A
!= ( aa @ TA @ TB @ D @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(3,axiom,
( hoare_531836380gleton
<=> ? [A: state,B: state] : A != B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_state__not__singleton__def) ).
thf(146,plain,
( ( hoare_531836380gleton
=> ? [A: state,B: state] : A != B )
& ( ? [A: state,B: state] : A != B
=> hoare_531836380gleton ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(73,axiom,
! [A: nat,B: nat] :
( ( ord_less @ nat @ B @ A )
=> ( A
!= ( zero_zero @ nat ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_gr__implies__not0) ).
thf(405,plain,
! [A: nat,B: nat] :
( ( ord_less @ nat @ B @ A )
=> ( A
!= ( zero_zero @ nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(10,axiom,
! [TA: $tType] :
( ( cl_HOL_Oequal @ TA )
=> ( ( equal_equal @ TA )
= ( fequal @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_equal) ).
thf(183,plain,
! [TA: $tType] :
( ( cl_HOL_Oequal @ TA )
=> ( ( equal_equal @ TA )
= ( fequal @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(139,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/sandbox2/benchmark/theBenchmark.p',help_fequal_1_1_T) ).
thf(564,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)],[139]) ).
thf(115,axiom,
sgn_if @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Osgn__if) ).
thf(532,plain,
sgn_if @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(42,axiom,
! [A: char] :
( ( size_size @ char @ A )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_size__char) ).
thf(283,plain,
! [A: char] :
( ( size_size @ char @ A )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(90,axiom,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: nat] :
~ ( ord_less @ TA @ ( semiring_1_of_nat @ TA @ A ) @ ( zero_zero @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_of__nat__less__0__iff) ).
thf(464,plain,
! [TA: $tType] :
( ( linordered_semidom @ TA )
=> ! [A: nat] :
~ ( ord_less @ TA @ ( semiring_1_of_nat @ TA @ A ) @ ( zero_zero @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(111,axiom,
semiring_char_0 @ int,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Nat_Osemiring__char__0) ).
thf(528,plain,
semiring_char_0 @ int,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(15,axiom,
! [TA: $tType,A: hoare_28830079triple @ TA] : ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ TA ) ) @ bool ) @ ( aa @ ( hoare_28830079triple @ TA ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ TA ) ) @ bool ) @ ( hoare_334633230triple @ TA ) @ A ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ TA ) ) @ bool ) @ ( hoare_711253694ep_set @ TA ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_Rep__triple) ).
thf(200,plain,
! [TA: $tType,A: hoare_28830079triple @ TA] : ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ TA ) ) @ bool ) @ ( aa @ ( hoare_28830079triple @ TA ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ TA ) ) @ bool ) @ ( hoare_334633230triple @ TA ) @ A ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ TA @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ TA ) ) @ bool ) @ ( hoare_711253694ep_set @ TA ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(39,axiom,
( ( bool_size @ fFalse )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_bool_Osize_I2_J) ).
thf(277,plain,
( ( bool_size @ fFalse )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(24,axiom,
! [TA: $tType,A: fun @ TA @ ( fun @ state @ bool ),B: com,C: fun @ TA @ ( fun @ state @ bool ),D: fun @ TA @ nat] :
( ( hoare_47506394e_size @ TA @ D @ ( hoare_1841697145triple @ TA @ C @ B @ A ) )
= ( zero_zero @ nat ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_triple_Osize_I1_J) ).
thf(227,plain,
! [TA: $tType,A: fun @ TA @ ( fun @ state @ bool ),B: com,C: fun @ TA @ ( fun @ state @ bool ),D: fun @ TA @ nat] :
( ( hoare_47506394e_size @ TA @ D @ ( hoare_1841697145triple @ TA @ C @ B @ A ) )
= ( zero_zero @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(57,axiom,
! [TA: $tType,A: nibble,B: nibble,C: fun @ nibble @ ( fun @ nibble @ TA )] :
( ( char_rec @ TA @ C @ ( char1 @ B @ A ) )
= ( aa @ nibble @ TA @ ( aa @ nibble @ ( fun @ nibble @ TA ) @ C @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_char_Orecs) ).
thf(337,plain,
! [TA: $tType,A: nibble,B: nibble,C: fun @ nibble @ ( fun @ nibble @ TA )] :
( ( char_rec @ TA @ C @ ( char1 @ B @ A ) )
= ( aa @ nibble @ TA @ ( aa @ nibble @ ( fun @ nibble @ TA ) @ C @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(126,axiom,
cl_HOL_Oequal @ bool,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL_Obool___HOL_Oequal) ).
thf(543,plain,
cl_HOL_Oequal @ bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(97,axiom,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ( uminus_uminus @ TA @ A )
= A )
<=> ( A
= ( zero_zero @ TA ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_neg__equal__zero) ).
thf(491,plain,
! [TA: $tType] :
( ( linord219039673up_add @ TA )
=> ! [A: TA] :
( ( ( ( uminus_uminus @ TA @ A )
= A )
=> ( A
= ( zero_zero @ TA ) ) )
& ( ( A
= ( zero_zero @ TA ) )
=> ( ( uminus_uminus @ TA @ A )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(575,plain,
$false,
inference(e,[status(thm)],[202,525,365,249,518,468,234,555,352,384,533,550,142,340,538,174,288,301,542,460,559,416,152,216,475,164,321,485,480,293,453,265,527,307,233,546,381,534,270,529,334,349,561,392,429,197,522,324,519,188,388,420,225,554,537,526,515,503,541,530,343,237,298,279,444,180,296,423,402,286,545,413,281,204,466,540,219,274,230,318,509,362,567,552,535,213,520,240,330,462,223,267,438,426,531,548,255,516,194,177,441,470,359,544,571,497,450,556,539,524,368,304,158,186,207,346,549,536,290,378,235,246,447,432,410,262,146,405,183,564,532,283,464,528,200,277,227,337,543,491]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SWW504_5 : TPTP v8.1.2. Released v6.0.0.
% 0.06/0.15 % Command : run_Leo-III %s %d
% 0.15/0.35 % Computer : n007.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Thu May 18 21:48:54 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.96/0.87 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.73/1.09 % [INFO] Parsing done (215ms).
% 1.73/1.10 % [INFO] Running in sequential loop mode.
% 2.21/1.30 % [INFO] eprover registered as external prover.
% 2.21/1.30 % [INFO] cvc4 registered as external prover.
% 2.21/1.30 % [INFO] Scanning for conjecture ...
% 2.58/1.40 % [INFO] Found a conjecture and 139 axioms. Running axiom selection ...
% 2.72/1.43 % [INFO] Axiom selection finished. Selected 139 axioms (removed 0 axioms).
% 3.18/1.57 % [INFO] Problem is typed first-order (TPTP TFF).
% 3.18/1.59 % [INFO] Type checking passed.
% 3.18/1.60 % [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 ...
% 3.50/1.72 % [INFO] [Domain constraints] Detected constraint on state
% 3.50/1.72 % [INFO] [Domain constraints] dom(state) ⊆ {sk1}
% 5.04/2.15 % [INFO] [Domain constraints] Detected constraint on bool
% 5.04/2.15 % [INFO] [Domain constraints] dom(bool) ⊆ {fTrue,fFalse}
% 5.04/2.15 % [INFO] [Domain constraints] Detected constraint on bool
% 5.04/2.15 % [INFO] [Domain constraints] dom(bool) ⊆ {fTrue,fFalse}
% 14.49/6.79 % External prover 'e' found a proof!
% 14.49/6.79 % [INFO] Killing All external provers ...
% 14.49/6.79 % Time passed: 6281ms (effective reasoning time: 5689ms)
% 14.49/6.79 % 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)>
% 14.49/6.79 % Axioms used in derivation (139): fact_93_neg__equal__iff__equal, fact_42_size__literal__def, arity_Nat_Onat___Groups_Ozero, fact_79_of__nat__1, fact_81_of__nat__less__iff, fact_54_char_Orecs, fact_44_nat_Osize_I3_J, arity_Int_Oint___Groups_Oone, arity_String_Ochar___Enum_Oenum, arity_Int_Oint___Rings_Olinordered__idom, fact_84_one__reorient, arity_Hoare__Mirabelle__vtrypsmcwp_Otriple___HOL_Oequal, arity_Nat_Onat___Rings_Osemiring__1, fact_43_size__bool, fact_80_of__nat__0, fact_25_type__definition_ORep, fact_3_triple_Oinject, fact_8_equal__refl, fact_4_triple_Orecs, fact_32_type__definition_ORep__induct, arity_fun___HOL_Oequal, fact_28_type__definition_OAbs__inverse, fact_63_nat__neq__iff, fact_90_sgn__1__pos, fact_53_char_Osimps_I2_J, fact_17_Abs__triple__induct, fact_92_sgn__1__neg, fact_68_nat__less__cases, fact_85_zero__less__one, help_fTrue_1_1_T, arity_Nat_Onat___HOL_Oequal, fact_26_type__definition_ORep__inverse, fact_75_mem__def, fact_62_less__not__refl, fact_31_type__definition_ORep__cases, fact_72_of__nat__0__less__iff, fact_2_Rep__triple__inject, arity_String_Ochar___HOL_Oequal, arity_HOL_Obool___HOL_Oequal, fact_7_equal, help_fTrue_1_1_U, fact_48_char_Oinject, fact_65_less__irrefl__nat, fact_30_zero__reorient, arity_Int_Oint___Rings_Osemiring__1, fact_61_less__zeroE, arity_fun___Enum_Oenum, help_fFalse_1_1_T, fact_86_not__one__less__zero, fact_94_neg__equal__zero, fact_74_ext, fact_77_sgn__pos, fact_59_neq0__conv, fact_27_type__definition_ORep__inject, arity_sum___HOL_Oequal, fact_18_Abs__triple__cases, arity_Com_Ocom___HOL_Oequal, fact_96_equal__neg__zero, fact_60_less__nat__zero__code, arity_sum___Enum_Oenum, arity_String_Onibble___HOL_Oequal, fact_78_of__nat__eq__iff, fact_58_linorder__neqE__linordered__idom, fact_52_char_Oexhaust, fact_34_type__definition_OAbs__cases, arity_HOL_Obool___Enum_Oenum, fact_5_triple_Osimps_I2_J, fact_33_type__definition_OAbs__induct, fact_13_Rep__triple__induct, fact_40_bool_Osize_I3_J, fact_45_char_Osize_I2_J, fact_76_Collect__def, fact_19_type__definition__triple, fact_15_Abs__triple__inject, fact_16_Abs__triple__inverse, fact_0_state__not__singleton__def, fact_10_eq__equal, fact_37_bool_Osize_I1_J, fact_20_induct__false__def, arity_Nat_Onat___Rings_Olinordered__semidom, help_fequal_1_1_T, fact_29_type__definition_OAbs__inject, arity_Com_Ostate___HOL_Oequal, fact_56_sgn__greater, arity_String_Onibble___Enum_Oenum, fact_83_one__neq__zero, fact_49_nat__size, fact_57_semigroup_Oassoc, arity_Int_Oint___Groups_Ogroup__add, fact_88_of__nat__less__imp__less, fact_55_sgn__less, fact_24_induct__trueI, fact_71_not__less0, fact_67_less__not__refl3, fact_97_neg__0__equal__iff__equal, fact_23_induct__true__def, fact_50_sgn__sgn, help_fequal_2_1_T, fact_6_triple_Oexhaust, fact_14_Rep__triple__cases, arity_Nat_Onat___Nat_Osemiring__char__0, fact_1_equal__triple__def, fact_22_triple_Osize_I2_J, fact_41_bool_Osize_I4_J, arity_Int_Oint___Rings_Ozero__neq__one, fact_91_zero__less__int__conv, fact_82_zero__neq__one, fact_21_triple_Osize_I1_J, help_fFalse_1_1_U, fact_46_char_Osize_I1_J, arity_Int_Oint___HOL_Oequal, arity_Nat_Onat___Groups_Oone, fact_66_less__not__refl2, arity_String_Oliteral___HOL_Oequal, fact_47_sgn0, fact_35_char__size, arity_Int_Oint___Groups_Osgn__if, fact_87_of__nat__less__0__iff, fact_64_linorder__neqE__nat, help_pp_1_1_U, fact_69_gr0I, fact_38_nat_Osize_I1_J, fact_73_infinite__descent0, arity_Int_Oint___Groups_Olinordered__ab__group__add, fact_39_size__char, fact_51_sgn__0__0, arity_Int_Oint___Groups_Ozero, fact_95_neg__equal__0__iff__equal, conj_0, arity_Int_Oint___Nat_Osemiring__char__0, help_pp_2_1_U, arity_Int_Oint___Rings_Olinordered__semidom, fact_9_equal__eq, arity_Nat_Onat___Rings_Ozero__neq__one, fact_11_Rep__triple__inverse, fact_89_less__imp__of__nat__less, fact_12_Rep__triple, fact_36_bool_Osize_I2_J, fact_70_gr__implies__not0
% 14.49/6.79 % No. of inferences in proof: 282
% 14.49/6.79 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 6281 ms resp. 5689 ms w/o parsing
% 15.11/6.92 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 15.11/6.92 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------