%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWW504_5 : TPTP v9.3.1. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 09:10:42 AM UTC 2026
% Result : Theorem 15.73s 6.43s
% Output : Refutation 16.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 140
% Syntax : Number of formulae : 282 ( 130 unt; 0 typ; 0 def)
% Number of atoms : 1148 ( 235 equ; 0 cnn)
% Maximal formula atoms : 34 ( 4 avg)
% Number of connectives : 3983 ( 88 ~; 11 |; 45 &;3585 @)
% ( 28 <=>; 226 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 6 avg)
% Number of types : 9 ( 8 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 51 ( 49 usr; 10 con; 0-5 aty)
% Number of variables : 552 ( 0 ^; 537 !; 15 ?; 552 :)
% 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_decl,type,
enum:
!>[TA: $tType] : $o ).
thf(cl_HOL_Oequal_decl,type,
cl_HOL_Oequal:
!>[TA: $tType] : $o ).
thf(one_decl,type,
one:
!>[TA: $tType] : $o ).
thf(zero_decl,type,
zero:
!>[TA: $tType] : $o ).
thf(sgn_if_decl,type,
sgn_if:
!>[TA: $tType] : $o ).
thf(group_add_decl,type,
group_add:
!>[TA: $tType] : $o ).
thf(semiring_1_decl,type,
semiring_1:
!>[TA: $tType] : $o ).
thf(zero_neq_one_decl,type,
zero_neq_one:
!>[TA: $tType] : $o ).
thf(semiring_char_0_decl,type,
semiring_char_0:
!>[TA: $tType] : $o ).
thf(linordered_idom_decl,type,
linordered_idom:
!>[TA: $tType] : $o ).
thf(linordered_semidom_decl,type,
linordered_semidom:
!>[TA: $tType] : $o ).
thf(linord219039673up_add_decl,type,
linord219039673up_add:
!>[TA: $tType] : $o ).
thf(one_one_decl,type,
one_one:
!>[TA: $tType] : TA ).
thf(semigroup_decl,type,
semigroup:
!>[TA: $tType] : ( ( TA @ ( TA @ fun ) @ ( TA @ fun ) ) > $o ) ).
thf(sgn_sgn_decl,type,
sgn_sgn:
!>[TA: $tType] : ( TA > TA ) ).
thf(uminus_uminus_decl,type,
uminus_uminus:
!>[TA: $tType] : ( TA > TA ) ).
thf(zero_zero_decl,type,
zero_zero:
!>[TA: $tType] : TA ).
thf(bool_size_decl,type,
bool_size: bool > nat ).
thf(equal_equal_decl,type,
equal_equal:
!>[TA: $tType] : ( bool @ ( TA @ fun ) @ ( TA @ fun ) ) ).
thf(induct_false_decl,type,
induct_false: $o ).
thf(induct_true_decl,type,
induct_true: $o ).
thf(hoare_689268419triple_decl,type,
hoare_689268419triple:
!>[TA: $tType] : ( TA @ hoare_28830079triple @ ( bool @ ( TA @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ fun ) ) ).
thf(hoare_334633230triple_decl,type,
hoare_334633230triple:
!>[TA: $tType] : ( bool @ ( TA @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ ( TA @ hoare_28830079triple @ fun ) ) ).
thf(hoare_531836380gleton_decl,type,
hoare_531836380gleton: $o ).
thf(hoare_1841697145triple_decl,type,
hoare_1841697145triple:
!>[TA: $tType] : ( ( bool @ ( state @ fun ) @ ( TA @ fun ) ) > com > ( bool @ ( state @ fun ) @ ( TA @ fun ) ) > ( TA @ hoare_28830079triple ) ) ).
thf(hoare_376461865e_case_decl,type,
hoare_376461865e_case:
!>[TA: $tType,TB: $tType] : ( ( TA @ ( bool @ ( state @ fun ) @ ( TB @ fun ) @ fun ) @ ( com @ fun ) @ ( bool @ ( state @ fun ) @ ( TB @ fun ) @ fun ) ) > ( TB @ hoare_28830079triple ) > TA ) ).
thf(hoare_678420151le_rec_decl,type,
hoare_678420151le_rec:
!>[TA: $tType,TB: $tType] : ( ( TA @ ( bool @ ( state @ fun ) @ ( TB @ fun ) @ fun ) @ ( com @ fun ) @ ( bool @ ( state @ fun ) @ ( TB @ fun ) @ fun ) ) > ( TB @ hoare_28830079triple ) > TA ) ).
thf(hoare_711253694ep_set_decl,type,
hoare_711253694ep_set:
!>[TA: $tType] : ( bool @ ( bool @ ( TA @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ fun ) ) ).
thf(hoare_47506394e_size_decl,type,
hoare_47506394e_size:
!>[TA: $tType] : ( ( nat @ ( TA @ fun ) ) > ( TA @ hoare_28830079triple ) > nat ) ).
thf(nat_size_decl,type,
nat_size: nat > nat ).
thf(semiring_1_of_nat_decl,type,
semiring_1_of_nat:
!>[TA: $tType] : ( nat > TA ) ).
thf(size_size_decl,type,
size_size:
!>[TA: $tType] : ( TA > nat ) ).
thf(ord_less_decl,type,
ord_less:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(collect_decl,type,
collect:
!>[TA: $tType] : ( ( bool @ ( TA @ fun ) ) > ( bool @ ( TA @ fun ) ) ) ).
thf(char1_decl,type,
char1: nibble > nibble > char ).
thf(char_case_decl,type,
char_case:
!>[TA: $tType] : ( ( TA @ ( nibble @ fun ) @ ( nibble @ fun ) ) > char > TA ) ).
thf(char_rec_decl,type,
char_rec:
!>[TA: $tType] : ( ( TA @ ( nibble @ fun ) @ ( nibble @ fun ) ) > char > TA ) ).
thf(char_size_decl,type,
char_size: char > nat ).
thf(type_definition_decl,type,
type_definition:
!>[TA: $tType,TB: $tType] : ( ( TA @ ( TB @ fun ) ) > ( TB @ ( TA @ fun ) ) > ( bool @ ( TA @ fun ) ) > $o ) ).
thf(aa_decl,type,
aa:
!>[TA: $tType,TB: $tType] : ( ( TA @ ( TB @ fun ) ) > TB > TA ) ).
thf(fFalse_decl,type,
fFalse: bool ).
thf(fTrue_decl,type,
fTrue: bool ).
thf(fequal_decl,type,
fequal:
!>[TA: $tType] : ( bool @ ( TA @ fun ) @ ( TA @ fun ) ) ).
thf(member_decl,type,
member:
!>[TA: $tType] : ( TA > ( bool @ ( TA @ fun ) ) > $o ) ).
thf(pp_decl,type,
pp: bool > $o ).
thf(60,axiom,
! [TA: $tType,A: TA,B: TA,C: TA,D: TA @ ( TA @ fun ) @ ( TA @ fun )] :
( ( D @ ( TA @ semigroup ) )
=> ( ( A @ ( B @ ( C @ ( D @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( D @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( D @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( C @ ( D @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_semigroup_Oassoc) ).
thf(365,plain,
! [TA: $tType,A: TA,B: TA,C: TA,D: TA @ ( TA @ fun ) @ ( TA @ fun )] :
( ( D @ ( TA @ semigroup ) )
=> ( ( A @ ( B @ ( C @ ( D @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( D @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) )
= ( A @ ( B @ ( D @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) @ ( C @ ( D @ ( TA @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( TA @ ( TA @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(55,axiom,
! [A: char] :
~ ! [B: nibble,C: nibble] :
( A
!= ( C @ ( B @ char1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_char_Oexhaust) ).
thf(347,plain,
! [A: char] :
~ ! [B: nibble,C: nibble] :
( A
!= ( C @ ( B @ char1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(104,axiom,
bool @ enum,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL_Obool___Enum_Oenum) ).
thf(555,plain,
bool @ enum,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(35,axiom,
! [TA: $tType,TB: $tType,A: bool @ ( TA @ fun ),B: TA,C: bool @ ( TA @ fun ),D: TB @ ( TA @ fun ),E: TA @ ( TB @ fun )] :
( ( C @ ( D @ ( E @ ( TA @ ( TB @ type_definition ) ) ) ) )
=> ( ( C @ ( B @ ( TA @ member ) ) )
=> ( ! [F: TB] : ( F @ ( E @ ( TA @ ( TB @ aa ) ) ) @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_type__definition_ORep__induct) ).
thf(276,plain,
! [TA: $tType,TB: $tType,A: bool @ ( TA @ fun ),B: TA,C: bool @ ( TA @ fun ),D: TB @ ( TA @ fun ),E: TA @ ( TB @ fun )] :
( ( C @ ( D @ ( E @ ( TA @ ( TB @ type_definition ) ) ) ) )
=> ( ( C @ ( B @ ( TA @ member ) ) )
=> ( ! [F: TB] : ( F @ ( E @ ( TA @ ( TB @ aa ) ) ) @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(63,axiom,
! [A: nat] :
~ ( nat @ zero_zero @ ( A @ ( nat @ ord_less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_less__nat__zero__code) ).
thf(379,plain,
! [A: nat] :
~ ( nat @ zero_zero @ ( A @ ( nat @ ord_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(97,axiom,
! [TA: $tType] :
( ( TA @ linord219039673up_add )
=> ! [A: TA] :
( ( ( A @ ( TA @ uminus_uminus ) )
= A )
<=> ( A
= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_neg__equal__zero) ).
thf(523,plain,
! [TA: $tType] :
( ( TA @ linord219039673up_add )
=> ! [A: TA] :
( ( ( A
= ( TA @ zero_zero ) )
=> ( ( A @ ( TA @ uminus_uminus ) )
= A ) )
& ( ( ( A @ ( TA @ uminus_uminus ) )
= A )
=> ( A
= ( TA @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(129,axiom,
! [TA: $tType,TB: $tType] : ( TA @ ( TB @ sum_sum ) @ cl_HOL_Oequal ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_sum___HOL_Oequal) ).
thf(582,plain,
! [TA: $tType,TB: $tType] : ( TA @ ( TB @ sum_sum ) @ cl_HOL_Oequal ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(14,axiom,
! [TA: $tType,A: TA @ hoare_28830079triple] :
( ( A @ ( TA @ hoare_334633230triple @ ( bool @ ( TA @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ ( TA @ hoare_28830079triple @ aa ) ) ) @ ( TA @ hoare_689268419triple @ ( TA @ hoare_28830079triple @ ( bool @ ( TA @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ aa ) ) ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_Rep__triple__inverse) ).
thf(202,plain,
! [TA: $tType,A: TA @ hoare_28830079triple] :
( ( A @ ( TA @ hoare_334633230triple @ ( bool @ ( TA @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ ( TA @ hoare_28830079triple @ aa ) ) ) @ ( TA @ hoare_689268419triple @ ( TA @ hoare_28830079triple @ ( bool @ ( TA @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ aa ) ) ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(138,axiom,
! [A: bool] :
( ( A = fFalse )
| ( A = fTrue ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fFalse_1_1_T) ).
thf(597,plain,
! [A: bool] :
( ( A = fFalse )
| ( A = fTrue ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(65,axiom,
! [A: nat] :
~ ( A @ ( A @ ( nat @ ord_less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_less__not__refl) ).
thf(385,plain,
! [A: nat] :
~ ( A @ ( A @ ( nat @ ord_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
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(54,axiom,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: TA] :
( ( ( A @ ( TA @ sgn_sgn ) )
= ( TA @ zero_zero ) )
<=> ( A
= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_sgn__0__0) ).
thf(340,plain,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: TA] :
( ( ( A
= ( TA @ zero_zero ) )
=> ( ( A @ ( TA @ sgn_sgn ) )
= ( TA @ zero_zero ) ) )
& ( ( ( A @ ( TA @ sgn_sgn ) )
= ( TA @ zero_zero ) )
=> ( A
= ( TA @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(4,axiom,
! [TA: $tType,A: TA @ hoare_28830079triple,B: TA @ hoare_28830079triple] :
( ( A @ ( B @ ( TA @ hoare_28830079triple @ equal_equal @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ ( TA @ hoare_28830079triple @ aa ) ) ) @ ( bool @ ( TA @ hoare_28830079triple @ aa ) ) ) @ pp )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_equal__triple__def) ).
thf(153,plain,
! [TA: $tType,A: TA @ hoare_28830079triple,B: TA @ hoare_28830079triple] :
( ( ( B = A )
=> ( A @ ( B @ ( TA @ hoare_28830079triple @ equal_equal @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ ( TA @ hoare_28830079triple @ aa ) ) ) @ ( bool @ ( TA @ hoare_28830079triple @ aa ) ) ) @ pp ) )
& ( ( A @ ( B @ ( TA @ hoare_28830079triple @ equal_equal @ ( bool @ ( TA @ hoare_28830079triple @ fun ) @ ( TA @ hoare_28830079triple @ aa ) ) ) @ ( bool @ ( TA @ hoare_28830079triple @ aa ) ) ) @ pp )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(44,axiom,
( ( fFalse @ ( bool @ size_size ) )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_bool_Osize_I4_J) ).
thf(301,plain,
( ( fFalse @ ( bool @ size_size ) )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(51,axiom,
! [A: nibble,B: nibble,C: nibble,D: nibble] :
( ( ( C @ ( D @ char1 ) )
= ( A @ ( B @ char1 ) ) )
<=> ( ( C = A )
& ( D = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_char_Oinject) ).
thf(320,plain,
! [A: nibble,B: nibble,C: nibble,D: nibble] :
( ( ( ( C = A )
& ( D = B ) )
=> ( ( C @ ( D @ char1 ) )
= ( A @ ( B @ char1 ) ) ) )
& ( ( ( C @ ( D @ char1 ) )
= ( A @ ( B @ char1 ) ) )
=> ( ( C = A )
& ( D = B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(112,axiom,
int @ zero_neq_one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Ozero__neq__one) ).
thf(565,plain,
int @ zero_neq_one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(117,axiom,
int @ one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Oone) ).
thf(570,plain,
int @ one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(9,axiom,
! [TA: $tType,A: TA @ hoare_28830079triple] :
~ ! [B: bool @ ( state @ fun ) @ ( TA @ fun ),C: com,D: bool @ ( state @ fun ) @ ( TA @ fun )] :
( A
!= ( D @ ( C @ ( B @ ( TA @ hoare_1841697145triple ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_triple_Oexhaust) ).
thf(184,plain,
! [TA: $tType,A: TA @ hoare_28830079triple] :
~ ! [B: bool @ ( state @ fun ) @ ( TA @ fun ),C: com,D: bool @ ( state @ fun ) @ ( TA @ fun )] :
( A
!= ( D @ ( C @ ( B @ ( TA @ hoare_1841697145triple ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(94,axiom,
! [A: nat] :
( ( A @ ( int @ semiring_1_of_nat ) @ ( int @ zero_zero @ ( int @ ord_less ) ) )
<=> ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_zero__less__int__conv) ).
thf(504,plain,
! [A: nat] :
( ( ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
=> ( A @ ( int @ semiring_1_of_nat ) @ ( int @ zero_zero @ ( int @ ord_less ) ) ) )
& ( ( A @ ( int @ semiring_1_of_nat ) @ ( int @ zero_zero @ ( int @ ord_less ) ) )
=> ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(58,axiom,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: TA] :
( ( TA @ zero_zero @ ( A @ ( TA @ sgn_sgn ) @ ( TA @ ord_less ) ) )
<=> ( TA @ zero_zero @ ( A @ ( TA @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_sgn__less) ).
thf(357,plain,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: TA] :
( ( ( TA @ zero_zero @ ( A @ ( TA @ ord_less ) ) )
=> ( TA @ zero_zero @ ( A @ ( TA @ sgn_sgn ) @ ( TA @ ord_less ) ) ) )
& ( ( TA @ zero_zero @ ( A @ ( TA @ sgn_sgn ) @ ( TA @ ord_less ) ) )
=> ( TA @ zero_zero @ ( A @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(90,axiom,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: nat] :
~ ( TA @ zero_zero @ ( A @ ( TA @ semiring_1_of_nat ) @ ( TA @ ord_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_of__nat__less__0__iff) ).
thf(492,plain,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: nat] :
~ ( TA @ zero_zero @ ( A @ ( TA @ semiring_1_of_nat ) @ ( TA @ ord_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(135,axiom,
fTrue @ pp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fTrue_1_1_U) ).
thf(591,plain,
fTrue @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(25,axiom,
! [TA: $tType,A: bool @ ( state @ fun ) @ ( TA @ fun ),B: com,C: bool @ ( state @ fun ) @ ( TA @ fun )] :
( ( A @ ( B @ ( C @ ( TA @ hoare_1841697145triple ) ) ) @ ( TA @ hoare_28830079triple @ size_size ) )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_triple_Osize_I2_J) ).
thf(238,plain,
! [TA: $tType,A: bool @ ( state @ fun ) @ ( TA @ fun ),B: com,C: bool @ ( state @ fun ) @ ( TA @ fun )] :
( ( A @ ( B @ ( C @ ( TA @ hoare_1841697145triple ) ) ) @ ( TA @ hoare_28830079triple @ size_size ) )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(121,axiom,
nat @ zero_neq_one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Ozero__neq__one) ).
thf(574,plain,
nat @ zero_neq_one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(87,axiom,
! [TA: $tType] :
( ( TA @ one )
=> ! [A: TA] :
( ( ( TA @ one_one )
= A )
<=> ( A
= ( TA @ one_one ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_one__reorient) ).
thf(480,plain,
! [TA: $tType] :
( ( TA @ one )
=> ! [A: TA] :
( ( ( A
= ( TA @ one_one ) )
=> ( ( TA @ one_one )
= A ) )
& ( ( ( TA @ one_one )
= A )
=> ( A
= ( TA @ one_one ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(28,axiom,
! [TA: $tType,TB: $tType,A: TB,B: bool @ ( TA @ fun ),C: TB @ ( TA @ fun ),D: TA @ ( TB @ fun )] :
( ( B @ ( C @ ( D @ ( TA @ ( TB @ type_definition ) ) ) ) )
=> ( B @ ( A @ ( D @ ( TA @ ( TB @ aa ) ) ) @ ( TA @ member ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_type__definition_ORep) ).
thf(243,plain,
! [TA: $tType,TB: $tType,A: TB,B: bool @ ( TA @ fun ),C: TB @ ( TA @ fun ),D: TA @ ( TB @ fun )] :
( ( B @ ( C @ ( D @ ( TA @ ( TB @ type_definition ) ) ) ) )
=> ( B @ ( A @ ( D @ ( TA @ ( TB @ aa ) ) ) @ ( TA @ member ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(33,axiom,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: TA] :
( ( ( TA @ zero_zero )
= A )
<=> ( A
= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_zero__reorient) ).
thf(265,plain,
! [TA: $tType] :
( ( TA @ zero )
=> ! [A: TA] :
( ( ( A
= ( TA @ zero_zero ) )
=> ( ( TA @ zero_zero )
= A ) )
& ( ( ( TA @ zero_zero )
= A )
=> ( A
= ( TA @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(40,axiom,
( ( fTrue @ bool_size )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_bool_Osize_I1_J) ).
thf(292,plain,
( ( fTrue @ bool_size )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(23,axiom,
~ induct_false,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_induct__false__def) ).
thf(233,plain,
~ induct_false,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(30,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TA,C: bool @ ( TB @ fun ),D: TA @ ( TB @ fun ),E: TB @ ( TA @ fun )] :
( ( C @ ( D @ ( E @ ( TB @ ( TA @ type_definition ) ) ) ) )
=> ( ( ( B @ ( E @ ( TB @ ( TA @ aa ) ) ) )
= ( A @ ( E @ ( TB @ ( TA @ aa ) ) ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_type__definition_ORep__inject) ).
thf(248,plain,
! [TA: $tType,TB: $tType,A: TA,B: TA,C: bool @ ( TB @ fun ),D: TA @ ( TB @ fun ),E: TB @ ( TA @ fun )] :
( ( C @ ( D @ ( E @ ( TB @ ( TA @ type_definition ) ) ) ) )
=> ( ( ( B = A )
=> ( ( B @ ( E @ ( TB @ ( TA @ aa ) ) ) )
= ( A @ ( E @ ( TB @ ( TA @ aa ) ) ) ) ) )
& ( ( ( B @ ( E @ ( TB @ ( TA @ aa ) ) ) )
= ( A @ ( E @ ( TB @ ( TA @ aa ) ) ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(76,axiom,
! [A: nat,B: bool @ ( nat @ fun )] :
( ( nat @ zero_zero @ ( B @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ( ! [C: nat] :
( ( C @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
=> ( ~ ( C @ ( B @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ? [D: nat] :
( ~ ( D @ ( B @ ( bool @ ( nat @ aa ) ) ) @ pp )
& ( C @ ( D @ ( nat @ ord_less ) ) ) ) ) )
=> ( A @ ( B @ ( bool @ ( nat @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_infinite__descent0) ).
thf(439,plain,
! [A: nat,B: bool @ ( nat @ fun )] :
( ( nat @ zero_zero @ ( B @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ( ! [C: nat] :
( ( C @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
=> ( ~ ( C @ ( B @ ( bool @ ( nat @ aa ) ) ) @ pp )
=> ? [D: nat] :
( ~ ( D @ ( B @ ( bool @ ( nat @ aa ) ) ) @ pp )
& ( C @ ( D @ ( nat @ ord_less ) ) ) ) ) )
=> ( A @ ( B @ ( bool @ ( nat @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(52,axiom,
! [A: nat] :
( ( A @ ( nat @ size_size ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_nat__size) ).
thf(334,plain,
! [A: nat] :
( ( A @ ( nat @ size_size ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(5,axiom,
! [TA: $tType,A: TA @ hoare_28830079triple,B: TA @ hoare_28830079triple] :
( ( ( B @ ( TA @ hoare_334633230triple @ ( bool @ ( TA @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ ( TA @ hoare_28830079triple @ aa ) ) ) )
= ( A @ ( TA @ hoare_334633230triple @ ( bool @ ( TA @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ ( TA @ hoare_28830079triple @ aa ) ) ) ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_Rep__triple__inject) ).
thf(160,plain,
! [TA: $tType,A: TA @ hoare_28830079triple,B: TA @ hoare_28830079triple] :
( ( ( B = A )
=> ( ( B @ ( TA @ hoare_334633230triple @ ( bool @ ( TA @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ ( TA @ hoare_28830079triple @ aa ) ) ) )
= ( A @ ( TA @ hoare_334633230triple @ ( bool @ ( TA @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ ( TA @ hoare_28830079triple @ aa ) ) ) ) ) )
& ( ( ( B @ ( TA @ hoare_334633230triple @ ( bool @ ( TA @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ ( TA @ hoare_28830079triple @ aa ) ) ) )
= ( A @ ( TA @ hoare_334633230triple @ ( bool @ ( TA @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ ( TA @ hoare_28830079triple @ aa ) ) ) ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(108,axiom,
int @ linord219039673up_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Olinordered__ab__group__add) ).
thf(561,plain,
int @ linord219039673up_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(72,axiom,
! [A: nat] :
( ( A
!= ( nat @ zero_zero ) )
=> ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_gr0I) ).
thf(424,plain,
! [A: nat] :
( ( A
!= ( nat @ zero_zero ) )
=> ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(12,axiom,
! [TA: $tType] :
( ( TA @ cl_HOL_Oequal )
=> ! [A: TA,B: TA] :
( ( A @ ( B @ ( TA @ equal_equal @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_equal__eq) ).
thf(192,plain,
! [TA: $tType] :
( ( TA @ cl_HOL_Oequal )
=> ! [A: TA,B: TA] :
( ( ( B = A )
=> ( A @ ( B @ ( TA @ equal_equal @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) )
& ( ( A @ ( B @ ( TA @ equal_equal @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(83,axiom,
! [TA: $tType] :
( ( TA @ semiring_1 )
=> ( ( nat @ zero_zero @ ( TA @ semiring_1_of_nat ) )
= ( TA @ zero_zero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_of__nat__0) ).
thf(467,plain,
! [TA: $tType] :
( ( TA @ semiring_1 )
=> ( ( nat @ zero_zero @ ( TA @ semiring_1_of_nat ) )
= ( TA @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(113,axiom,
int @ semiring_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Osemiring__1) ).
thf(566,plain,
int @ semiring_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(59,axiom,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: TA] :
( ( A @ ( TA @ sgn_sgn ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
<=> ( A @ ( TA @ zero_zero @ ( TA @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_sgn__greater) ).
thf(361,plain,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: TA] :
( ( ( A @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( A @ ( TA @ sgn_sgn ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) ) )
& ( ( A @ ( TA @ sgn_sgn ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( A @ ( TA @ zero_zero @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(75,axiom,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: nat] :
( ( A @ ( TA @ semiring_1_of_nat ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
<=> ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_of__nat__0__less__iff) ).
thf(435,plain,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: nat] :
( ( ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
=> ( A @ ( TA @ semiring_1_of_nat ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) ) )
& ( ( A @ ( TA @ semiring_1_of_nat ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(101,axiom,
nibble @ enum,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_String_Onibble___Enum_Oenum) ).
thf(551,plain,
nibble @ enum,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(125,axiom,
nat @ cl_HOL_Oequal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___HOL_Oequal) ).
thf(578,plain,
nat @ cl_HOL_Oequal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(50,axiom,
! [TA: $tType] :
( ( TA @ sgn_if )
=> ( ( TA @ zero_zero @ ( TA @ sgn_sgn ) )
= ( TA @ zero_zero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_sgn0) ).
thf(317,plain,
! [TA: $tType] :
( ( TA @ sgn_if )
=> ( ( TA @ zero_zero @ ( TA @ sgn_sgn ) )
= ( TA @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(66,axiom,
! [A: nat,B: nat] :
( ( B != A )
<=> ( ( B @ ( A @ ( nat @ ord_less ) ) )
| ( A @ ( B @ ( nat @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_nat__neq__iff) ).
thf(388,plain,
! [A: nat,B: nat] :
( ( ( ( B @ ( A @ ( nat @ ord_less ) ) )
| ( A @ ( B @ ( nat @ ord_less ) ) ) )
=> ( B != A ) )
& ( ( B != A )
=> ( ( B @ ( A @ ( nat @ ord_less ) ) )
| ( A @ ( B @ ( nat @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(88,axiom,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ( TA @ one_one @ ( TA @ zero_zero @ ( TA @ ord_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_zero__less__one) ).
thf(488,plain,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ( TA @ one_one @ ( TA @ zero_zero @ ( TA @ ord_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(103,axiom,
char @ enum,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_String_Ochar___Enum_Oenum) ).
thf(554,plain,
char @ enum,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(99,axiom,
! [TA: $tType] :
( ( TA @ linord219039673up_add )
=> ! [A: TA] :
( ( A
= ( A @ ( TA @ uminus_uminus ) ) )
<=> ( A
= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_equal__neg__zero) ).
thf(537,plain,
! [TA: $tType] :
( ( TA @ linord219039673up_add )
=> ! [A: TA] :
( ( ( A
= ( TA @ zero_zero ) )
=> ( A
= ( A @ ( TA @ uminus_uminus ) ) ) )
& ( ( A
= ( A @ ( TA @ uminus_uminus ) ) )
=> ( A
= ( TA @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(134,axiom,
fTrue @ pp,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_2_1_U) ).
thf(590,plain,
fTrue @ pp,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(18,axiom,
! [TA: $tType,A: bool @ ( TA @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ),B: bool @ ( TA @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ ( com @ sum_sum ) @ node ) @ fun )] :
( ( TA @ hoare_711253694ep_set @ ( bool @ ( TA @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ collect ) @ ( B @ ( bool @ ( TA @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ member ) ) )
=> ( ( TA @ hoare_711253694ep_set @ ( bool @ ( TA @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ collect ) @ ( A @ ( bool @ ( TA @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ member ) ) )
=> ( ( ( B @ ( TA @ hoare_689268419triple @ ( TA @ hoare_28830079triple @ ( bool @ ( TA @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ aa ) ) ) )
= ( A @ ( TA @ hoare_689268419triple @ ( TA @ hoare_28830079triple @ ( bool @ ( TA @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ aa ) ) ) ) )
<=> ( B = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_Abs__triple__inject) ).
thf(212,plain,
! [TA: $tType,A: bool @ ( TA @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ),B: bool @ ( TA @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ ( com @ sum_sum ) @ node ) @ fun )] :
( ( TA @ hoare_711253694ep_set @ ( bool @ ( TA @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ collect ) @ ( B @ ( bool @ ( TA @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ member ) ) )
=> ( ( TA @ hoare_711253694ep_set @ ( bool @ ( TA @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ collect ) @ ( A @ ( bool @ ( TA @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ member ) ) )
=> ( ( ( B = A )
=> ( ( B @ ( TA @ hoare_689268419triple @ ( TA @ hoare_28830079triple @ ( bool @ ( TA @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ aa ) ) ) )
= ( A @ ( TA @ hoare_689268419triple @ ( TA @ hoare_28830079triple @ ( bool @ ( TA @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ aa ) ) ) ) ) )
& ( ( ( B @ ( TA @ hoare_689268419triple @ ( TA @ hoare_28830079triple @ ( bool @ ( TA @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ aa ) ) ) )
= ( A @ ( TA @ hoare_689268419triple @ ( TA @ hoare_28830079triple @ ( bool @ ( TA @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ aa ) ) ) ) )
=> ( B = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(81,axiom,
! [TA: $tType] :
( ( TA @ semiring_char_0 )
=> ! [A: nat,B: nat] :
( ( ( B @ ( TA @ semiring_1_of_nat ) )
= ( A @ ( TA @ semiring_1_of_nat ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_of__nat__eq__iff) ).
thf(457,plain,
! [TA: $tType] :
( ( TA @ semiring_char_0 )
=> ! [A: nat,B: nat] :
( ( ( B = A )
=> ( ( B @ ( TA @ semiring_1_of_nat ) )
= ( A @ ( TA @ semiring_1_of_nat ) ) ) )
& ( ( ( B @ ( TA @ semiring_1_of_nat ) )
= ( A @ ( TA @ semiring_1_of_nat ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(116,axiom,
int @ zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ozero) ).
thf(569,plain,
int @ zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(62,axiom,
! [A: nat] :
( ( A
!= ( nat @ zero_zero ) )
<=> ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_neq0__conv) ).
thf(371,plain,
! [A: nat] :
( ( ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
=> ( A
!= ( nat @ zero_zero ) ) )
& ( ( A
!= ( nat @ zero_zero ) )
=> ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(15,axiom,
! [TA: $tType,A: TA @ hoare_28830079triple] : ( TA @ hoare_711253694ep_set @ ( bool @ ( TA @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ collect ) @ ( A @ ( TA @ hoare_334633230triple @ ( bool @ ( TA @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ ( TA @ hoare_28830079triple @ aa ) ) ) @ ( bool @ ( TA @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ member ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_Rep__triple) ).
thf(205,plain,
! [TA: $tType,A: TA @ hoare_28830079triple] : ( TA @ hoare_711253694ep_set @ ( bool @ ( TA @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ collect ) @ ( A @ ( TA @ hoare_334633230triple @ ( bool @ ( TA @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ ( TA @ hoare_28830079triple @ aa ) ) ) @ ( bool @ ( TA @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ member ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(48,axiom,
! [A: nibble,B: nibble] :
( ( A @ ( B @ char1 ) @ ( char @ size_size ) )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_char_Osize_I2_J) ).
thf(311,plain,
! [A: nibble,B: nibble] :
( ( A @ ( B @ char1 ) @ ( char @ size_size ) )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(106,axiom,
! [TA: $tType,TB: $tType] :
( ( ( TB @ enum )
& ( TA @ cl_HOL_Oequal ) )
=> ( TA @ ( TB @ fun ) @ cl_HOL_Oequal ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun___HOL_Oequal) ).
thf(558,plain,
! [TA: $tType,TB: $tType] :
( ( ( TB @ enum )
& ( TA @ cl_HOL_Oequal ) )
=> ( TA @ ( TB @ fun ) @ cl_HOL_Oequal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(98,axiom,
! [TA: $tType] :
( ( TA @ group_add )
=> ! [A: TA] :
( ( ( A @ ( TA @ uminus_uminus ) )
= ( TA @ zero_zero ) )
<=> ( A
= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_neg__equal__0__iff__equal) ).
thf(530,plain,
! [TA: $tType] :
( ( TA @ group_add )
=> ! [A: TA] :
( ( ( A
= ( TA @ zero_zero ) )
=> ( ( A @ ( TA @ uminus_uminus ) )
= ( TA @ zero_zero ) ) )
& ( ( ( A @ ( TA @ uminus_uminus ) )
= ( TA @ zero_zero ) )
=> ( A
= ( TA @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(132,axiom,
! [TA: $tType] : ( TA @ hoare_28830079triple @ cl_HOL_Oequal ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Hoare__Mirabelle__vtrypsmcwp_Otriple___HOL_Oequal) ).
thf(586,plain,
! [TA: $tType] : ( TA @ hoare_28830079triple @ cl_HOL_Oequal ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(120,axiom,
nat @ semiring_char_0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Nat_Osemiring__char__0) ).
thf(573,plain,
nat @ semiring_char_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(42,axiom,
! [A: char] :
( ( A @ ( char @ size_size ) )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_size__char) ).
thf(296,plain,
! [A: char] :
( ( A @ ( char @ size_size ) )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(77,axiom,
! [TA: $tType,TB: $tType,A: TB @ ( TA @ fun ),B: TB @ ( TA @ fun )] :
( ! [C: TA] :
( ( C @ ( B @ ( TB @ ( TA @ aa ) ) ) )
= ( C @ ( A @ ( TB @ ( TA @ aa ) ) ) ) )
=> ( B = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_ext) ).
thf(444,plain,
! [TA: $tType,TB: $tType,A: TB @ ( TA @ fun ),B: TB @ ( TA @ fun )] :
( ! [C: TA] :
( ( C @ ( B @ ( TB @ ( TA @ aa ) ) ) )
= ( C @ ( A @ ( TB @ ( TA @ aa ) ) ) ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(130,axiom,
nibble @ cl_HOL_Oequal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_String_Onibble___HOL_Oequal) ).
thf(584,plain,
nibble @ cl_HOL_Oequal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(109,axiom,
int @ linordered_semidom,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__semidom) ).
thf(562,plain,
int @ linordered_semidom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(68,axiom,
! [A: nat] :
~ ( A @ ( A @ ( nat @ ord_less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_less__irrefl__nat) ).
thf(402,plain,
! [A: nat] :
~ ( A @ ( A @ ( nat @ ord_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(124,axiom,
nat @ one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Oone) ).
thf(577,plain,
nat @ one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(126,axiom,
bool @ cl_HOL_Oequal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL_Obool___HOL_Oequal) ).
thf(579,plain,
bool @ cl_HOL_Oequal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(71,axiom,
! [A: bool @ ( nat @ fun ) @ ( nat @ fun ),B: nat,C: nat] :
( ( ( B @ ( C @ ( nat @ ord_less ) ) )
=> ( C @ ( B @ ( A @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) )
=> ( ( ( C = B )
=> ( C @ ( B @ ( A @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) )
=> ( ( ( C @ ( B @ ( nat @ ord_less ) ) )
=> ( C @ ( B @ ( A @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) )
=> ( C @ ( B @ ( A @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_nat__less__cases) ).
thf(413,plain,
! [A: bool @ ( nat @ fun ) @ ( nat @ fun ),B: nat,C: nat] :
( ( ( B @ ( C @ ( nat @ ord_less ) ) )
=> ( C @ ( B @ ( A @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) )
=> ( ( ( C = B )
=> ( C @ ( B @ ( A @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) )
=> ( ( ( C @ ( B @ ( nat @ ord_less ) ) )
=> ( C @ ( B @ ( A @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) )
=> ( C @ ( B @ ( A @ ( bool @ ( nat @ fun ) @ ( nat @ aa ) ) ) @ ( bool @ ( nat @ aa ) ) ) @ pp ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(64,axiom,
! [A: nat] :
~ ( nat @ zero_zero @ ( A @ ( nat @ ord_less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_less__zeroE) ).
thf(382,plain,
! [A: nat] :
~ ( nat @ zero_zero @ ( A @ ( nat @ ord_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(119,axiom,
nat @ linordered_semidom,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Olinordered__semidom) ).
thf(572,plain,
nat @ linordered_semidom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(93,axiom,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: TA] :
( ( ( A @ ( TA @ sgn_sgn ) )
= ( TA @ one_one ) )
<=> ( A @ ( TA @ zero_zero @ ( TA @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_sgn__1__pos) ).
thf(498,plain,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: TA] :
( ( ( A @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( ( A @ ( TA @ sgn_sgn ) )
= ( TA @ one_one ) ) )
& ( ( ( A @ ( TA @ sgn_sgn ) )
= ( TA @ one_one ) )
=> ( A @ ( TA @ zero_zero @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(8,axiom,
! [TA: $tType,TB: $tType,A: bool @ ( state @ fun ) @ ( TA @ fun ),B: com,C: bool @ ( state @ fun ) @ ( TA @ fun ),D: TB @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ fun ) @ ( com @ fun ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ fun )] :
( ( A @ ( B @ ( C @ ( TA @ hoare_1841697145triple ) ) ) @ ( D @ ( TB @ ( TA @ hoare_376461865e_case ) ) ) )
= ( A @ ( B @ ( C @ ( D @ ( TB @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ fun ) @ ( com @ fun ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ fun ) @ ( com @ aa ) ) ) @ ( TB @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_triple_Osimps_I2_J) ).
thf(181,plain,
! [TA: $tType,TB: $tType,A: bool @ ( state @ fun ) @ ( TA @ fun ),B: com,C: bool @ ( state @ fun ) @ ( TA @ fun ),D: TB @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ fun ) @ ( com @ fun ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ fun )] :
( ( A @ ( B @ ( C @ ( TA @ hoare_1841697145triple ) ) ) @ ( D @ ( TB @ ( TA @ hoare_376461865e_case ) ) ) )
= ( A @ ( B @ ( C @ ( D @ ( TB @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ fun ) @ ( com @ fun ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ fun ) @ ( com @ aa ) ) ) @ ( TB @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(10,axiom,
! [TA: $tType] :
( ( TA @ cl_HOL_Oequal )
=> ( ( TA @ equal_equal )
= ( TA @ fequal ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_equal) ).
thf(187,plain,
! [TA: $tType] :
( ( TA @ cl_HOL_Oequal )
=> ( ( TA @ equal_equal )
= ( TA @ fequal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(19,axiom,
! [TA: $tType,A: bool @ ( TA @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ ( com @ sum_sum ) @ node ) @ fun )] :
( ( TA @ hoare_711253694ep_set @ ( bool @ ( TA @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ collect ) @ ( A @ ( bool @ ( TA @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ member ) ) )
=> ( ( A @ ( TA @ hoare_689268419triple @ ( TA @ hoare_28830079triple @ ( bool @ ( TA @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ aa ) ) ) @ ( TA @ hoare_334633230triple @ ( bool @ ( TA @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ ( TA @ hoare_28830079triple @ aa ) ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_Abs__triple__inverse) ).
thf(219,plain,
! [TA: $tType,A: bool @ ( TA @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ ( com @ sum_sum ) @ node ) @ fun )] :
( ( TA @ hoare_711253694ep_set @ ( bool @ ( TA @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ collect ) @ ( A @ ( bool @ ( TA @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ member ) ) )
=> ( ( A @ ( TA @ hoare_689268419triple @ ( TA @ hoare_28830079triple @ ( bool @ ( TA @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ aa ) ) ) @ ( TA @ hoare_334633230triple @ ( bool @ ( TA @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ ( TA @ hoare_28830079triple @ aa ) ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(29,axiom,
! [TA: $tType,TB: $tType,A: TA,B: bool @ ( TB @ fun ),C: TA @ ( TB @ fun ),D: TB @ ( TA @ fun )] :
( ( B @ ( C @ ( D @ ( TB @ ( TA @ type_definition ) ) ) ) )
=> ( ( A @ ( D @ ( TB @ ( TA @ aa ) ) ) @ ( C @ ( TA @ ( TB @ aa ) ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_type__definition_ORep__inverse) ).
thf(245,plain,
! [TA: $tType,TB: $tType,A: TA,B: bool @ ( TB @ fun ),C: TA @ ( TB @ fun ),D: TB @ ( TA @ fun )] :
( ( B @ ( C @ ( D @ ( TB @ ( TA @ type_definition ) ) ) ) )
=> ( ( A @ ( D @ ( TB @ ( TA @ aa ) ) ) @ ( C @ ( TA @ ( TB @ aa ) ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(45,axiom,
! [A: literal] :
( ( A @ ( literal @ size_size ) )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_size__literal__def) ).
thf(303,plain,
! [A: literal] :
( ( A @ ( literal @ size_size ) )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(79,axiom,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( A @ ( TA @ collect ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_Collect__def) ).
thf(451,plain,
! [TA: $tType,A: bool @ ( TA @ fun )] :
( ( A @ ( TA @ collect ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(114,axiom,
int @ group_add,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Ogroup__add) ).
thf(567,plain,
int @ group_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(86,axiom,
! [TA: $tType] :
( ( TA @ zero_neq_one )
=> ( ( TA @ one_one )
!= ( TA @ zero_zero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_one__neq__zero) ).
thf(477,plain,
! [TA: $tType] :
( ( TA @ zero_neq_one )
=> ( ( TA @ one_one )
!= ( TA @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(91,axiom,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: nat,B: nat] :
( ( A @ ( TA @ semiring_1_of_nat ) @ ( B @ ( TA @ semiring_1_of_nat ) @ ( TA @ ord_less ) ) )
=> ( A @ ( B @ ( nat @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_of__nat__less__imp__less) ).
thf(494,plain,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: nat,B: nat] :
( ( A @ ( TA @ semiring_1_of_nat ) @ ( B @ ( TA @ semiring_1_of_nat ) @ ( TA @ ord_less ) ) )
=> ( A @ ( B @ ( nat @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(102,axiom,
! [TA: $tType,TB: $tType] :
( ( ( TB @ enum )
& ( TA @ enum ) )
=> ( TA @ ( TB @ sum_sum ) @ enum ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_sum___Enum_Oenum) ).
thf(552,plain,
! [TA: $tType,TB: $tType] :
( ( ( TB @ enum )
& ( TA @ enum ) )
=> ( TA @ ( TB @ sum_sum ) @ enum ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(67,axiom,
! [A: nat,B: nat] :
( ( B != A )
=> ( ~ ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( B @ ( A @ ( nat @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_linorder__neqE__nat) ).
thf(399,plain,
! [A: nat,B: nat] :
( ( B != A )
=> ( ~ ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( B @ ( A @ ( nat @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(36,axiom,
! [TA: $tType,TB: $tType,A: TA,B: bool @ ( TA @ fun ),C: bool @ ( TB @ fun ),D: TA @ ( TB @ fun ),E: TB @ ( TA @ fun )] :
( ( C @ ( D @ ( E @ ( TB @ ( TA @ type_definition ) ) ) ) )
=> ( ! [F: TB] :
( ( C @ ( F @ ( TB @ member ) ) )
=> ( F @ ( D @ ( TA @ ( TB @ aa ) ) ) @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp ) )
=> ( A @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_type__definition_OAbs__induct) ).
thf(278,plain,
! [TA: $tType,TB: $tType,A: TA,B: bool @ ( TA @ fun ),C: bool @ ( TB @ fun ),D: TA @ ( TB @ fun ),E: TB @ ( TA @ fun )] :
( ( C @ ( D @ ( E @ ( TB @ ( TA @ type_definition ) ) ) ) )
=> ( ! [F: TB] :
( ( C @ ( F @ ( TB @ member ) ) )
=> ( F @ ( D @ ( TA @ ( TB @ aa ) ) ) @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp ) )
=> ( A @ ( B @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(46,axiom,
! [A: bool] :
( ( A @ ( bool @ size_size ) )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_size__bool) ).
thf(306,plain,
! [A: bool] :
( ( A @ ( bool @ size_size ) )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(110,axiom,
int @ linordered_idom,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__idom) ).
thf(563,plain,
int @ linordered_idom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(43,axiom,
( ( fTrue @ ( bool @ size_size ) )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_bool_Osize_I3_J) ).
thf(299,plain,
( ( fTrue @ ( bool @ size_size ) )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(21,axiom,
! [TA: $tType,A: TA @ hoare_28830079triple] :
~ ! [B: bool @ ( TA @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ ( com @ sum_sum ) @ node ) @ fun )] :
( ( A
= ( B @ ( TA @ hoare_689268419triple @ ( TA @ hoare_28830079triple @ ( bool @ ( TA @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ aa ) ) ) ) )
=> ~ ( TA @ hoare_711253694ep_set @ ( bool @ ( TA @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ collect ) @ ( B @ ( bool @ ( TA @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ member ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_Abs__triple__cases) ).
thf(226,plain,
! [TA: $tType,A: TA @ hoare_28830079triple] :
~ ! [B: bool @ ( TA @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ ( com @ sum_sum ) @ node ) @ fun )] :
( ( A
= ( B @ ( TA @ hoare_689268419triple @ ( TA @ hoare_28830079triple @ ( bool @ ( TA @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ aa ) ) ) ) )
=> ~ ( TA @ hoare_711253694ep_set @ ( bool @ ( TA @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ collect ) @ ( B @ ( bool @ ( TA @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ member ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(26,axiom,
induct_true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_induct__true__def) ).
thf(241,plain,
induct_true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(6,axiom,
! [TA: $tType,A: bool @ ( state @ fun ) @ ( TA @ fun ),B: com,C: bool @ ( state @ fun ) @ ( TA @ fun ),D: bool @ ( state @ fun ) @ ( TA @ fun ),E: com,F: bool @ ( state @ fun ) @ ( TA @ fun )] :
( ( ( D @ ( E @ ( F @ ( TA @ hoare_1841697145triple ) ) ) )
= ( A @ ( B @ ( C @ ( TA @ hoare_1841697145triple ) ) ) ) )
<=> ( ( D = A )
& ( E = B )
& ( F = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_triple_Oinject) ).
thf(167,plain,
! [TA: $tType,A: bool @ ( state @ fun ) @ ( TA @ fun ),B: com,C: bool @ ( state @ fun ) @ ( TA @ fun ),D: bool @ ( state @ fun ) @ ( TA @ fun ),E: com,F: bool @ ( state @ fun ) @ ( TA @ fun )] :
( ( ( ( D = A )
& ( E = B )
& ( F = C ) )
=> ( ( D @ ( E @ ( F @ ( TA @ hoare_1841697145triple ) ) ) )
= ( A @ ( B @ ( C @ ( TA @ hoare_1841697145triple ) ) ) ) ) )
& ( ( ( D @ ( E @ ( F @ ( TA @ hoare_1841697145triple ) ) ) )
= ( A @ ( B @ ( C @ ( TA @ hoare_1841697145triple ) ) ) ) )
=> ( ( D = A )
& ( E = B )
& ( F = C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(89,axiom,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ~ ( TA @ zero_zero @ ( TA @ one_one @ ( TA @ ord_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_not__one__less__zero) ).
thf(490,plain,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ~ ( TA @ zero_zero @ ( TA @ one_one @ ( TA @ ord_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(31,axiom,
! [TA: $tType,TB: $tType,A: TA,B: bool @ ( TA @ fun ),C: TB @ ( TA @ fun ),D: TA @ ( TB @ fun )] :
( ( B @ ( C @ ( D @ ( TA @ ( TB @ type_definition ) ) ) ) )
=> ( ( B @ ( A @ ( TA @ member ) ) )
=> ( ( A @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( D @ ( TA @ ( TB @ aa ) ) ) )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_type__definition_OAbs__inverse) ).
thf(255,plain,
! [TA: $tType,TB: $tType,A: TA,B: bool @ ( TA @ fun ),C: TB @ ( TA @ fun ),D: TA @ ( TB @ fun )] :
( ( B @ ( C @ ( D @ ( TA @ ( TB @ type_definition ) ) ) ) )
=> ( ( B @ ( A @ ( TA @ member ) ) )
=> ( ( A @ ( C @ ( TB @ ( TA @ aa ) ) ) @ ( D @ ( TA @ ( TB @ aa ) ) ) )
= A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(17,axiom,
! [TA: $tType,A: bool @ ( TA @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ ( com @ sum_sum ) @ node ) @ fun )] :
( ( TA @ hoare_711253694ep_set @ ( bool @ ( TA @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ collect ) @ ( A @ ( bool @ ( TA @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ member ) ) )
=> ~ ! [B: TA @ hoare_28830079triple] :
( A
!= ( B @ ( TA @ hoare_334633230triple @ ( bool @ ( TA @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ ( TA @ hoare_28830079triple @ aa ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_Rep__triple__cases) ).
thf(209,plain,
! [TA: $tType,A: bool @ ( TA @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ ( com @ sum_sum ) @ node ) @ fun )] :
( ( TA @ hoare_711253694ep_set @ ( bool @ ( TA @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ collect ) @ ( A @ ( bool @ ( TA @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ member ) ) )
=> ~ ! [B: TA @ hoare_28830079triple] :
( A
!= ( B @ ( TA @ hoare_334633230triple @ ( bool @ ( TA @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ ( TA @ hoare_28830079triple @ aa ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(96,axiom,
! [TA: $tType] :
( ( TA @ group_add )
=> ! [A: TA,B: TA] :
( ( ( B @ ( TA @ uminus_uminus ) )
= ( A @ ( TA @ uminus_uminus ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_neg__equal__iff__equal) ).
thf(516,plain,
! [TA: $tType] :
( ( TA @ group_add )
=> ! [A: TA,B: TA] :
( ( ( B = A )
=> ( ( B @ ( TA @ uminus_uminus ) )
= ( A @ ( TA @ uminus_uminus ) ) ) )
& ( ( ( B @ ( TA @ uminus_uminus ) )
= ( A @ ( TA @ uminus_uminus ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(127,axiom,
state @ cl_HOL_Oequal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Com_Ostate___HOL_Oequal) ).
thf(580,plain,
state @ cl_HOL_Oequal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(37,axiom,
! [TA: $tType,TB: $tType,A: TB,B: bool @ ( TA @ fun ),C: TB @ ( TA @ fun ),D: TA @ ( TB @ fun )] :
( ( B @ ( C @ ( D @ ( TA @ ( TB @ type_definition ) ) ) ) )
=> ~ ! [E: TA] :
( ( A
= ( E @ ( C @ ( TB @ ( TA @ aa ) ) ) ) )
=> ~ ( B @ ( E @ ( TA @ member ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_type__definition_OAbs__cases) ).
thf(282,plain,
! [TA: $tType,TB: $tType,A: TB,B: bool @ ( TA @ fun ),C: TB @ ( TA @ fun ),D: TA @ ( TB @ fun )] :
( ( B @ ( C @ ( D @ ( TA @ ( TB @ type_definition ) ) ) ) )
=> ~ ! [E: TA] :
( ( A
= ( E @ ( C @ ( TB @ ( TA @ aa ) ) ) ) )
=> ~ ( B @ ( E @ ( TA @ member ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(70,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( B != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_less__not__refl3) ).
thf(409,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(13,axiom,
! [TA: $tType] :
( ( TA @ cl_HOL_Oequal )
=> ( ( TA @ fequal )
= ( TA @ equal_equal ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_eq__equal) ).
thf(199,plain,
! [TA: $tType] :
( ( TA @ cl_HOL_Oequal )
=> ( ( TA @ fequal )
= ( TA @ equal_equal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(131,axiom,
literal @ cl_HOL_Oequal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_String_Oliteral___HOL_Oequal) ).
thf(585,plain,
literal @ cl_HOL_Oequal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(100,axiom,
! [TA: $tType] :
( ( TA @ group_add )
=> ! [A: TA] :
( ( ( TA @ zero_zero )
= ( A @ ( TA @ uminus_uminus ) ) )
<=> ( ( TA @ zero_zero )
= A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_neg__0__equal__iff__equal) ).
thf(544,plain,
! [TA: $tType] :
( ( TA @ group_add )
=> ! [A: TA] :
( ( ( ( TA @ zero_zero )
= A )
=> ( ( TA @ zero_zero )
= ( A @ ( TA @ uminus_uminus ) ) ) )
& ( ( ( TA @ zero_zero )
= ( A @ ( TA @ uminus_uminus ) ) )
=> ( ( TA @ zero_zero )
= A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(84,axiom,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: nat,B: nat] :
( ( A @ ( TA @ semiring_1_of_nat ) @ ( B @ ( TA @ semiring_1_of_nat ) @ ( TA @ ord_less ) ) )
<=> ( A @ ( B @ ( nat @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_of__nat__less__iff) ).
thf(470,plain,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: nat,B: nat] :
( ( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( A @ ( TA @ semiring_1_of_nat ) @ ( B @ ( TA @ semiring_1_of_nat ) @ ( TA @ ord_less ) ) ) )
& ( ( A @ ( TA @ semiring_1_of_nat ) @ ( B @ ( TA @ semiring_1_of_nat ) @ ( TA @ ord_less ) ) )
=> ( A @ ( B @ ( nat @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(123,axiom,
nat @ zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Groups_Ozero) ).
thf(576,plain,
nat @ zero,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(139,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( B = A )
| ~ ( A @ ( B @ ( TA @ fequal @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_1_1_T) ).
thf(600,plain,
! [TA: $tType,A: TA,B: TA] :
( ( B = A )
| ~ ( A @ ( B @ ( TA @ fequal @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(49,axiom,
! [A: nibble,B: nibble] :
( ( A @ ( B @ char1 ) @ char_size )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_char_Osize_I1_J) ).
thf(314,plain,
! [A: nibble,B: nibble] :
( ( A @ ( B @ char1 ) @ char_size )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(118,axiom,
int @ cl_HOL_Oequal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___HOL_Oequal) ).
thf(571,plain,
int @ cl_HOL_Oequal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(137,axiom,
~ ( fFalse @ pp ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fFalse_1_1_U) ).
thf(595,plain,
~ ( fFalse @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(22,axiom,
! [TA: $tType] : ( TA @ hoare_711253694ep_set @ ( bool @ ( TA @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ collect ) @ ( TA @ hoare_689268419triple @ ( TA @ hoare_334633230triple @ ( bool @ ( TA @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ ( TA @ hoare_28830079triple @ type_definition ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_type__definition__triple) ).
thf(231,plain,
! [TA: $tType] : ( TA @ hoare_711253694ep_set @ ( bool @ ( TA @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ collect ) @ ( TA @ hoare_689268419triple @ ( TA @ hoare_334633230triple @ ( bool @ ( TA @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ ( TA @ hoare_28830079triple @ type_definition ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(105,axiom,
! [TA: $tType,TB: $tType] :
( ( ( TB @ enum )
& ( TA @ enum ) )
=> ( TA @ ( TB @ fun ) @ enum ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun___Enum_Oenum) ).
thf(556,plain,
! [TA: $tType,TB: $tType] :
( ( ( TB @ enum )
& ( TA @ enum ) )
=> ( TA @ ( TB @ fun ) @ enum ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(128,axiom,
char @ cl_HOL_Oequal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_String_Ochar___HOL_Oequal) ).
thf(581,plain,
char @ cl_HOL_Oequal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(61,axiom,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: TA,B: TA] :
( ( B != A )
=> ( ~ ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( B @ ( A @ ( TA @ ord_less ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_linorder__neqE__linordered__idom) ).
thf(368,plain,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: TA,B: TA] :
( ( B != A )
=> ( ~ ( A @ ( B @ ( TA @ ord_less ) ) )
=> ( B @ ( A @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(133,axiom,
~ ( fFalse @ pp ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_pp_1_1_U) ).
thf(588,plain,
~ ( fFalse @ pp ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(32,axiom,
! [TA: $tType,TB: $tType,A: TA,B: TA,C: bool @ ( TA @ fun ),D: TB @ ( TA @ fun ),E: TA @ ( TB @ fun )] :
( ( C @ ( D @ ( E @ ( TA @ ( TB @ type_definition ) ) ) ) )
=> ( ( C @ ( B @ ( TA @ member ) ) )
=> ( ( C @ ( A @ ( TA @ member ) ) )
=> ( ( ( B @ ( D @ ( TB @ ( TA @ aa ) ) ) )
= ( A @ ( D @ ( TB @ ( TA @ aa ) ) ) ) )
<=> ( B = A ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_type__definition_OAbs__inject) ).
thf(258,plain,
! [TA: $tType,TB: $tType,A: TA,B: TA,C: bool @ ( TA @ fun ),D: TB @ ( TA @ fun ),E: TA @ ( TB @ fun )] :
( ( C @ ( D @ ( E @ ( TA @ ( TB @ type_definition ) ) ) ) )
=> ( ( C @ ( B @ ( TA @ member ) ) )
=> ( ( C @ ( A @ ( TA @ member ) ) )
=> ( ( ( B = A )
=> ( ( B @ ( D @ ( TB @ ( TA @ aa ) ) ) )
= ( A @ ( D @ ( TB @ ( TA @ aa ) ) ) ) ) )
& ( ( ( B @ ( D @ ( TB @ ( TA @ aa ) ) ) )
= ( A @ ( D @ ( TB @ ( TA @ aa ) ) ) ) )
=> ( B = A ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(56,axiom,
! [TA: $tType,A: nibble,B: nibble,C: TA @ ( nibble @ fun ) @ ( nibble @ fun )] :
( ( A @ ( B @ char1 ) @ ( C @ ( TA @ char_case ) ) )
= ( A @ ( B @ ( C @ ( TA @ ( nibble @ fun ) @ ( nibble @ aa ) ) ) @ ( TA @ ( nibble @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_char_Osimps_I2_J) ).
thf(351,plain,
! [TA: $tType,A: nibble,B: nibble,C: TA @ ( nibble @ fun ) @ ( nibble @ fun )] :
( ( A @ ( B @ char1 ) @ ( C @ ( TA @ char_case ) ) )
= ( A @ ( B @ ( C @ ( TA @ ( nibble @ fun ) @ ( nibble @ aa ) ) ) @ ( TA @ ( nibble @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(115,axiom,
int @ sgn_if,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Osgn__if) ).
thf(568,plain,
int @ sgn_if,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(39,axiom,
( ( fFalse @ bool_size )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_bool_Osize_I2_J) ).
thf(290,plain,
( ( fFalse @ bool_size )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(24,axiom,
! [TA: $tType,A: bool @ ( state @ fun ) @ ( TA @ fun ),B: com,C: bool @ ( state @ fun ) @ ( TA @ fun ),D: nat @ ( TA @ fun )] :
( ( A @ ( B @ ( C @ ( TA @ hoare_1841697145triple ) ) ) @ ( D @ ( TA @ hoare_47506394e_size ) ) )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_triple_Osize_I1_J) ).
thf(235,plain,
! [TA: $tType,A: bool @ ( state @ fun ) @ ( TA @ fun ),B: com,C: bool @ ( state @ fun ) @ ( TA @ fun ),D: nat @ ( TA @ fun )] :
( ( A @ ( B @ ( C @ ( TA @ hoare_1841697145triple ) ) ) @ ( D @ ( TA @ hoare_47506394e_size ) ) )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(95,axiom,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: TA] :
( ( ( A @ ( TA @ sgn_sgn ) )
= ( TA @ one_one @ ( TA @ uminus_uminus ) ) )
<=> ( TA @ zero_zero @ ( A @ ( TA @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_sgn__1__neg) ).
thf(510,plain,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: TA] :
( ( ( TA @ zero_zero @ ( A @ ( TA @ ord_less ) ) )
=> ( ( A @ ( TA @ sgn_sgn ) )
= ( TA @ one_one @ ( TA @ uminus_uminus ) ) ) )
& ( ( ( A @ ( TA @ sgn_sgn ) )
= ( TA @ one_one @ ( TA @ uminus_uminus ) ) )
=> ( TA @ zero_zero @ ( A @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(16,axiom,
! [TA: $tType,A: bool @ ( bool @ ( TA @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ fun ),B: bool @ ( TA @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ ( com @ sum_sum ) @ node ) @ fun )] :
( ( TA @ hoare_711253694ep_set @ ( bool @ ( TA @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ collect ) @ ( B @ ( bool @ ( TA @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ member ) ) )
=> ( ! [C: TA @ hoare_28830079triple] : ( C @ ( TA @ hoare_334633230triple @ ( bool @ ( TA @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ ( TA @ hoare_28830079triple @ aa ) ) ) @ ( A @ ( bool @ ( bool @ ( TA @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ aa ) ) ) @ pp )
=> ( B @ ( A @ ( bool @ ( bool @ ( TA @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ aa ) ) ) @ pp ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_Rep__triple__induct) ).
thf(207,plain,
! [TA: $tType,A: bool @ ( bool @ ( TA @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ fun ),B: bool @ ( TA @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ ( com @ sum_sum ) @ node ) @ fun )] :
( ( TA @ hoare_711253694ep_set @ ( bool @ ( TA @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ collect ) @ ( B @ ( bool @ ( TA @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ member ) ) )
=> ( ! [C: TA @ hoare_28830079triple] : ( C @ ( TA @ hoare_334633230triple @ ( bool @ ( TA @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ ( TA @ hoare_28830079triple @ aa ) ) ) @ ( A @ ( bool @ ( bool @ ( TA @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ aa ) ) ) @ pp )
=> ( B @ ( A @ ( bool @ ( bool @ ( TA @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(38,axiom,
! [A: char] :
( ( A @ char_size )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_char__size) ).
thf(287,plain,
! [A: char] :
( ( A @ char_size )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(78,axiom,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA] :
( ( A @ ( B @ ( TA @ member ) ) )
<=> ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_75_mem__def) ).
thf(447,plain,
! [TA: $tType,A: bool @ ( TA @ fun ),B: TA] :
( ( ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp )
=> ( A @ ( B @ ( TA @ member ) ) ) )
& ( ( A @ ( B @ ( TA @ member ) ) )
=> ( B @ ( A @ ( bool @ ( TA @ aa ) ) ) @ pp ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(74,axiom,
! [A: nat] :
~ ( nat @ zero_zero @ ( A @ ( nat @ ord_less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_not__less0) ).
thf(432,plain,
! [A: nat] :
~ ( nat @ zero_zero @ ( A @ ( nat @ ord_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
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,
( ( ? [A: state,B: state] : ( A != B )
=> hoare_531836380gleton )
& ( hoare_531836380gleton
=> ? [A: state,B: state] : ( A != B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(69,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_less__not__refl2) ).
thf(405,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(11,axiom,
! [TA: $tType] :
( ( TA @ cl_HOL_Oequal )
=> ! [A: TA] : ( A @ ( A @ ( TA @ equal_equal @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_equal__refl) ).
thf(190,plain,
! [TA: $tType] :
( ( TA @ cl_HOL_Oequal )
=> ! [A: TA] : ( A @ ( A @ ( TA @ equal_equal @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(34,axiom,
! [TA: $tType,TB: $tType,A: TB,B: bool @ ( TB @ fun ),C: TA @ ( TB @ fun ),D: TB @ ( TA @ fun )] :
( ( B @ ( C @ ( D @ ( TB @ ( TA @ type_definition ) ) ) ) )
=> ( ( B @ ( A @ ( TB @ member ) ) )
=> ~ ! [E: TA] :
( A
!= ( E @ ( D @ ( TB @ ( TA @ aa ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_type__definition_ORep__cases) ).
thf(273,plain,
! [TA: $tType,TB: $tType,A: TB,B: bool @ ( TB @ fun ),C: TA @ ( TB @ fun ),D: TB @ ( TA @ fun )] :
( ( B @ ( C @ ( D @ ( TB @ ( TA @ type_definition ) ) ) ) )
=> ( ( B @ ( A @ ( TB @ member ) ) )
=> ~ ! [E: TA] :
( A
!= ( E @ ( D @ ( TB @ ( TA @ aa ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(140,axiom,
! [TA: $tType,A: TA,B: TA] :
( ( A @ ( B @ ( TA @ fequal @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
| ( B != A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fequal_2_1_T) ).
thf(603,plain,
! [TA: $tType,A: TA,B: TA] :
( ( A @ ( B @ ( TA @ fequal @ ( bool @ ( TA @ fun ) @ ( TA @ aa ) ) ) @ ( bool @ ( TA @ aa ) ) ) @ pp )
| ( B != A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(111,axiom,
int @ semiring_char_0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Nat_Osemiring__char__0) ).
thf(564,plain,
int @ semiring_char_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(27,axiom,
induct_true,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_induct__trueI) ).
thf(242,plain,
induct_true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(41,axiom,
( ( nat @ zero_zero @ nat_size )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_nat_Osize_I1_J) ).
thf(294,plain,
( ( nat @ zero_zero @ nat_size )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(85,axiom,
! [TA: $tType] :
( ( TA @ zero_neq_one )
=> ( ( TA @ zero_zero )
!= ( TA @ one_one ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_zero__neq__one) ).
thf(474,plain,
! [TA: $tType] :
( ( TA @ zero_neq_one )
=> ( ( TA @ zero_zero )
!= ( TA @ one_one ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(82,axiom,
! [TA: $tType] :
( ( TA @ semiring_1 )
=> ( ( nat @ one_one @ ( TA @ semiring_1_of_nat ) )
= ( TA @ one_one ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_of__nat__1) ).
thf(464,plain,
! [TA: $tType] :
( ( TA @ semiring_1 )
=> ( ( nat @ one_one @ ( TA @ semiring_1_of_nat ) )
= ( TA @ one_one ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(122,axiom,
nat @ semiring_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Osemiring__1) ).
thf(575,plain,
nat @ semiring_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(73,axiom,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( A
!= ( nat @ zero_zero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_gr__implies__not0) ).
thf(427,plain,
! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( A
!= ( nat @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(7,axiom,
! [TA: $tType,TB: $tType,A: bool @ ( state @ fun ) @ ( TA @ fun ),B: com,C: bool @ ( state @ fun ) @ ( TA @ fun ),D: TB @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ fun ) @ ( com @ fun ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ fun )] :
( ( A @ ( B @ ( C @ ( TA @ hoare_1841697145triple ) ) ) @ ( D @ ( TB @ ( TA @ hoare_678420151le_rec ) ) ) )
= ( A @ ( B @ ( C @ ( D @ ( TB @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ fun ) @ ( com @ fun ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ fun ) @ ( com @ aa ) ) ) @ ( TB @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_triple_Orecs) ).
thf(178,plain,
! [TA: $tType,TB: $tType,A: bool @ ( state @ fun ) @ ( TA @ fun ),B: com,C: bool @ ( state @ fun ) @ ( TA @ fun ),D: TB @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ fun ) @ ( com @ fun ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ fun )] :
( ( A @ ( B @ ( C @ ( TA @ hoare_1841697145triple ) ) ) @ ( D @ ( TB @ ( TA @ hoare_678420151le_rec ) ) ) )
= ( A @ ( B @ ( C @ ( D @ ( TB @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ fun ) @ ( com @ fun ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ aa ) ) ) @ ( TB @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ fun ) @ ( com @ aa ) ) ) @ ( TB @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(141,axiom,
? [A: state,B: state] : ( A != B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(607,plain,
? [A: state,B: state] : ( A != B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(53,axiom,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: TA] :
( ( A @ ( TA @ sgn_sgn ) @ ( TA @ sgn_sgn ) )
= ( A @ ( TA @ sgn_sgn ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_sgn__sgn) ).
thf(337,plain,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: TA] :
( ( A @ ( TA @ sgn_sgn ) @ ( TA @ sgn_sgn ) )
= ( A @ ( TA @ sgn_sgn ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(57,axiom,
! [TA: $tType,A: nibble,B: nibble,C: TA @ ( nibble @ fun ) @ ( nibble @ fun )] :
( ( A @ ( B @ char1 ) @ ( C @ ( TA @ char_rec ) ) )
= ( A @ ( B @ ( C @ ( TA @ ( nibble @ fun ) @ ( nibble @ aa ) ) ) @ ( TA @ ( nibble @ aa ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_char_Orecs) ).
thf(354,plain,
! [TA: $tType,A: nibble,B: nibble,C: TA @ ( nibble @ fun ) @ ( nibble @ fun )] :
( ( A @ ( B @ char1 ) @ ( C @ ( TA @ char_rec ) ) )
= ( A @ ( B @ ( C @ ( TA @ ( nibble @ fun ) @ ( nibble @ aa ) ) ) @ ( TA @ ( nibble @ aa ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(47,axiom,
( ( nat @ zero_zero @ ( nat @ size_size ) )
= ( nat @ zero_zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_nat_Osize_I3_J) ).
thf(309,plain,
( ( nat @ zero_zero @ ( nat @ size_size ) )
= ( nat @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(107,axiom,
com @ cl_HOL_Oequal,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Com_Ocom___HOL_Oequal) ).
thf(560,plain,
com @ cl_HOL_Oequal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(20,axiom,
! [TA: $tType,A: TA @ hoare_28830079triple,B: bool @ ( TA @ hoare_28830079triple @ fun )] :
( ! [C: bool @ ( TA @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ ( com @ sum_sum ) @ node ) @ fun )] :
( ( TA @ hoare_711253694ep_set @ ( bool @ ( TA @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ collect ) @ ( C @ ( bool @ ( TA @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ member ) ) )
=> ( C @ ( TA @ hoare_689268419triple @ ( TA @ hoare_28830079triple @ ( bool @ ( TA @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ aa ) ) ) @ ( B @ ( bool @ ( TA @ hoare_28830079triple @ aa ) ) ) @ pp ) )
=> ( A @ ( B @ ( bool @ ( TA @ hoare_28830079triple @ aa ) ) ) @ pp ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_Abs__triple__induct) ).
thf(222,plain,
! [TA: $tType,A: TA @ hoare_28830079triple,B: bool @ ( TA @ hoare_28830079triple @ fun )] :
( ! [C: bool @ ( TA @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ ( com @ sum_sum ) @ node ) @ fun )] :
( ( TA @ hoare_711253694ep_set @ ( bool @ ( TA @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ collect ) @ ( C @ ( bool @ ( TA @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ member ) ) )
=> ( C @ ( TA @ hoare_689268419triple @ ( TA @ hoare_28830079triple @ ( bool @ ( TA @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( TA @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ aa ) ) ) @ ( B @ ( bool @ ( TA @ hoare_28830079triple @ aa ) ) ) @ pp ) )
=> ( A @ ( B @ ( bool @ ( TA @ hoare_28830079triple @ aa ) ) ) @ pp ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(136,axiom,
! [A: bool] :
( ( A = fFalse )
| ( A = fTrue ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fTrue_1_1_T) ).
thf(592,plain,
! [A: bool] :
( ( A = fFalse )
| ( A = fTrue ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(92,axiom,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( A @ ( TA @ semiring_1_of_nat ) @ ( B @ ( TA @ semiring_1_of_nat ) @ ( TA @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_less__imp__of__nat__less) ).
thf(496,plain,
! [TA: $tType] :
( ( TA @ linordered_semidom )
=> ! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( A @ ( TA @ semiring_1_of_nat ) @ ( B @ ( TA @ semiring_1_of_nat ) @ ( TA @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(80,axiom,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: TA] :
( ( A @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( ( A @ ( TA @ sgn_sgn ) )
= ( TA @ one_one ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_sgn__pos) ).
thf(454,plain,
! [TA: $tType] :
( ( TA @ linordered_idom )
=> ! [A: TA] :
( ( A @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( ( A @ ( TA @ sgn_sgn ) )
= ( TA @ one_one ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(615,plain,
$false,
inference(e,[status(thm)],[365,347,555,276,379,523,582,202,597,385,142,340,153,301,320,565,570,184,504,357,492,591,238,574,480,243,265,292,233,248,439,334,160,561,424,192,467,566,361,435,551,578,317,388,488,554,537,590,212,457,569,371,205,311,558,530,586,573,296,444,584,562,402,577,579,413,382,572,498,181,187,219,245,303,451,567,477,494,552,399,278,306,563,299,226,241,167,490,255,209,516,580,282,409,199,585,544,470,576,600,314,571,595,231,556,581,368,588,258,351,568,290,235,510,207,287,447,432,146,405,190,273,603,564,242,294,474,464,575,427,178,607,337,354,309,560,222,592,496,454]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW504_5 : TPTP v9.3.1. Released v6.0.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.11/0.39 % Computer : n002.cluster.edu
% 0.11/0.39 % Model : x86_64 x86_64
% 0.11/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.39 % Memory : 8046.5625MB
% 0.11/0.39 % OS : Linux 6.8.0-71-generic
% 0.11/0.39 % CPULimit : 300
% 0.11/0.39 % WCLimit : 300
% 0.11/0.39 % DateTime : Sat Sep 26 16:12:20 UTC 2026
% 0.11/0.39 % CPUTime :
% 0.11/0.39 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.59/0.67 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.05/0.87 % [INFO] Parsing done (194ms).
% 1.05/0.88 % [INFO] Running in sequential loop mode.
% 1.94/1.07 % [INFO] eprover registered as external prover.
% 1.94/1.07 % [INFO] Scanning for conjecture ...
% 2.22/1.16 % [INFO] Found a conjecture (or negated_conjecture) and 139 axioms. Running axiom selection ...
% 2.22/1.19 % [INFO] Axiom selection finished. Selected 139 axioms (removed 0 axioms).
% 2.76/1.33 % [INFO] Problem is typed first-order (TPTP TFF).
% 2.76/1.35 % [INFO] Type checking passed.
% 2.76/1.35 % [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 ...
% 3.09/1.47 % [INFO] [Domain constraints] Detected constraint on state
% 3.09/1.47 % [INFO] [Domain constraints] dom(state) ⊆ {sk1}
% 6.42/2.15 % [INFO] [Domain constraints] Detected constraint on bool
% 6.42/2.15 % [INFO] [Domain constraints] dom(bool) ⊆ {fTrue,fFalse}
% 6.42/2.16 % [INFO] [Domain constraints] Detected constraint on bool
% 6.42/2.16 % [INFO] [Domain constraints] dom(bool) ⊆ {fTrue,fFalse}
% 15.73/6.42 % External prover 'e' found a proof!
% 15.73/6.43 % [INFO] Killing All external provers ...
% 15.73/6.43 % Time passed: 5952ms (effective reasoning time: 5547ms)
% 15.73/6.43 % 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)>
% 15.73/6.43 % 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
% 15.73/6.43 % No. of inferences in proof: 282
% 15.73/6.43 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 5952 ms resp. 5547 ms w/o parsing
% 16.07/6.57 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 16.07/6.57 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------