TSTP Solution File: SWW469+5 by Leo-III---1.7.12
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.12
% Problem : SWW469+5 : TPTP v8.2.0. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n032.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 06:49:46 EDT 2024
% Result : Theorem 6.27s 2.41s
% Output : Refutation 6.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 88
% Syntax : Number of formulae : 153 ( 64 unt; 25 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 : 27 ( 27 >; 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_type,type,
ti: $i > $i > $i ).
thf(state_type,type,
state: $i ).
thf(hBOOL_type,type,
hBOOL: $i > $o ).
thf(hoare_1883395792gleton_type,type,
hoare_1883395792gleton: $i ).
thf(hAPP_type,type,
hAPP: $i > $i > $i > $i > $i ).
thf(fun_type,type,
fun: $i > $i > $i ).
thf(bool_type,type,
bool: $i ).
thf(type_definition_type,type,
type_definition: $i > $i > $i ).
thf(member_type,type,
member: $i > $i ).
thf(cl_HOL_Oequal_type,type,
cl_HOL_Oequal: $i > $o ).
thf(fequal_type,type,
fequal: $i > $i ).
thf(equal_equal_type,type,
equal_equal: $i > $i ).
thf(enum_type,type,
enum: $i > $o ).
thf(induct_false_type,type,
induct_false: $i ).
thf(com_type,type,
com: $i ).
thf(sum_sum_type,type,
sum_sum: $i > $i > $i ).
thf(induct_true_type,type,
induct_true: $i ).
thf(hoare_509422987triple_type,type,
hoare_509422987triple: $i > $i ).
thf(node_type,type,
node: $i > $i > $i ).
thf(hoare_2037801986triple_type,type,
hoare_2037801986triple: $i > $i ).
thf(collect_type,type,
collect: $i > $i ).
thf(hoare_1580379338ep_set_type,type,
hoare_1580379338ep_set: $i > $i ).
thf(hoare_244953527triple_type,type,
hoare_244953527triple: $i > $i ).
thf(undefined_type,type,
undefined: $i > $i ).
thf(induct_equal_type,type,
induct_equal: $i > $i ).
thf(53,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ ( hoare_509422987triple @ A ) @ ( hoare_244953527triple @ A ) @ ( hAPP @ ( hoare_509422987triple @ A ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ ( hoare_2037801986triple @ A ) @ B ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_Rep__triple__inverse) ).
thf(217,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ ( hoare_509422987triple @ A ) @ ( hoare_244953527triple @ A ) @ ( hAPP @ ( hoare_509422987triple @ A ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ ( hoare_2037801986triple @ A ) @ B ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(32,axiom,
cl_HOL_Oequal @ state,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Com_Ostate___HOL_Oequal) ).
thf(142,plain,
cl_HOL_Oequal @ state,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(42,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) ) @ ( type_definition @ B @ A ) @ D ) @ E ) @ F ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ F ) )
=> ~ ! [G: $i] :
( ( ti @ A @ C )
!= ( hAPP @ B @ A @ D @ G ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_type__definition_ORep__cases) ).
thf(174,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) ) @ ( type_definition @ B @ A ) @ D ) @ E ) @ F ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ F ) )
=> ~ ! [G: $i] :
( ( ti @ A @ C )
!= ( hAPP @ B @ A @ D @ G ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(45,axiom,
! [A: $i] :
( ( ti @ ( fun @ A @ ( fun @ A @ bool ) ) @ ( induct_equal @ A ) )
= ( induct_equal @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_HOL_Oinduct__equal_res) ).
thf(184,plain,
! [A: $i] :
( ( ti @ ( fun @ A @ ( fun @ A @ bool ) ) @ ( induct_equal @ A ) )
= ( induct_equal @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(28,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( fequal @ A ) @ B ) @ C ) )
| ( ( ti @ A @ B )
= ( ti @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_1_1_T) ).
thf(129,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( fequal @ A ) @ B ) @ C ) )
| ( ( ti @ A @ B )
= ( ti @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(5,axiom,
! [A: $i] :
( ( cl_HOL_Oequal @ A )
=> ( ( fequal @ A )
= ( equal_equal @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_eq__equal) ).
thf(73,plain,
! [A: $i] :
( ( cl_HOL_Oequal @ A )
=> ( ( fequal @ A )
= ( equal_equal @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(50,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( hoare_509422987triple @ A ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ ( hoare_2037801986triple @ A ) @ B )
= ( hAPP @ ( hoare_509422987triple @ A ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ ( hoare_2037801986triple @ A ) @ C ) )
<=> ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_Rep__triple__inject) ).
thf(204,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( hAPP @ ( hoare_509422987triple @ A ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ ( hoare_2037801986triple @ A ) @ B )
= ( hAPP @ ( hoare_509422987triple @ A ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ ( hoare_2037801986triple @ A ) @ C ) )
=> ( B = C ) )
& ( ( B = C )
=> ( ( hAPP @ ( hoare_509422987triple @ A ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ ( hoare_2037801986triple @ A ) @ B )
= ( hAPP @ ( hoare_509422987triple @ A ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ ( hoare_2037801986triple @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(22,axiom,
! [A: $i] : ( cl_HOL_Oequal @ ( hoare_509422987triple @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Hoare__Mirabelle__pjuwniqynr_Otriple___HOL_Oequal) ).
thf(112,plain,
! [A: $i] : ( cl_HOL_Oequal @ ( hoare_509422987triple @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(33,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) ) @ ( type_definition @ B @ A ) @ D ) @ E ) @ F ) )
=> ~ ! [G: $i] :
( ( ( ti @ B @ C )
= ( hAPP @ A @ B @ E @ G ) )
=> ~ ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ G ) @ F ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_type__definition_OAbs__cases) ).
thf(143,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) ) @ ( type_definition @ B @ A ) @ D ) @ E ) @ F ) )
=> ~ ! [G: $i] :
( ( ( ti @ B @ C )
= ( hAPP @ A @ B @ E @ G ) )
=> ~ ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ G ) @ F ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(43,axiom,
! [A: $i] :
( ( ti @ ( fun @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) ) @ ( member @ A ) )
= ( member @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_member_res) ).
thf(178,plain,
! [A: $i] :
( ( ti @ ( fun @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) ) @ ( member @ A ) )
= ( member @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(20,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ A ) @ bool @ ( hAPP @ ( hoare_509422987triple @ A ) @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( equal_equal @ ( hoare_509422987triple @ A ) ) @ B ) @ C ) )
<=> ( B = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_equal__triple__def) ).
thf(100,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ A ) @ bool @ ( hAPP @ ( hoare_509422987triple @ A ) @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( equal_equal @ ( hoare_509422987triple @ A ) ) @ B ) @ C ) )
=> ( B = C ) )
& ( ( B = C )
=> ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ A ) @ bool @ ( hAPP @ ( hoare_509422987triple @ A ) @ ( fun @ ( hoare_509422987triple @ A ) @ bool ) @ ( equal_equal @ ( hoare_509422987triple @ A ) ) @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(3,axiom,
hBOOL @ hoare_1883395792gleton,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(69,plain,
hBOOL @ hoare_1883395792gleton,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(62,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( induct_equal @ A ) @ B ) @ C ) )
<=> ( ( ti @ A @ B )
= ( ti @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_induct__equal__def) ).
thf(249,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( induct_equal @ A ) @ B ) @ C ) )
=> ( ( ti @ A @ B )
= ( ti @ A @ C ) ) )
& ( ( ( ti @ A @ B )
= ( ti @ A @ C ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( induct_equal @ A ) @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(12,axiom,
cl_HOL_Oequal @ com,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Com_Ocom___HOL_Oequal) ).
thf(88,plain,
cl_HOL_Oequal @ com,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(16,axiom,
cl_HOL_Oequal @ bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___HOL_Oequal) ).
thf(93,plain,
cl_HOL_Oequal @ bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(35,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) ) @ ( type_definition @ B @ A ) @ E ) @ F ) @ G ) )
=> ( ( ( hAPP @ B @ A @ E @ C )
= ( hAPP @ B @ A @ E @ D ) )
<=> ( ( ti @ B @ C )
= ( ti @ B @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_type__definition_ORep__inject) ).
thf(152,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) ) @ ( type_definition @ B @ A ) @ E ) @ F ) @ G ) )
=> ( ( ( ( hAPP @ B @ A @ E @ C )
= ( hAPP @ B @ A @ E @ D ) )
=> ( ( ti @ B @ C )
= ( ti @ B @ D ) ) )
& ( ( ( ti @ B @ C )
= ( ti @ B @ D ) )
=> ( ( hAPP @ B @ A @ E @ C )
= ( hAPP @ B @ A @ E @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(38,axiom,
( ( ti @ bool @ induct_false )
= induct_false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_HOL_Oinduct__false_res) ).
thf(164,plain,
( ( ti @ bool @ induct_false )
= induct_false ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(51,axiom,
! [A: $i] :
( ( ti @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ ( hoare_1580379338ep_set @ A ) )
= ( hoare_1580379338ep_set @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Hoare__Mirabelle__pjuwniqynr_Otriple_Otriple__rep__set_res) ).
thf(211,plain,
! [A: $i] :
( ( ti @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ ( hoare_1580379338ep_set @ A ) )
= ( hoare_1580379338ep_set @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(26,axiom,
! [A: $i] :
( ( hBOOL @ ( ti @ bool @ A ) )
<=> ( hBOOL @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_hBOOL_arg1) ).
thf(121,plain,
! [A: $i] :
( ( ( hBOOL @ ( ti @ bool @ A ) )
=> ( hBOOL @ A ) )
& ( ( hBOOL @ A )
=> ( hBOOL @ ( ti @ bool @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( ( enum @ B )
& ( enum @ A ) )
=> ( enum @ ( fun @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Enum_Oenum) ).
thf(84,plain,
! [A: $i,B: $i] :
( ( ( enum @ B )
& ( enum @ A ) )
=> ( enum @ ( fun @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(34,axiom,
! [A: $i,B: $i] :
~ ! [C: $i] :
( ( B
= ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ ( hoare_509422987triple @ A ) @ ( hoare_244953527triple @ A ) @ C ) )
=> ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) ) @ C ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_Abs__triple__cases) ).
thf(147,plain,
! [A: $i,B: $i] :
~ ! [C: $i] :
( ( B
= ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ ( hoare_509422987triple @ A ) @ ( hoare_244953527triple @ A ) @ C ) )
=> ~ ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) ) @ C ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(29,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) ) @ ( type_definition @ B @ A ) @ D ) @ E ) @ F ) )
=> ( ( hAPP @ A @ B @ E @ ( hAPP @ B @ A @ D @ C ) )
= ( ti @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_type__definition_ORep__inverse) ).
thf(132,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) ) @ ( type_definition @ B @ A ) @ D ) @ E ) @ F ) )
=> ( ( hAPP @ A @ B @ E @ ( hAPP @ B @ A @ D @ C ) )
= ( ti @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( ( enum @ B )
& ( enum @ A ) )
=> ( enum @ ( sum_sum @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_sum___Enum_Oenum) ).
thf(89,plain,
! [A: $i,B: $i] :
( ( ( enum @ B )
& ( enum @ A ) )
=> ( enum @ ( sum_sum @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(58,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) ) @ B ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ A ) ) ) )
=> ( ( hAPP @ ( hoare_509422987triple @ A ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ ( hoare_2037801986triple @ A ) @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ ( hoare_509422987triple @ A ) @ ( hoare_244953527triple @ A ) @ B ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_Abs__triple__inverse) ).
thf(233,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) ) @ B ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ A ) ) ) )
=> ( ( hAPP @ ( hoare_509422987triple @ A ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ ( hoare_2037801986triple @ A ) @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ ( hoare_509422987triple @ A ) @ ( hoare_244953527triple @ A ) @ B ) )
= B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(24,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) ) @ ( hAPP @ ( hoare_509422987triple @ A ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ ( hoare_2037801986triple @ A ) @ B ) ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_Rep__triple) ).
thf(117,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) ) @ ( hAPP @ ( hoare_509422987triple @ A ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ ( hoare_2037801986triple @ A ) @ B ) ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(54,axiom,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) ) @ D ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ A ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ A ) @ bool @ C @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ ( hoare_509422987triple @ A ) @ ( hoare_244953527triple @ A ) @ D ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ A ) @ bool @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_Abs__triple__induct) ).
thf(220,plain,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) ) @ D ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ A ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ A ) @ bool @ C @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ ( hoare_509422987triple @ A ) @ ( hoare_244953527triple @ A ) @ D ) ) ) )
=> ( hBOOL @ ( hAPP @ ( hoare_509422987triple @ A ) @ bool @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(64,axiom,
! [A: $i] :
( ( cl_HOL_Oequal @ A )
=> ( ( ti @ ( fun @ A @ ( fun @ A @ bool ) ) @ ( equal_equal @ A ) )
= ( equal_equal @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_HOL_Oequal__class_Oequal_res) ).
thf(260,plain,
! [A: $i] :
( ( cl_HOL_Oequal @ A )
=> ( ( ti @ ( fun @ A @ ( fun @ A @ bool ) ) @ ( equal_equal @ A ) )
= ( equal_equal @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) ) @ ( type_definition @ B @ A ) @ E ) @ F ) @ G ) )
=> ( ! [H: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ H ) @ G ) )
=> ( hBOOL @ ( hAPP @ B @ bool @ D @ ( hAPP @ A @ B @ F @ H ) ) ) )
=> ( hBOOL @ ( hAPP @ B @ bool @ D @ C ) ) ) ),
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] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) ) @ ( type_definition @ B @ A ) @ E ) @ F ) @ G ) )
=> ( ! [H: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ H ) @ G ) )
=> ( hBOOL @ ( hAPP @ B @ bool @ D @ ( hAPP @ A @ B @ F @ H ) ) ) )
=> ( hBOOL @ ( hAPP @ B @ bool @ D @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(48,axiom,
( ( hBOOL @ hoare_1883395792gleton )
<=> ? [A: $i,B: $i] :
( ( ti @ state @ A )
!= ( ti @ state @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_state__not__singleton__def) ).
thf(192,plain,
( ( ( hBOOL @ hoare_1883395792gleton )
=> ? [A: $i,B: $i] :
( ( ti @ state @ A )
!= ( ti @ state @ B ) ) )
& ( ? [A: $i,B: $i] :
( ( ti @ state @ A )
!= ( ti @ state @ B ) )
=> ( hBOOL @ hoare_1883395792gleton ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(15,axiom,
hBOOL @ induct_true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_induct__trueI) ).
thf(92,plain,
hBOOL @ induct_true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(1,conjecture,
! [A: $i] :
~ ! [B: $i] :
( ( ti @ state @ B )
= ( ti @ state @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
~ ! [B: $i] :
( ( ti @ state @ B )
= ( ti @ state @ A ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(65,plain,
~ ! [A: $i] :
~ ! [B: $i] :
( ( ti @ state @ B )
= ( ti @ state @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(63,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) ) @ B ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ A ) ) ) )
=> ~ ! [C: $i] :
( B
!= ( hAPP @ ( hoare_509422987triple @ A ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ ( hoare_2037801986triple @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_Rep__triple__cases) ).
thf(256,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) ) @ B ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ A ) ) ) )
=> ~ ! [C: $i] :
( B
!= ( hAPP @ ( hoare_509422987triple @ A ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ ( hoare_2037801986triple @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(56,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) ) @ ( type_definition @ B @ A ) @ E ) @ F ) @ G ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ D ) @ G ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ G ) )
=> ( ( ( hAPP @ A @ B @ F @ D )
= ( hAPP @ A @ B @ F @ C ) )
<=> ( ( ti @ A @ D )
= ( ti @ A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_type__definition_OAbs__inject) ).
thf(225,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) ) @ ( type_definition @ B @ A ) @ E ) @ F ) @ G ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ D ) @ G ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ G ) )
=> ( ( ( ( hAPP @ A @ B @ F @ D )
= ( hAPP @ A @ B @ F @ C ) )
=> ( ( ti @ A @ D )
= ( ti @ A @ C ) ) )
& ( ( ( ti @ A @ D )
= ( ti @ A @ C ) )
=> ( ( hAPP @ A @ B @ F @ D )
= ( hAPP @ A @ B @ F @ C ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(18,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) ) @ ( type_definition @ B @ A ) @ E ) @ F ) @ G ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ D ) @ G ) )
=> ( ! [H: $i] : ( hBOOL @ ( hAPP @ A @ bool @ C @ ( hAPP @ B @ A @ E @ H ) ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ C @ D ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_type__definition_ORep__induct) ).
thf(96,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) ) @ ( type_definition @ B @ A ) @ E ) @ F ) @ G ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ D ) @ G ) )
=> ( ! [H: $i] : ( hBOOL @ ( hAPP @ A @ bool @ C @ ( hAPP @ B @ A @ E @ H ) ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ C @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(39,axiom,
( ( ti @ bool @ induct_true )
= induct_true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_HOL_Oinduct__true_res) ).
thf(166,plain,
( ( ti @ bool @ induct_true )
= induct_true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(37,axiom,
! [A: $i] :
( ( ti @ ( fun @ ( hoare_509422987triple @ A ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) ) @ ( hoare_2037801986triple @ A ) )
= ( hoare_2037801986triple @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Hoare__Mirabelle__pjuwniqynr_ORep__triple_res) ).
thf(161,plain,
! [A: $i] :
( ( ti @ ( fun @ ( hoare_509422987triple @ A ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) ) @ ( hoare_2037801986triple @ A ) )
= ( hoare_2037801986triple @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(59,axiom,
! [A: $i] :
( ( ti @ ( fun @ A @ ( fun @ A @ bool ) ) @ ( fequal @ A ) )
= ( fequal @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_fequal_res) ).
thf(236,plain,
! [A: $i] :
( ( ti @ ( fun @ A @ ( fun @ A @ bool ) ) @ ( fequal @ A ) )
= ( fequal @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(44,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( ti @ A @ B )
!= ( ti @ A @ C ) )
| ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( fequal @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_T) ).
thf(181,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ti @ A @ B )
!= ( ti @ A @ C ) )
| ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( fequal @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(11,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) ) @ ( type_definition @ B @ A ) @ D ) @ E ) @ F ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ ( hAPP @ B @ A @ D @ C ) ) @ F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_type__definition_ORep) ).
thf(86,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) ) @ ( type_definition @ B @ A ) @ D ) @ E ) @ F ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ ( hAPP @ B @ A @ D @ C ) ) @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(46,axiom,
! [A: $i,B: $i] :
( ( ti @ ( fun @ ( fun @ A @ B ) @ ( fun @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ bool ) ) ) @ ( type_definition @ A @ B ) )
= ( type_definition @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Typedef_Otype__definition_res) ).
thf(187,plain,
! [A: $i,B: $i] :
( ( ti @ ( fun @ ( fun @ A @ B ) @ ( fun @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ bool ) ) ) @ ( type_definition @ A @ B ) )
= ( type_definition @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(57,axiom,
! [A: $i] :
( ( ti @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( collect @ A ) )
= ( collect @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Set_OCollect_res) ).
thf(230,plain,
! [A: $i] :
( ( ti @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( collect @ A ) )
= ( collect @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(6,axiom,
! [A: $i] :
( ( cl_HOL_Oequal @ A )
=> ( ( equal_equal @ A )
= ( fequal @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_equal) ).
thf(76,plain,
! [A: $i] :
( ( cl_HOL_Oequal @ A )
=> ( ( equal_equal @ A )
= ( fequal @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(19,axiom,
! [A: $i] :
( ( cl_HOL_Oequal @ A )
=> ! [B: $i] : ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( equal_equal @ A ) @ B ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_equal__refl) ).
thf(98,plain,
! [A: $i] :
( ( cl_HOL_Oequal @ A )
=> ! [B: $i] : ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( equal_equal @ A ) @ B ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(14,axiom,
hBOOL @ induct_true,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_induct__true__def) ).
thf(91,plain,
hBOOL @ induct_true,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(49,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) ) @ C ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ A ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) ) @ B ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ A ) ) ) )
=> ( ( ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ ( hoare_509422987triple @ A ) @ ( hoare_244953527triple @ A ) @ C )
= ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ ( hoare_509422987triple @ A ) @ ( hoare_244953527triple @ A ) @ B ) )
<=> ( C = B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_Abs__triple__inject) ).
thf(198,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) ) @ C ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ A ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) ) @ B ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ A ) ) ) )
=> ( ( ( ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ ( hoare_509422987triple @ A ) @ ( hoare_244953527triple @ A ) @ C )
= ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ ( hoare_509422987triple @ A ) @ ( hoare_244953527triple @ A ) @ B ) )
=> ( C = B ) )
& ( ( C = B )
=> ( ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ ( hoare_509422987triple @ A ) @ ( hoare_244953527triple @ A ) @ C )
= ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ ( hoare_509422987triple @ A ) @ ( hoare_244953527triple @ A ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(55,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) ) @ C ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ A ) ) ) )
=> ( ! [D: $i] : ( hBOOL @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool @ B @ ( hAPP @ ( hoare_509422987triple @ A ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ ( hoare_2037801986triple @ A ) @ D ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool @ B @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_Rep__triple__induct) ).
thf(223,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ bool ) @ ( member @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) ) @ C ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ A ) ) ) )
=> ( ! [D: $i] : ( hBOOL @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool @ B @ ( hAPP @ ( hoare_509422987triple @ A ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ ( hoare_2037801986triple @ A ) @ D ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(8,axiom,
~ ( hBOOL @ induct_false ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_induct__false__def) ).
thf(80,plain,
~ ( hBOOL @ induct_false ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(36,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ B )
= ( ti @ ( fun @ A @ bool ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_Collect__def) ).
thf(158,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ B )
= ( ti @ ( fun @ A @ bool ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(23,axiom,
! [A: $i,B: $i] :
( ( ti @ A @ ( ti @ A @ B ) )
= ( ti @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_ti_idem) ).
thf(114,plain,
! [A: $i,B: $i] :
( ( ti @ A @ ( ti @ A @ B ) )
= ( ti @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(41,axiom,
! [A: $i] :
( ( ti @ A @ ( undefined @ A ) )
= ( undefined @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_HOL_Oundefined_res) ).
thf(171,plain,
! [A: $i] :
( ( ti @ A @ ( undefined @ A ) )
= ( undefined @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(31,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ A @ B @ ( ti @ ( fun @ A @ B ) @ C ) @ D )
= ( hAPP @ A @ B @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_hAPP_arg1) ).
thf(139,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ A @ B @ ( ti @ ( fun @ A @ B ) @ C ) @ D )
= ( hAPP @ A @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(25,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ ( hoare_509422987triple @ A ) ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ bool ) @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ ( hoare_509422987triple @ A ) ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ bool ) ) @ ( type_definition @ ( hoare_509422987triple @ A ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) ) @ ( hoare_2037801986triple @ A ) ) @ ( hoare_244953527triple @ A ) ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_type__definition__triple) ).
thf(119,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ bool @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ ( hoare_509422987triple @ A ) ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ bool ) @ ( hAPP @ ( fun @ ( hoare_509422987triple @ A ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ ( hoare_509422987triple @ A ) ) @ ( fun @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ bool ) ) @ ( type_definition @ ( hoare_509422987triple @ A ) @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) ) @ ( hoare_2037801986triple @ A ) ) @ ( hoare_244953527triple @ A ) ) @ ( hAPP @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ bool ) @ ( collect @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) ) @ ( hoare_1580379338ep_set @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(61,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) ) @ ( type_definition @ B @ A ) @ D ) @ E ) @ F ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ F ) )
=> ( ( hAPP @ B @ A @ D @ ( hAPP @ A @ B @ E @ C ) )
= ( ti @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_type__definition_OAbs__inverse) ).
thf(246,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ bool ) ) @ ( type_definition @ B @ A ) @ D ) @ E ) @ F ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ F ) )
=> ( ( hAPP @ B @ A @ D @ ( hAPP @ A @ B @ E @ C ) )
= ( ti @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( ( cl_HOL_Oequal @ B )
& ( enum @ A ) )
=> ( cl_HOL_Oequal @ ( fun @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___HOL_Oequal) ).
thf(82,plain,
! [A: $i,B: $i] :
( ( ( cl_HOL_Oequal @ B )
& ( enum @ A ) )
=> ( cl_HOL_Oequal @ ( fun @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(52,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ti @ A @ ( hAPP @ B @ A @ C @ D ) )
= ( hAPP @ B @ A @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_hAPP_res) ).
thf(214,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ti @ A @ ( hAPP @ B @ A @ C @ D ) )
= ( hAPP @ B @ A @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(40,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i] :
( ( hAPP @ A @ B @ C @ E )
= ( hAPP @ A @ B @ D @ E ) )
=> ( ( ti @ ( fun @ A @ B ) @ C )
= ( ti @ ( fun @ A @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_ext) ).
thf(168,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i] :
( ( hAPP @ A @ B @ C @ E )
= ( hAPP @ A @ B @ D @ E ) )
=> ( ( ti @ ( fun @ A @ B ) @ C )
= ( ti @ ( fun @ A @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(47,axiom,
( ( ti @ bool @ hoare_1883395792gleton )
= hoare_1883395792gleton ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Hoare__Mirabelle__pjuwniqynr_Ostate__not__singleton_res) ).
thf(190,plain,
( ( ti @ bool @ hoare_1883395792gleton )
= hoare_1883395792gleton ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(21,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ C ) )
<=> ( hBOOL @ ( hAPP @ A @ bool @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_mem__def) ).
thf(107,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ C @ B ) ) )
& ( ( hBOOL @ ( hAPP @ A @ bool @ C @ B ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(60,axiom,
! [A: $i] :
( ( cl_HOL_Oequal @ A )
=> ! [B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( equal_equal @ A ) @ B ) @ C ) )
<=> ( ( ti @ A @ B )
= ( ti @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_equal__eq) ).
thf(239,plain,
! [A: $i] :
( ( cl_HOL_Oequal @ A )
=> ! [B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( equal_equal @ A ) @ B ) @ C ) )
=> ( ( ti @ A @ B )
= ( ti @ A @ C ) ) )
& ( ( ( ti @ A @ B )
= ( ti @ A @ C ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( equal_equal @ A ) @ B ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(7,axiom,
enum @ bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Enum_Oenum) ).
thf(79,plain,
enum @ bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(17,axiom,
! [A: $i,B: $i] : ( cl_HOL_Oequal @ ( sum_sum @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_sum___HOL_Oequal) ).
thf(94,plain,
! [A: $i,B: $i] : ( cl_HOL_Oequal @ ( sum_sum @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(27,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ A @ B @ C @ ( ti @ A @ D ) )
= ( hAPP @ A @ B @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_hAPP_arg2) ).
thf(126,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ A @ B @ C @ ( ti @ A @ D ) )
= ( hAPP @ A @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(30,axiom,
! [A: $i] :
( ( ti @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ ( hoare_509422987triple @ A ) ) @ ( hoare_244953527triple @ A ) )
= ( hoare_244953527triple @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Hoare__Mirabelle__pjuwniqynr_OAbs__triple_res) ).
thf(136,plain,
! [A: $i] :
( ( ti @ ( fun @ ( fun @ ( node @ ( sum_sum @ com @ ( fun @ A @ ( fun @ state @ bool ) ) ) @ ( sum_sum @ state @ A ) ) @ bool ) @ ( hoare_509422987triple @ A ) ) @ ( hoare_244953527triple @ A ) )
= ( hoare_244953527triple @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(263,plain,
$false,
inference(e,[status(thm)],[217,142,174,184,129,73,204,112,143,178,100,69,249,88,93,152,164,211,121,84,147,132,89,233,117,220,260,70,192,92,65,256,225,96,166,161,236,181,86,187,230,76,98,91,198,223,80,158,114,171,139,119,246,82,214,168,190,107,239,79,94,126,136]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.01/0.11 % Problem : SWW469+5 : TPTP v8.2.0. Released v5.3.0.
% 0.12/0.13 % Command : run_Leo-III %s %d
% 0.13/0.32 % Computer : n032.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Sat May 18 19:33:08 EDT 2024
% 0.13/0.32 % CPUTime :
% 0.73/0.76 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.34/0.94 % [INFO] Parsing done (179ms).
% 1.34/0.95 % [INFO] Running in sequential loop mode.
% 1.58/1.16 % [INFO] eprover registered as external prover.
% 1.58/1.16 % [INFO] cvc4 registered as external prover.
% 1.58/1.17 % [INFO] Scanning for conjecture ...
% 1.90/1.26 % [INFO] Found a conjecture (or negated_conjecture) and 62 axioms. Running axiom selection ...
% 2.25/1.33 % [INFO] Axiom selection finished. Selected 62 axioms (removed 0 axioms).
% 2.55/1.44 % [INFO] Problem is first-order (TPTP FOF).
% 2.55/1.45 % [INFO] Type checking passed.
% 2.55/1.46 % [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 ...
% 6.27/2.40 % External prover 'e' found a proof!
% 6.27/2.40 % [INFO] Killing All external provers ...
% 6.27/2.40 % Time passed: 1973ms (effective reasoning time: 1453ms)
% 6.27/2.41 % 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)>
% 6.27/2.41 % 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
% 6.27/2.41 % No. of inferences in proof: 128
% 6.27/2.41 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 1973 ms resp. 1453 ms w/o parsing
% 6.69/2.50 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 6.69/2.50 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------