%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWW469+5 : TPTP v9.3.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n018.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 09:10:13 AM UTC 2026
% Result : Theorem 8.84s 2.86s
% Output : Refutation 9.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 63
% Syntax : Number of formulae : 128 ( 64 unt; 0 typ; 0 def)
% Number of atoms : 250 ( 103 equ; 0 cnn)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 4730 ( 30 ~; 4 |; 16 &;4578 @)
% ( 10 <=>; 92 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 27 ( 25 usr; 7 con; 0-4 aty)
% Number of variables : 318 ( 0 ^; 312 !; 6 ?; 318 :)
% Comments :
%------------------------------------------------------------------------------
thf(ti_decl,type,
ti: $i > $i > $i ).
thf(state_decl,type,
state: $i ).
thf(hBOOL_decl,type,
hBOOL: $i > $o ).
thf(hoare_1883395792gleton_decl,type,
hoare_1883395792gleton: $i ).
thf(hAPP_decl,type,
hAPP: $i > $i > $i > $i > $i ).
thf(fun_decl,type,
fun: $i > $i > $i ).
thf(bool_decl,type,
bool: $i ).
thf(type_definition_decl,type,
type_definition: $i > $i > $i ).
thf(member_decl,type,
member: $i > $i ).
thf(cl_HOL_Oequal_decl,type,
cl_HOL_Oequal: $i > $o ).
thf(fequal_decl,type,
fequal: $i > $i ).
thf(equal_equal_decl,type,
equal_equal: $i > $i ).
thf(enum_decl,type,
enum: $i > $o ).
thf(induct_false_decl,type,
induct_false: $i ).
thf(com_decl,type,
com: $i ).
thf(sum_sum_decl,type,
sum_sum: $i > $i > $i ).
thf(induct_true_decl,type,
induct_true: $i ).
thf(hoare_509422987triple_decl,type,
hoare_509422987triple: $i > $i ).
thf(node_decl,type,
node: $i > $i > $i ).
thf(hoare_2037801986triple_decl,type,
hoare_2037801986triple: $i > $i ).
thf(collect_decl,type,
collect: $i > $i ).
thf(hoare_1580379338ep_set_decl,type,
hoare_1580379338ep_set: $i > $i ).
thf(hoare_244953527triple_decl,type,
hoare_244953527triple: $i > $i ).
thf(undefined_decl,type,
undefined: $i > $i ).
thf(induct_equal_decl,type,
induct_equal: $i > $i ).
thf(43,axiom,
! [A: $i] :
( ( A @ member @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ fun ) @ ti ) )
= ( A @ member ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_member_res) ).
thf(185,plain,
! [A: $i] :
( ( A @ member @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ fun ) @ ti ) )
= ( A @ member ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(44,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ fequal @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
| ( ( B @ ( A @ ti ) )
!= ( C @ ( A @ ti ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_T) ).
thf(188,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ fequal @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
| ( ( B @ ( A @ ti ) )
!= ( C @ ( A @ ti ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(39,axiom,
( ( induct_true @ ( bool @ ti ) )
= induct_true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_HOL_Oinduct__true_res) ).
thf(173,plain,
( ( induct_true @ ( bool @ ti ) )
= induct_true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(46,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ type_definition ) @ ( bool @ ( bool @ ( B @ fun ) @ fun ) @ ( A @ ( B @ fun ) @ fun ) @ ( B @ ( A @ fun ) @ fun ) @ ti ) )
= ( B @ ( A @ type_definition ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Typedef_Otype__definition_res) ).
thf(194,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ type_definition ) @ ( bool @ ( bool @ ( B @ fun ) @ fun ) @ ( A @ ( B @ fun ) @ fun ) @ ( B @ ( A @ fun ) @ fun ) @ ti ) )
= ( B @ ( A @ type_definition ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(17,axiom,
! [A: $i,B: $i] : ( B @ ( A @ sum_sum ) @ cl_HOL_Oequal ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_sum___HOL_Oequal) ).
thf(95,plain,
! [A: $i,B: $i] : ( B @ ( A @ sum_sum ) @ cl_HOL_Oequal ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(48,axiom,
( ( hoare_1883395792gleton @ hBOOL )
<=> ? [A: $i,B: $i] :
( ( A @ ( state @ ti ) )
!= ( B @ ( state @ ti ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_state__not__singleton__def) ).
thf(199,plain,
( ( ? [A: $i,B: $i] :
( ( A @ ( state @ ti ) )
!= ( B @ ( state @ ti ) ) )
=> ( hoare_1883395792gleton @ hBOOL ) )
& ( ( hoare_1883395792gleton @ hBOOL )
=> ? [A: $i,B: $i] :
( ( A @ ( state @ ti ) )
!= ( B @ ( state @ ti ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(41,axiom,
! [A: $i] :
( ( A @ undefined @ ( A @ ti ) )
= ( A @ undefined ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_HOL_Oundefined_res) ).
thf(178,plain,
! [A: $i] :
( ( A @ undefined @ ( A @ ti ) )
= ( A @ undefined ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(3,axiom,
hoare_1883395792gleton @ hBOOL,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(69,plain,
hoare_1883395792gleton @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(20,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ hoare_509422987triple @ equal_equal @ ( bool @ ( A @ hoare_509422987triple @ fun ) @ ( A @ hoare_509422987triple @ hAPP ) ) ) @ ( bool @ ( A @ hoare_509422987triple @ hAPP ) ) ) @ hBOOL )
<=> ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_equal__triple__def) ).
thf(101,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B = C )
=> ( C @ ( B @ ( A @ hoare_509422987triple @ equal_equal @ ( bool @ ( A @ hoare_509422987triple @ fun ) @ ( A @ hoare_509422987triple @ hAPP ) ) ) @ ( bool @ ( A @ hoare_509422987triple @ hAPP ) ) ) @ hBOOL ) )
& ( ( C @ ( B @ ( A @ hoare_509422987triple @ equal_equal @ ( bool @ ( A @ hoare_509422987triple @ fun ) @ ( A @ hoare_509422987triple @ hAPP ) ) ) @ ( bool @ ( A @ hoare_509422987triple @ hAPP ) ) ) @ hBOOL )
=> ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(55,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ hoare_1580379338ep_set @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ collect @ ( bool @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ fun ) @ ( bool @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ fun ) @ hAPP ) ) ) @ ( C @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ member @ ( bool @ ( bool @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ fun ) @ fun ) @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( ! [D: $i] : ( D @ ( A @ hoare_2037801986triple @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ ( A @ hoare_509422987triple @ hAPP ) ) ) @ ( B @ ( bool @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( C @ ( B @ ( bool @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_Rep__triple__induct) ).
thf(234,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ hoare_1580379338ep_set @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ collect @ ( bool @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ fun ) @ ( bool @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ fun ) @ hAPP ) ) ) @ ( C @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ member @ ( bool @ ( bool @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ fun ) @ fun ) @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( ! [D: $i] : ( D @ ( A @ hoare_2037801986triple @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ ( A @ hoare_509422987triple @ hAPP ) ) ) @ ( B @ ( bool @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( C @ ( B @ ( bool @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(22,axiom,
! [A: $i] : ( A @ hoare_509422987triple @ cl_HOL_Oequal ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Hoare__Mirabelle__pjuwniqynr_Otriple___HOL_Oequal) ).
thf(115,plain,
! [A: $i] : ( A @ hoare_509422987triple @ cl_HOL_Oequal ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(24,axiom,
! [A: $i,B: $i] : ( A @ hoare_1580379338ep_set @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ collect @ ( bool @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ fun ) @ ( bool @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ fun ) @ hAPP ) ) ) @ ( B @ ( A @ hoare_2037801986triple @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ ( A @ hoare_509422987triple @ hAPP ) ) ) @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ member @ ( bool @ ( bool @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ fun ) @ fun ) @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ fun ) @ hAPP ) ) ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_Rep__triple) ).
thf(120,plain,
! [A: $i,B: $i] : ( A @ hoare_1580379338ep_set @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ collect @ ( bool @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ fun ) @ ( bool @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ fun ) @ hAPP ) ) ) @ ( B @ ( A @ hoare_2037801986triple @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ ( A @ hoare_509422987triple @ hAPP ) ) ) @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ member @ ( bool @ ( bool @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ fun ) @ fun ) @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ fun ) @ hAPP ) ) ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(15,axiom,
induct_true @ hBOOL,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_induct__trueI) ).
thf(93,plain,
induct_true @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(34,axiom,
! [A: $i,B: $i] :
~ ! [C: $i] :
( ( B
= ( C @ ( A @ hoare_244953527triple @ ( A @ hoare_509422987triple @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ hAPP ) ) ) ) )
=> ~ ( A @ hoare_1580379338ep_set @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ collect @ ( bool @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ fun ) @ ( bool @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ fun ) @ hAPP ) ) ) @ ( C @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ member @ ( bool @ ( bool @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ fun ) @ fun ) @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ fun ) @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_Abs__triple__cases) ).
thf(152,plain,
! [A: $i,B: $i] :
~ ! [C: $i] :
( ( B
= ( C @ ( A @ hoare_244953527triple @ ( A @ hoare_509422987triple @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ hAPP ) ) ) ) )
=> ~ ( A @ hoare_1580379338ep_set @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ collect @ ( bool @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ fun ) @ ( bool @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ fun ) @ hAPP ) ) ) @ ( C @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ member @ ( bool @ ( bool @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ fun ) @ fun ) @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ fun ) @ hAPP ) ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(33,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( D @ ( A @ ( B @ type_definition ) @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( B @ ( A @ fun ) @ fun ) @ ( A @ ( B @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( B @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ~ ! [G: $i] :
( ( ( C @ ( B @ ti ) )
= ( G @ ( E @ ( B @ ( A @ hAPP ) ) ) ) )
=> ~ ( F @ ( G @ ( A @ member @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_type__definition_OAbs__cases) ).
thf(147,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( D @ ( A @ ( B @ type_definition ) @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( B @ ( A @ fun ) @ fun ) @ ( A @ ( B @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( B @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ~ ! [G: $i] :
( ( ( C @ ( B @ ti ) )
= ( G @ ( E @ ( B @ ( A @ hAPP ) ) ) ) )
=> ~ ( F @ ( G @ ( A @ member @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(51,axiom,
! [A: $i] :
( ( A @ hoare_1580379338ep_set @ ( bool @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ fun ) @ ti ) )
= ( A @ hoare_1580379338ep_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Hoare__Mirabelle__pjuwniqynr_Otriple_Otriple__rep__set_res) ).
thf(221,plain,
! [A: $i] :
( ( A @ hoare_1580379338ep_set @ ( bool @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ fun ) @ ti ) )
= ( A @ hoare_1580379338ep_set ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(5,axiom,
! [A: $i] :
( ( A @ cl_HOL_Oequal )
=> ( ( A @ fequal )
= ( A @ equal_equal ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_eq__equal) ).
thf(74,plain,
! [A: $i] :
( ( A @ cl_HOL_Oequal )
=> ( ( A @ fequal )
= ( A @ equal_equal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(49,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ hoare_1580379338ep_set @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ collect @ ( bool @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ fun ) @ ( bool @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ fun ) @ hAPP ) ) ) @ ( C @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ member @ ( bool @ ( bool @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ fun ) @ fun ) @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( ( A @ hoare_1580379338ep_set @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ collect @ ( bool @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ fun ) @ ( bool @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ fun ) @ hAPP ) ) ) @ ( B @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ member @ ( bool @ ( bool @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ fun ) @ fun ) @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( ( ( C @ ( A @ hoare_244953527triple @ ( A @ hoare_509422987triple @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ hAPP ) ) ) )
= ( B @ ( A @ hoare_244953527triple @ ( A @ hoare_509422987triple @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ hAPP ) ) ) ) )
<=> ( C = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_Abs__triple__inject) ).
thf(206,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ hoare_1580379338ep_set @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ collect @ ( bool @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ fun ) @ ( bool @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ fun ) @ hAPP ) ) ) @ ( C @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ member @ ( bool @ ( bool @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ fun ) @ fun ) @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( ( A @ hoare_1580379338ep_set @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ collect @ ( bool @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ fun ) @ ( bool @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ fun ) @ hAPP ) ) ) @ ( B @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ member @ ( bool @ ( bool @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ fun ) @ fun ) @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( ( ( C = B )
=> ( ( C @ ( A @ hoare_244953527triple @ ( A @ hoare_509422987triple @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ hAPP ) ) ) )
= ( B @ ( A @ hoare_244953527triple @ ( A @ hoare_509422987triple @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ hAPP ) ) ) ) ) )
& ( ( ( C @ ( A @ hoare_244953527triple @ ( A @ hoare_509422987triple @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ hAPP ) ) ) )
= ( B @ ( A @ hoare_244953527triple @ ( A @ hoare_509422987triple @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ hAPP ) ) ) ) )
=> ( C = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(12,axiom,
com @ cl_HOL_Oequal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Com_Ocom___HOL_Oequal) ).
thf(89,plain,
com @ cl_HOL_Oequal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(28,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ti ) )
= ( C @ ( A @ ti ) ) )
| ~ ( C @ ( B @ ( A @ fequal @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_1_1_T) ).
thf(133,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ ti ) )
= ( C @ ( A @ ti ) ) )
| ~ ( C @ ( B @ ( A @ fequal @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(59,axiom,
! [A: $i] :
( ( A @ fequal @ ( bool @ ( A @ fun ) @ ( A @ fun ) @ ti ) )
= ( A @ fequal ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_fequal_res) ).
thf(248,plain,
! [A: $i] :
( ( A @ fequal @ ( bool @ ( A @ fun ) @ ( A @ fun ) @ ti ) )
= ( A @ fequal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(23,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ti ) @ ( A @ ti ) )
= ( B @ ( A @ ti ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_ti_idem) ).
thf(117,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ti ) @ ( A @ ti ) )
= ( B @ ( A @ ti ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(63,axiom,
! [A: $i,B: $i] :
( ( A @ hoare_1580379338ep_set @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ collect @ ( bool @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ fun ) @ ( bool @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ fun ) @ hAPP ) ) ) @ ( B @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ member @ ( bool @ ( bool @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ fun ) @ fun ) @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ~ ! [C: $i] :
( B
!= ( C @ ( A @ hoare_2037801986triple @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ ( A @ hoare_509422987triple @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_Rep__triple__cases) ).
thf(270,plain,
! [A: $i,B: $i] :
( ( A @ hoare_1580379338ep_set @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ collect @ ( bool @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ fun ) @ ( bool @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ fun ) @ hAPP ) ) ) @ ( B @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ member @ ( bool @ ( bool @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ fun ) @ fun ) @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ~ ! [C: $i] :
( B
!= ( C @ ( A @ hoare_2037801986triple @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ ( A @ hoare_509422987triple @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( ( A @ enum )
& ( B @ enum ) )
=> ( B @ ( A @ fun ) @ enum ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Enum_Oenum) ).
thf(85,plain,
! [A: $i,B: $i] :
( ( ( A @ enum )
& ( B @ enum ) )
=> ( B @ ( A @ fun ) @ enum ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( G @ ( F @ ( E @ ( A @ ( B @ type_definition ) @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( B @ ( A @ fun ) @ fun ) @ ( A @ ( B @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( B @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( ! [H: $i] :
( ( G @ ( H @ ( A @ member @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( H @ ( F @ ( B @ ( A @ hAPP ) ) ) @ ( D @ ( bool @ ( B @ hAPP ) ) ) @ hBOOL ) )
=> ( C @ ( D @ ( bool @ ( B @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_type__definition_OAbs__induct) ).
thf(70,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( G @ ( F @ ( E @ ( A @ ( B @ type_definition ) @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( B @ ( A @ fun ) @ fun ) @ ( A @ ( B @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( B @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( ! [H: $i] :
( ( G @ ( H @ ( A @ member @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( H @ ( F @ ( B @ ( A @ hAPP ) ) ) @ ( D @ ( bool @ ( B @ hAPP ) ) ) @ hBOOL ) )
=> ( C @ ( D @ ( bool @ ( B @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(36,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ collect @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) )
= ( B @ ( bool @ ( A @ fun ) @ ti ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_Collect__def) ).
thf(165,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ collect @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) )
= ( B @ ( bool @ ( A @ fun ) @ ti ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(14,axiom,
induct_true @ hBOOL,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_induct__true__def) ).
thf(92,plain,
induct_true @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(47,axiom,
( ( hoare_1883395792gleton @ ( bool @ ti ) )
= hoare_1883395792gleton ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Hoare__Mirabelle__pjuwniqynr_Ostate__not__singleton_res) ).
thf(197,plain,
( ( hoare_1883395792gleton @ ( bool @ ti ) )
= hoare_1883395792gleton ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(1,conjecture,
! [A: $i] :
~ ! [B: $i] :
( ( B @ ( state @ ti ) )
= ( A @ ( state @ ti ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
~ ! [B: $i] :
( ( B @ ( state @ ti ) )
= ( A @ ( state @ ti ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(65,plain,
~ ! [A: $i] :
~ ! [B: $i] :
( ( B @ ( state @ ti ) )
= ( A @ ( state @ ti ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(18,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( G @ ( F @ ( E @ ( A @ ( B @ type_definition ) @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( B @ ( A @ fun ) @ fun ) @ ( A @ ( B @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( B @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( ( G @ ( D @ ( A @ member @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( ! [H: $i] : ( H @ ( E @ ( A @ ( B @ hAPP ) ) ) @ ( C @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( D @ ( C @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_type__definition_ORep__induct) ).
thf(97,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( G @ ( F @ ( E @ ( A @ ( B @ type_definition ) @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( B @ ( A @ fun ) @ fun ) @ ( A @ ( B @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( B @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( ( G @ ( D @ ( A @ member @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( ! [H: $i] : ( H @ ( E @ ( A @ ( B @ hAPP ) ) ) @ ( C @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( D @ ( C @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(52,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( A @ ( B @ hAPP ) ) ) @ ( A @ ti ) )
= ( D @ ( C @ ( A @ ( B @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_hAPP_res) ).
thf(224,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( A @ ( B @ hAPP ) ) ) @ ( A @ ti ) )
= ( D @ ( C @ ( A @ ( B @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(21,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ member @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
<=> ( B @ ( C @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_mem__def) ).
thf(109,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( C @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( C @ ( B @ ( A @ member @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL ) )
& ( ( C @ ( B @ ( A @ member @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( C @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(26,axiom,
! [A: $i] :
( ( A @ ( bool @ ti ) @ hBOOL )
<=> ( A @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_hBOOL_arg1) ).
thf(124,plain,
! [A: $i] :
( ( ( A @ hBOOL )
=> ( A @ ( bool @ ti ) @ hBOOL ) )
& ( ( A @ ( bool @ ti ) @ hBOOL )
=> ( A @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(6,axiom,
! [A: $i] :
( ( A @ cl_HOL_Oequal )
=> ( ( A @ equal_equal )
= ( A @ fequal ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_equal) ).
thf(77,plain,
! [A: $i] :
( ( A @ cl_HOL_Oequal )
=> ( ( A @ equal_equal )
= ( A @ fequal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(45,axiom,
! [A: $i] :
( ( A @ induct_equal @ ( bool @ ( A @ fun ) @ ( A @ fun ) @ ti ) )
= ( A @ induct_equal ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_HOL_Oinduct__equal_res) ).
thf(191,plain,
! [A: $i] :
( ( A @ induct_equal @ ( bool @ ( A @ fun ) @ ( A @ fun ) @ ti ) )
= ( A @ induct_equal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(61,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( D @ ( A @ ( B @ type_definition ) @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( B @ ( A @ fun ) @ fun ) @ ( A @ ( B @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( B @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( ( F @ ( C @ ( A @ member @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( ( C @ ( E @ ( B @ ( A @ hAPP ) ) ) @ ( D @ ( A @ ( B @ hAPP ) ) ) )
= ( C @ ( A @ ti ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_type__definition_OAbs__inverse) ).
thf(259,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( D @ ( A @ ( B @ type_definition ) @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( B @ ( A @ fun ) @ fun ) @ ( A @ ( B @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( B @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( ( F @ ( C @ ( A @ member @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( ( C @ ( E @ ( B @ ( A @ hAPP ) ) ) @ ( D @ ( A @ ( B @ hAPP ) ) ) )
= ( C @ ( A @ ti ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(56,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( G @ ( F @ ( E @ ( A @ ( B @ type_definition ) @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( B @ ( A @ fun ) @ fun ) @ ( A @ ( B @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( B @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( ( G @ ( D @ ( A @ member @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( ( G @ ( C @ ( A @ member @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( ( ( D @ ( F @ ( B @ ( A @ hAPP ) ) ) )
= ( C @ ( F @ ( B @ ( A @ hAPP ) ) ) ) )
<=> ( ( D @ ( A @ ti ) )
= ( C @ ( A @ ti ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_type__definition_OAbs__inject) ).
thf(236,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( G @ ( F @ ( E @ ( A @ ( B @ type_definition ) @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( B @ ( A @ fun ) @ fun ) @ ( A @ ( B @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( B @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( ( G @ ( D @ ( A @ member @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( ( G @ ( C @ ( A @ member @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( ( ( ( D @ ( A @ ti ) )
= ( C @ ( A @ ti ) ) )
=> ( ( D @ ( F @ ( B @ ( A @ hAPP ) ) ) )
= ( C @ ( F @ ( B @ ( A @ hAPP ) ) ) ) ) )
& ( ( ( D @ ( F @ ( B @ ( A @ hAPP ) ) ) )
= ( C @ ( F @ ( B @ ( A @ hAPP ) ) ) ) )
=> ( ( D @ ( A @ ti ) )
= ( C @ ( A @ ti ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(42,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( D @ ( A @ ( B @ type_definition ) @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( B @ ( A @ fun ) @ fun ) @ ( A @ ( B @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( B @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( ( F @ ( C @ ( A @ member @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ~ ! [G: $i] :
( ( C @ ( A @ ti ) )
!= ( G @ ( D @ ( A @ ( B @ hAPP ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_type__definition_ORep__cases) ).
thf(181,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( D @ ( A @ ( B @ type_definition ) @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( B @ ( A @ fun ) @ fun ) @ ( A @ ( B @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( B @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( ( F @ ( C @ ( A @ member @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ~ ! [G: $i] :
( ( C @ ( A @ ti ) )
!= ( G @ ( D @ ( A @ ( B @ hAPP ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(64,axiom,
! [A: $i] :
( ( A @ cl_HOL_Oequal )
=> ( ( A @ equal_equal @ ( bool @ ( A @ fun ) @ ( A @ fun ) @ ti ) )
= ( A @ equal_equal ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_HOL_Oequal__class_Oequal_res) ).
thf(274,plain,
! [A: $i] :
( ( A @ cl_HOL_Oequal )
=> ( ( A @ equal_equal @ ( bool @ ( A @ fun ) @ ( A @ fun ) @ ti ) )
= ( A @ equal_equal ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(8,axiom,
~ ( induct_false @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_induct__false__def) ).
thf(81,plain,
~ ( induct_false @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(54,axiom,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] :
( ( A @ hoare_1580379338ep_set @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ collect @ ( bool @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ fun ) @ ( bool @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ fun ) @ hAPP ) ) ) @ ( D @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ member @ ( bool @ ( bool @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ fun ) @ fun ) @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( D @ ( A @ hoare_244953527triple @ ( A @ hoare_509422987triple @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ hAPP ) ) ) @ ( C @ ( bool @ ( A @ hoare_509422987triple @ hAPP ) ) ) @ hBOOL ) )
=> ( B @ ( C @ ( bool @ ( A @ hoare_509422987triple @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_Abs__triple__induct) ).
thf(230,plain,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] :
( ( A @ hoare_1580379338ep_set @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ collect @ ( bool @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ fun ) @ ( bool @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ fun ) @ hAPP ) ) ) @ ( D @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ member @ ( bool @ ( bool @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ fun ) @ fun ) @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( D @ ( A @ hoare_244953527triple @ ( A @ hoare_509422987triple @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ hAPP ) ) ) @ ( C @ ( bool @ ( A @ hoare_509422987triple @ hAPP ) ) ) @ hBOOL ) )
=> ( B @ ( C @ ( bool @ ( A @ hoare_509422987triple @ hAPP ) ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(58,axiom,
! [A: $i,B: $i] :
( ( A @ hoare_1580379338ep_set @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ collect @ ( bool @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ fun ) @ ( bool @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ fun ) @ hAPP ) ) ) @ ( B @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ member @ ( bool @ ( bool @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ fun ) @ fun ) @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( A @ hoare_244953527triple @ ( A @ hoare_509422987triple @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ hAPP ) ) ) @ ( A @ hoare_2037801986triple @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ ( A @ hoare_509422987triple @ hAPP ) ) ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_Abs__triple__inverse) ).
thf(245,plain,
! [A: $i,B: $i] :
( ( A @ hoare_1580379338ep_set @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ collect @ ( bool @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ fun ) @ ( bool @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ fun ) @ hAPP ) ) ) @ ( B @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ member @ ( bool @ ( bool @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ fun ) @ fun ) @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( A @ hoare_244953527triple @ ( A @ hoare_509422987triple @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ hAPP ) ) ) @ ( A @ hoare_2037801986triple @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ ( A @ hoare_509422987triple @ hAPP ) ) ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(30,axiom,
! [A: $i] :
( ( A @ hoare_244953527triple @ ( A @ hoare_509422987triple @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ fun ) @ ti ) )
= ( A @ hoare_244953527triple ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Hoare__Mirabelle__pjuwniqynr_OAbs__triple_res) ).
thf(140,plain,
! [A: $i] :
( ( A @ hoare_244953527triple @ ( A @ hoare_509422987triple @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ fun ) @ ti ) )
= ( A @ hoare_244953527triple ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(50,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ hoare_2037801986triple @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ ( A @ hoare_509422987triple @ hAPP ) ) ) )
= ( C @ ( A @ hoare_2037801986triple @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ ( A @ hoare_509422987triple @ hAPP ) ) ) ) )
<=> ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_Rep__triple__inject) ).
thf(213,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B = C )
=> ( ( B @ ( A @ hoare_2037801986triple @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ ( A @ hoare_509422987triple @ hAPP ) ) ) )
= ( C @ ( A @ hoare_2037801986triple @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ ( A @ hoare_509422987triple @ hAPP ) ) ) ) ) )
& ( ( ( B @ ( A @ hoare_2037801986triple @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ ( A @ hoare_509422987triple @ hAPP ) ) ) )
= ( C @ ( A @ hoare_2037801986triple @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ ( A @ hoare_509422987triple @ hAPP ) ) ) ) )
=> ( B = C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(60,axiom,
! [A: $i] :
( ( A @ cl_HOL_Oequal )
=> ! [B: $i,C: $i] :
( ( C @ ( B @ ( A @ equal_equal @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
<=> ( ( B @ ( A @ ti ) )
= ( C @ ( A @ ti ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_equal__eq) ).
thf(251,plain,
! [A: $i] :
( ( A @ cl_HOL_Oequal )
=> ! [B: $i,C: $i] :
( ( ( ( B @ ( A @ ti ) )
= ( C @ ( A @ ti ) ) )
=> ( C @ ( B @ ( A @ equal_equal @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) )
& ( ( C @ ( B @ ( A @ equal_equal @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( A @ ti ) )
= ( C @ ( A @ ti ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(27,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( A @ ti ) @ ( C @ ( B @ ( A @ hAPP ) ) ) )
= ( D @ ( C @ ( B @ ( A @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_hAPP_arg2) ).
thf(130,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( A @ ti ) @ ( C @ ( B @ ( A @ hAPP ) ) ) )
= ( D @ ( C @ ( B @ ( A @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(7,axiom,
bool @ enum,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Enum_Oenum) ).
thf(80,plain,
bool @ enum,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(40,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i] :
( ( E @ ( C @ ( B @ ( A @ hAPP ) ) ) )
= ( E @ ( D @ ( B @ ( A @ hAPP ) ) ) ) )
=> ( ( C @ ( B @ ( A @ fun ) @ ti ) )
= ( D @ ( B @ ( A @ fun ) @ ti ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_ext) ).
thf(175,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i] :
( ( E @ ( C @ ( B @ ( A @ hAPP ) ) ) )
= ( E @ ( D @ ( B @ ( A @ hAPP ) ) ) ) )
=> ( ( C @ ( B @ ( A @ fun ) @ ti ) )
= ( D @ ( B @ ( A @ fun ) @ ti ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(31,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ fun ) @ ti ) @ ( B @ ( A @ hAPP ) ) ) )
= ( D @ ( C @ ( B @ ( A @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_hAPP_arg1) ).
thf(143,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ fun ) @ ti ) @ ( B @ ( A @ hAPP ) ) ) )
= ( D @ ( C @ ( B @ ( A @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(19,axiom,
! [A: $i] :
( ( A @ cl_HOL_Oequal )
=> ! [B: $i] : ( B @ ( B @ ( A @ equal_equal @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_equal__refl) ).
thf(99,plain,
! [A: $i] :
( ( A @ cl_HOL_Oequal )
=> ! [B: $i] : ( B @ ( B @ ( A @ equal_equal @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(11,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( D @ ( A @ ( B @ type_definition ) @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( B @ ( A @ fun ) @ fun ) @ ( A @ ( B @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( B @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( F @ ( C @ ( D @ ( A @ ( B @ hAPP ) ) ) @ ( A @ member @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_type__definition_ORep) ).
thf(87,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( D @ ( A @ ( B @ type_definition ) @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( B @ ( A @ fun ) @ fun ) @ ( A @ ( B @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( B @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( F @ ( C @ ( D @ ( A @ ( B @ hAPP ) ) ) @ ( A @ member @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(35,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( G @ ( F @ ( E @ ( A @ ( B @ type_definition ) @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( B @ ( A @ fun ) @ fun ) @ ( A @ ( B @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( B @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( ( ( C @ ( E @ ( A @ ( B @ hAPP ) ) ) )
= ( D @ ( E @ ( A @ ( B @ hAPP ) ) ) ) )
<=> ( ( C @ ( B @ ti ) )
= ( D @ ( B @ ti ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_type__definition_ORep__inject) ).
thf(158,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( G @ ( F @ ( E @ ( A @ ( B @ type_definition ) @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( B @ ( A @ fun ) @ fun ) @ ( A @ ( B @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( B @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( ( ( ( C @ ( B @ ti ) )
= ( D @ ( B @ ti ) ) )
=> ( ( C @ ( E @ ( A @ ( B @ hAPP ) ) ) )
= ( D @ ( E @ ( A @ ( B @ hAPP ) ) ) ) ) )
& ( ( ( C @ ( E @ ( A @ ( B @ hAPP ) ) ) )
= ( D @ ( E @ ( A @ ( B @ hAPP ) ) ) ) )
=> ( ( C @ ( B @ ti ) )
= ( D @ ( B @ ti ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(38,axiom,
( ( induct_false @ ( bool @ ti ) )
= induct_false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_HOL_Oinduct__false_res) ).
thf(171,plain,
( ( induct_false @ ( bool @ ti ) )
= induct_false ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(32,axiom,
state @ cl_HOL_Oequal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Com_Ostate___HOL_Oequal) ).
thf(146,plain,
state @ cl_HOL_Oequal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(37,axiom,
! [A: $i] :
( ( A @ hoare_2037801986triple @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ ( A @ hoare_509422987triple @ fun ) @ ti ) )
= ( A @ hoare_2037801986triple ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Hoare__Mirabelle__pjuwniqynr_ORep__triple_res) ).
thf(168,plain,
! [A: $i] :
( ( A @ hoare_2037801986triple @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ ( A @ hoare_509422987triple @ fun ) @ ti ) )
= ( A @ hoare_2037801986triple ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(62,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ induct_equal @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
<=> ( ( B @ ( A @ ti ) )
= ( C @ ( A @ ti ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_induct__equal__def) ).
thf(262,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( B @ ( A @ ti ) )
= ( C @ ( A @ ti ) ) )
=> ( C @ ( B @ ( A @ induct_equal @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) )
& ( ( C @ ( B @ ( A @ induct_equal @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( A @ ti ) )
= ( C @ ( A @ ti ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(57,axiom,
! [A: $i] :
( ( A @ collect @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ti ) )
= ( A @ collect ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Set_OCollect_res) ).
thf(242,plain,
! [A: $i] :
( ( A @ collect @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ti ) )
= ( A @ collect ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(29,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( D @ ( A @ ( B @ type_definition ) @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( B @ ( A @ fun ) @ fun ) @ ( A @ ( B @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( B @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( ( C @ ( D @ ( A @ ( B @ hAPP ) ) ) @ ( E @ ( B @ ( A @ hAPP ) ) ) )
= ( C @ ( B @ ti ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_type__definition_ORep__inverse) ).
thf(136,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( D @ ( A @ ( B @ type_definition ) @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( B @ ( A @ fun ) @ fun ) @ ( A @ ( B @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( B @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( ( C @ ( D @ ( A @ ( B @ hAPP ) ) ) @ ( E @ ( B @ ( A @ hAPP ) ) ) )
= ( C @ ( B @ ti ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(16,axiom,
bool @ cl_HOL_Oequal,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___HOL_Oequal) ).
thf(94,plain,
bool @ cl_HOL_Oequal,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( ( A @ enum )
& ( B @ enum ) )
=> ( B @ ( A @ sum_sum ) @ enum ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_sum___Enum_Oenum) ).
thf(90,plain,
! [A: $i,B: $i] :
( ( ( A @ enum )
& ( B @ enum ) )
=> ( B @ ( A @ sum_sum ) @ enum ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(53,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ hoare_2037801986triple @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ ( A @ hoare_509422987triple @ hAPP ) ) ) @ ( A @ hoare_244953527triple @ ( A @ hoare_509422987triple @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ hAPP ) ) ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_Rep__triple__inverse) ).
thf(227,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ hoare_2037801986triple @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ ( A @ hoare_509422987triple @ hAPP ) ) ) @ ( A @ hoare_244953527triple @ ( A @ hoare_509422987triple @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ hAPP ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(25,axiom,
! [A: $i] : ( A @ hoare_1580379338ep_set @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ collect @ ( bool @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ fun ) @ ( bool @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ fun ) @ hAPP ) ) ) @ ( A @ hoare_244953527triple @ ( A @ hoare_2037801986triple @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ ( A @ hoare_509422987triple @ type_definition ) @ ( bool @ ( bool @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ fun ) @ fun ) @ ( A @ hoare_509422987triple @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ fun ) @ fun ) @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ ( A @ hoare_509422987triple @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ fun ) @ fun ) @ ( A @ hoare_509422987triple @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ fun ) @ hAPP ) ) ) @ hBOOL ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_type__definition__triple) ).
thf(122,plain,
! [A: $i] : ( A @ hoare_1580379338ep_set @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ collect @ ( bool @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ fun ) @ ( bool @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ fun ) @ hAPP ) ) ) @ ( A @ hoare_244953527triple @ ( A @ hoare_2037801986triple @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ ( A @ hoare_509422987triple @ type_definition ) @ ( bool @ ( bool @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ fun ) @ fun ) @ ( A @ hoare_509422987triple @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ fun ) @ fun ) @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ ( A @ hoare_509422987triple @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ fun ) @ fun ) @ ( A @ hoare_509422987triple @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( bool @ ( A @ ( state @ sum_sum ) @ ( bool @ ( state @ fun ) @ ( A @ fun ) @ ( com @ sum_sum ) @ node ) @ fun ) @ fun ) @ hAPP ) ) ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( ( A @ enum )
& ( B @ cl_HOL_Oequal ) )
=> ( B @ ( A @ fun ) @ cl_HOL_Oequal ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___HOL_Oequal) ).
thf(83,plain,
! [A: $i,B: $i] :
( ( ( A @ enum )
& ( B @ cl_HOL_Oequal ) )
=> ( B @ ( A @ fun ) @ cl_HOL_Oequal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(277,plain,
$false,
inference(e,[status(thm)],[185,188,173,194,95,199,178,69,101,234,115,120,93,152,147,221,74,206,89,133,248,117,270,85,70,165,92,197,65,97,224,109,124,77,191,259,236,181,274,81,230,245,140,213,251,130,80,175,143,99,87,158,171,146,168,262,242,136,94,90,227,122,83]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWW469+5 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.11/0.38 % Computer : n018.cluster.edu
% 0.11/0.38 % Model : x86_64 x86_64
% 0.11/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.38 % Memory : 8046.5625MB
% 0.11/0.38 % OS : Linux 6.8.0-71-generic
% 0.11/0.38 % CPULimit : 300
% 0.11/0.38 % WCLimit : 300
% 0.11/0.38 % DateTime : Sat Sep 26 15:59:52 UTC 2026
% 0.11/0.38 % CPUTime :
% 0.11/0.38 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.71/0.70 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.95/0.87 % [INFO] Parsing done (168ms).
% 0.95/0.88 % [INFO] Running in sequential loop mode.
% 1.78/1.09 % [INFO] eprover registered as external prover.
% 1.78/1.09 % [INFO] Scanning for conjecture ...
% 2.06/1.18 % [INFO] Found a conjecture (or negated_conjecture) and 62 axioms. Running axiom selection ...
% 2.32/1.25 % [INFO] Axiom selection finished. Selected 62 axioms (removed 0 axioms).
% 2.78/1.39 % [INFO] Problem is first-order (TPTP FOF).
% 3.24/1.40 % [INFO] Type checking passed.
% 3.24/1.41 % [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 ...
% 8.84/2.85 % External prover 'e' found a proof!
% 8.84/2.85 % [INFO] Killing All external provers ...
% 8.84/2.85 % Time passed: 2364ms (effective reasoning time: 1969ms)
% 8.84/2.85 % 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)>
% 8.84/2.86 % Axioms used in derivation (62): fact_3_equal, fact_7_Rep__triple__inverse, fact_21_induct__false__def, fact_0_state__not__singleton__def, tsy_c_HOL_Oundefined_res, tsy_c_HOL_Oequal__class_Oequal_res, fact_12_type__definition__triple, tsy_c_HOL_Oinduct__equal_res, fact_14_Abs__triple__induct, fact_11_Abs__triple__inverse, fact_24_type__definition_OAbs__induct, tsy_c_Hoare__Mirabelle__pjuwniqynr_Otriple_Otriple__rep__set_res, fact_28_induct__equal__def, fact_8_Rep__triple, arity_fun___HOL_Oequal, tsy_c_member_res, fact_19_type__definition_ORep__inverse, fact_22_type__definition_ORep__cases, fact_27_induct__true__def, tsy_c_HOL_Oinduct__false_res, tsy_c_Typedef_Otype__definition_res, fact_26_induct__trueI, tsy_c_hAPP_res, fact_2_Rep__triple__inject, tsy_c_Set_OCollect_res, tsy_c_hAPP_arg1, arity_HOL_Obool___HOL_Oequal, tsy_c_Hoare__Mirabelle__pjuwniqynr_ORep__triple_res, arity_fun___Enum_Oenum, tsy_c_hBOOL_arg1, fact_23_type__definition_OAbs__cases, fact_6_eq__equal, arity_sum___HOL_Oequal, arity_Com_Ocom___HOL_Oequal, arity_sum___Enum_Oenum, fact_31_Collect__def, arity_HOL_Obool___Enum_Oenum, tsy_c_hAPP_arg2, fact_13_Abs__triple__inject, help_ti_idem, help_fequal_1_1_T, fact_18_type__definition_ORep__inject, fact_10_Rep__triple__cases, tsy_c_fequal_res, arity_Com_Ostate___HOL_Oequal, fact_25_type__definition_ORep__induct, tsy_c_HOL_Oinduct__true_res, fact_20_type__definition_ORep, fact_16_type__definition_OAbs__inject, arity_Hoare__Mirabelle__pjuwniqynr_Otriple___HOL_Oequal, help_fequal_2_1_T, fact_15_Abs__triple__cases, fact_1_equal__triple__def, fact_29_ext, tsy_c_Hoare__Mirabelle__pjuwniqynr_Ostate__not__singleton_res, fact_17_type__definition_OAbs__inverse, fact_30_mem__def, fact_4_equal__refl, tsy_c_Hoare__Mirabelle__pjuwniqynr_OAbs__triple_res, fact_9_Rep__triple__induct, fact_5_equal__eq, conj_0
% 8.84/2.86 % No. of inferences in proof: 128
% 8.84/2.86 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2364 ms resp. 1969 ms w/o parsing
% 9.26/3.03 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 9.76/3.03 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------