%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWW473+5 : TPTP v9.3.1. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n004.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 09:10:20 AM UTC 2026
% Result : Theorem 27.16s 12.60s
% Output : Refutation 27.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 161
% Syntax : Number of formulae : 367 ( 163 unt; 0 typ; 0 def)
% Number of atoms : 758 ( 243 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 13745 ( 111 ~; 69 |; 44 &;13257 @)
% ( 19 <=>; 245 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 39 ( 36 usr; 17 con; 0-4 aty)
% Number of variables : 849 ( 0 ^; 833 !; 16 ?; 849 :)
% Comments :
%------------------------------------------------------------------------------
thf(hBOOL_decl,type,
hBOOL: $i > $o ).
thf(hAPP_decl,type,
hAPP: $i > $i > $i > $i > $i ).
thf(fun_decl,type,
fun: $i > $i > $i ).
thf(x_a_decl,type,
x_a: $i ).
thf(bool_decl,type,
bool: $i ).
thf(ord_less_eq_decl,type,
ord_less_eq: $i > $i ).
thf(insert_decl,type,
insert: $i > $i ).
thf(pname_decl,type,
pname: $i ).
thf(mgt_call_decl,type,
mgt_call: $i ).
thf(pn_decl,type,
pn: $i ).
thf(g_decl,type,
g: $i ).
thf(image_decl,type,
image: $i > $i > $i ).
thf(u_decl,type,
u: $i ).
thf(ti_decl,type,
ti: $i > $i > $i ).
thf(undefined_decl,type,
undefined: $i > $i ).
thf(order_decl,type,
order: $i > $o ).
thf(nat_decl,type,
nat: $i ).
thf(preorder_decl,type,
preorder: $i > $o ).
thf(na_decl,type,
na: $i ).
thf(member_decl,type,
member: $i > $i ).
thf(fNot_decl,type,
fNot: $i ).
thf(fdisj_decl,type,
fdisj: $i ).
thf(combb_decl,type,
combb: $i > $i > $i > $i ).
thf(p_decl,type,
p: $i ).
thf(collect_decl,type,
collect: $i > $i ).
thf(finite_finite_decl,type,
finite_finite: $i > $i ).
thf(combs_decl,type,
combs: $i > $i > $i > $i ).
thf(combc_decl,type,
combc: $i > $i > $i > $i ).
thf(fequal_decl,type,
fequal: $i > $i ).
thf(finite_card_decl,type,
finite_card: $i > $i ).
thf(suc_decl,type,
suc: $i ).
thf(minus_minus_decl,type,
minus_minus: $i > $i ).
thf(fimplies_decl,type,
fimplies: $i ).
thf(finite_finite_1_decl,type,
finite_finite_1: $i > $o ).
thf(fconj_decl,type,
fconj: $i ).
thf(combi_decl,type,
combi: $i > $i ).
thf(76,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ combs ) ) @ ( C @ ( A @ fun ) @ ( B @ ( A @ fun ) @ fun ) @ ( C @ ( B @ fun ) @ ( A @ fun ) @ fun ) @ ti ) )
= ( C @ ( B @ ( A @ combs ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_COMBS_res) ).
thf(385,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ combs ) ) @ ( C @ ( A @ fun ) @ ( B @ ( A @ fun ) @ fun ) @ ( C @ ( B @ fun ) @ ( A @ fun ) @ fun ) @ ti ) )
= ( C @ ( B @ ( A @ combs ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(156,axiom,
! [A: $i] :
( ( A @ preorder )
=> ( ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ fun ) @ ti ) )
= ( A @ ord_less_eq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Orderings_Oord__class_Oless__eq_res) ).
thf(645,plain,
! [A: $i] :
( ( A @ preorder )
=> ( ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ fun ) @ ti ) )
= ( A @ ord_less_eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(152,axiom,
( ( u @ ( bool @ ( pname @ fun ) @ ti ) )
= u ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_v_U_res) ).
thf(628,plain,
( ( u @ ( bool @ ( pname @ fun ) @ ti ) )
= u ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(629,plain,
( ( u @ ( bool @ ( pname @ fun ) @ ti ) )
= u ),
inference(lifteq,[status(thm)],[628]) ).
thf(62,axiom,
bool @ order,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Oorder) ).
thf(347,plain,
bool @ order,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(120,axiom,
! [A: $i,B: $i] :
( ( B @ ( suc @ ( nat @ ( nat @ hAPP ) ) ) @ ( A @ ( suc @ ( nat @ ( nat @ hAPP ) ) ) @ ( nat @ minus_minus @ ( nat @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( nat @ ( nat @ hAPP ) ) ) )
= ( B @ ( A @ ( nat @ minus_minus @ ( nat @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( nat @ ( nat @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_38_diff__Suc__Suc) ).
thf(518,plain,
! [A: $i,B: $i] :
( ( B @ ( suc @ ( nat @ ( nat @ hAPP ) ) ) @ ( A @ ( suc @ ( nat @ ( nat @ hAPP ) ) ) @ ( nat @ minus_minus @ ( nat @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( nat @ ( nat @ hAPP ) ) ) )
= ( B @ ( A @ ( nat @ minus_minus @ ( nat @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( nat @ ( nat @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(64,axiom,
bool @ finite_finite_1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL_Obool___Finite__Set_Ofinite) ).
thf(352,plain,
bool @ finite_finite_1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(56,axiom,
! [A: $i] :
( ( A @ finite_finite_1 )
=> ! [B: $i] : ( B @ ( A @ finite_finite @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_15_finite) ).
thf(333,plain,
! [A: $i] :
( ( A @ finite_finite_1 )
=> ! [B: $i] : ( B @ ( A @ finite_finite @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(122,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( B @ member @ ( bool @ ( bool @ ( B @ fun ) @ fun ) @ ( B @ hAPP ) ) ) @ ( bool @ ( bool @ ( B @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( ( ( C @ ( A @ ti ) )
= ( E @ ( D @ ( A @ ( B @ hAPP ) ) ) ) )
=> ( F @ ( D @ ( A @ ( B @ image ) @ ( bool @ ( A @ fun ) @ ( bool @ ( B @ fun ) @ fun ) @ ( A @ ( B @ fun ) @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( B @ fun ) @ hAPP ) ) ) @ ( C @ ( A @ member @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_rev__image__eqI) ).
thf(523,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( B @ member @ ( bool @ ( bool @ ( B @ fun ) @ fun ) @ ( B @ hAPP ) ) ) @ ( bool @ ( bool @ ( B @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( ( ( C @ ( A @ ti ) )
= ( E @ ( D @ ( A @ ( B @ hAPP ) ) ) ) )
=> ( F @ ( D @ ( A @ ( B @ image ) @ ( bool @ ( A @ fun ) @ ( bool @ ( B @ fun ) @ fun ) @ ( A @ ( B @ fun ) @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( B @ fun ) @ hAPP ) ) ) @ ( C @ ( A @ member @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(48,axiom,
! [A: $i] :
( ( A @ ( suc @ ( nat @ ( nat @ hAPP ) ) ) )
!= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_18_Suc__n__not__n) ).
thf(308,plain,
! [A: $i] :
( ( A @ ( suc @ ( nat @ ( nat @ hAPP ) ) ) )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(30,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( A @ insert @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( B @ ( A @ member @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
<=> ( ( D @ ( B @ ( A @ member @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
| ( ( B @ ( A @ ti ) )
= ( C @ ( A @ ti ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_60_insert__iff) ).
thf(247,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( D @ ( B @ ( A @ member @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
| ( ( B @ ( A @ ti ) )
= ( C @ ( A @ ti ) ) ) )
=> ( D @ ( C @ ( A @ insert @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( B @ ( A @ member @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL ) )
& ( ( D @ ( C @ ( A @ insert @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( B @ ( A @ member @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( ( D @ ( B @ ( A @ member @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
| ( ( B @ ( A @ ti ) )
= ( C @ ( A @ ti ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(160,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( bool @ ( A @ fun ) @ ti ) )
= ( C @ ( bool @ ( A @ fun ) @ ti ) ) )
=> ( C @ ( B @ ( bool @ ( A @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_67_equalityD1) ).
thf(655,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( bool @ ( A @ fun ) @ ti ) )
= ( C @ ( bool @ ( A @ fun ) @ ti ) ) )
=> ( C @ ( B @ ( bool @ ( A @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(147,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ collect @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) )
= ( B @ ( bool @ ( A @ fun ) @ ti ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_76_Collect__def) ).
thf(614,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)],[147]) ).
thf(82,axiom,
! [A: $i,B: $i] :
( ~ ( B @ ( A @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
<=> ( A @ ( B @ ( suc @ ( nat @ ( nat @ hAPP ) ) ) @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_not__less__eq__eq) ).
thf(408,plain,
! [A: $i,B: $i] :
( ( ( A @ ( B @ ( suc @ ( nat @ ( nat @ hAPP ) ) ) @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ~ ( B @ ( A @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) )
& ( ~ ( B @ ( A @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( A @ ( B @ ( suc @ ( nat @ ( nat @ hAPP ) ) ) @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(5,axiom,
nat @ order,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Oorder) ).
thf(170,plain,
nat @ order,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(8,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( bool @ ( A @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( ( C @ ( B @ ( A @ member @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( D @ ( B @ ( A @ member @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_set__mp) ).
thf(174,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( bool @ ( A @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( ( C @ ( B @ ( A @ member @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( D @ ( B @ ( A @ member @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(41,axiom,
( ( p @ ( bool @ ( bool @ ( x_a @ fun ) @ fun ) @ ( bool @ ( x_a @ fun ) @ fun ) @ ti ) )
= p ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_v_P_res) ).
thf(287,plain,
( ( p @ ( bool @ ( bool @ ( x_a @ fun ) @ fun ) @ ( bool @ ( x_a @ fun ) @ fun ) @ ti ) )
= p ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(288,plain,
( ( p @ ( bool @ ( bool @ ( x_a @ fun ) @ fun ) @ ( bool @ ( x_a @ fun ) @ fun ) @ ti ) )
= p ),
inference(lifteq,[status(thm)],[287]) ).
thf(31,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( ( A @ ( B @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_le__antisym) ).
thf(257,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( ( A @ ( B @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(52,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/sandbox2/benchmark/theBenchmark.p',help_fequal_1_1_T) ).
thf(320,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)],[52]) ).
thf(133,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( suc @ ( nat @ ( nat @ hAPP ) ) ) @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( A @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_30_Suc__leD) ).
thf(565,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( suc @ ( nat @ ( nat @ hAPP ) ) ) @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( A @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(149,axiom,
! [A: $i,B: $i] :
( ( A = B )
=> ( B @ ( A @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_22_eq__imp__le) ).
thf(619,plain,
! [A: $i,B: $i] :
( ( A = B )
=> ( B @ ( A @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(61,axiom,
! [A: $i] :
( ( A @ finite_finite @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ti ) )
= ( A @ finite_finite ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Finite__Set_Ofinite_res) ).
thf(344,plain,
! [A: $i] :
( ( A @ finite_finite @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ti ) )
= ( A @ finite_finite ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(67,axiom,
! [A: $i] :
( ( A @ combi @ ( A @ ( A @ fun ) @ ti ) )
= ( A @ combi ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_COMBI_res) ).
thf(357,plain,
! [A: $i] :
( ( A @ combi @ ( A @ ( A @ fun ) @ ti ) )
= ( A @ combi ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(14,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( bool @ ( A @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( D @ ( B @ ( A @ insert @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( C @ ( bool @ ( A @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_subset__insertI2) ).
thf(196,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( bool @ ( A @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( D @ ( B @ ( A @ insert @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( C @ ( bool @ ( A @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(132,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( B @ finite_finite @ ( bool @ ( bool @ ( B @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( ( D @ ( C @ ( B @ ( A @ image ) @ ( bool @ ( B @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( B @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( B @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( E @ ( bool @ ( B @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( B @ fun ) @ fun ) @ ( bool @ ( B @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( B @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ? [F: $i] :
( ( ( E @ ( bool @ ( B @ fun ) @ ti ) )
= ( F @ ( C @ ( B @ ( A @ image ) @ ( bool @ ( B @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( B @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( B @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) ) )
& ( F @ ( A @ finite_finite @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
& ( D @ ( F @ ( bool @ ( A @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_47_finite__subset__image) ).
thf(559,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( B @ finite_finite @ ( bool @ ( bool @ ( B @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( ( D @ ( C @ ( B @ ( A @ image ) @ ( bool @ ( B @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( B @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( B @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( E @ ( bool @ ( B @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( B @ fun ) @ fun ) @ ( bool @ ( B @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( B @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ? [F: $i] :
( ( ( E @ ( bool @ ( B @ fun ) @ ti ) )
= ( F @ ( C @ ( B @ ( A @ image ) @ ( bool @ ( B @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( B @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( B @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) ) )
& ( F @ ( A @ finite_finite @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
& ( D @ ( F @ ( bool @ ( A @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ image ) @ ( bool @ ( B @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( B @ ( A @ fun ) @ fun ) @ ti ) )
= ( B @ ( A @ image ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Set_Oimage_res) ).
thf(189,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ image ) @ ( bool @ ( B @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( B @ ( A @ fun ) @ fun ) @ ti ) )
= ( B @ ( A @ image ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(146,axiom,
! [A: $i] :
( ( A @ ( nat @ finite_finite @ ( bool @ ( bool @ ( nat @ fun ) @ hAPP ) ) ) @ hBOOL )
<=> ? [B: $i] :
! [C: $i] :
( ( A @ ( C @ ( nat @ member @ ( bool @ ( bool @ ( nat @ fun ) @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( bool @ ( nat @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( C @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_98_finite__nat__set__iff__bounded__le) ).
thf(606,plain,
! [A: $i] :
( ( ? [B: $i] :
! [C: $i] :
( ( A @ ( C @ ( nat @ member @ ( bool @ ( bool @ ( nat @ fun ) @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( bool @ ( nat @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( C @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) )
=> ( A @ ( nat @ finite_finite @ ( bool @ ( bool @ ( nat @ fun ) @ hAPP ) ) ) @ hBOOL ) )
& ( ( A @ ( nat @ finite_finite @ ( bool @ ( bool @ ( nat @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ? [B: $i] :
! [C: $i] :
( ( A @ ( C @ ( nat @ member @ ( bool @ ( bool @ ( nat @ fun ) @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( bool @ ( nat @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( C @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(40,axiom,
! [A: $i] :
( ( A @ fequal @ ( bool @ ( A @ fun ) @ ( A @ fun ) @ ti ) )
= ( A @ fequal ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_fequal_res) ).
thf(284,plain,
! [A: $i] :
( ( A @ fequal @ ( bool @ ( A @ fun ) @ ( A @ fun ) @ ti ) )
= ( A @ fequal ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(84,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ insert @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( B @ ( A @ insert @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) )
= ( C @ ( B @ ( A @ insert @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_58_insert__absorb2) ).
thf(416,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ insert @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( B @ ( A @ insert @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) )
= ( C @ ( B @ ( A @ insert @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(54,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( D @ ( A @ ( B @ image ) @ ( bool @ ( A @ fun ) @ ( bool @ ( B @ fun ) @ fun ) @ ( A @ ( B @ fun ) @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( B @ fun ) @ hAPP ) ) ) @ ( C @ ( A @ member @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ~ ! [F: $i] :
( ( ( C @ ( A @ ti ) )
= ( F @ ( D @ ( A @ ( B @ hAPP ) ) ) ) )
=> ~ ( E @ ( F @ ( B @ member @ ( bool @ ( bool @ ( B @ fun ) @ fun ) @ ( B @ hAPP ) ) ) @ ( bool @ ( bool @ ( B @ fun ) @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_92_imageE) ).
thf(325,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( D @ ( A @ ( B @ image ) @ ( bool @ ( A @ fun ) @ ( bool @ ( B @ fun ) @ fun ) @ ( A @ ( B @ fun ) @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( B @ fun ) @ hAPP ) ) ) @ ( C @ ( A @ member @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ~ ! [F: $i] :
( ( ( C @ ( A @ ti ) )
= ( F @ ( D @ ( A @ ( B @ hAPP ) ) ) ) )
=> ~ ( E @ ( F @ ( B @ member @ ( bool @ ( bool @ ( B @ fun ) @ fun ) @ ( B @ hAPP ) ) ) @ ( bool @ ( bool @ ( B @ fun ) @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(42,axiom,
u @ ( pname @ finite_finite @ ( bool @ ( bool @ ( pname @ fun ) @ hAPP ) ) ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
thf(289,plain,
u @ ( pname @ finite_finite @ ( bool @ ( bool @ ( pname @ fun ) @ hAPP ) ) ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(96,axiom,
! [A: $i] :
( ( A @ finite_finite_1 )
=> ! [B: $i] : ( B @ ( A @ finite_finite @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_14_finite__code) ).
thf(448,plain,
! [A: $i] :
( ( A @ finite_finite_1 )
=> ! [B: $i] : ( B @ ( A @ finite_finite @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ti ) @ ( A @ ti ) )
= ( B @ ( A @ ti ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_ti_idem) ).
thf(164,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ti ) @ ( A @ ti ) )
= ( B @ ( A @ ti ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(94,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( A @ finite_finite @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( C @ ( B @ ( A @ insert @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( A @ finite_card @ ( nat @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( C @ ( A @ finite_card @ ( nat @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_7_card__insert__le) ).
thf(443,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( A @ finite_finite @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( C @ ( B @ ( A @ insert @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( A @ finite_card @ ( nat @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( C @ ( A @ finite_card @ ( nat @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(72,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( bool @ ( A @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( ( C @ ( A @ finite_finite @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( A @ finite_finite @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_28_finite__subset) ).
thf(376,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( bool @ ( A @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( ( C @ ( A @ finite_finite @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( A @ finite_finite @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(150,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( A @ ( C @ ( nat @ minus_minus @ ( nat @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( A @ ( B @ ( nat @ minus_minus @ ( nat @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_43_diff__le__mono) ).
thf(623,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( A @ ( C @ ( nat @ minus_minus @ ( nat @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( A @ ( B @ ( nat @ minus_minus @ ( nat @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(118,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
| ( B @ ( A @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_23_nat__le__linear) ).
thf(514,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
| ( B @ ( A @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(63,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ collect @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( A @ finite_finite @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
| ( C @ ( A @ collect @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( A @ finite_finite @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL ) )
=> ( B @ ( C @ ( fconj @ ( A @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) @ ( bool @ ( bool @ fun ) @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ ( bool @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ fun ) @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ combs ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( A @ collect @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( A @ finite_finite @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_10_finite__Collect__conjI) ).
thf(348,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ collect @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( A @ finite_finite @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
| ( C @ ( A @ collect @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( A @ finite_finite @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL ) )
=> ( B @ ( C @ ( fconj @ ( A @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) @ ( bool @ ( bool @ fun ) @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ ( bool @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ fun ) @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ combs ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( A @ collect @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( A @ finite_finite @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(65,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( fdisj @ ( bool @ ( bool @ fun ) @ ( bool @ hAPP ) ) ) @ ( bool @ ( bool @ hAPP ) ) ) @ hBOOL )
| ~ ( B @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fdisj_2_1_U) ).
thf(353,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( fdisj @ ( bool @ ( bool @ fun ) @ ( bool @ hAPP ) ) ) @ ( bool @ ( bool @ hAPP ) ) ) @ hBOOL )
| ~ ( B @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(107,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( A @ insert @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( B @ ( A @ member @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( ( ( B @ ( A @ ti ) )
!= ( C @ ( A @ ti ) ) )
=> ( D @ ( B @ ( A @ member @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_54_insertE) ).
thf(480,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( A @ insert @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( B @ ( A @ member @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( ( ( B @ ( A @ ti ) )
!= ( C @ ( A @ ti ) ) )
=> ( D @ ( B @ ( A @ member @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(162,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( D @ ( C @ ( A @ member @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( ~ ( B @ ( C @ ( A @ member @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( ( ( D @ ( C @ ( A @ insert @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) )
= ( B @ ( C @ ( A @ insert @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) ) )
<=> ( ( D @ ( bool @ ( A @ fun ) @ ti ) )
= ( B @ ( bool @ ( A @ fun ) @ ti ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_62_insert__ident) ).
thf(660,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( D @ ( C @ ( A @ member @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( ~ ( B @ ( C @ ( A @ member @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( ( ( ( D @ ( bool @ ( A @ fun ) @ ti ) )
= ( B @ ( bool @ ( A @ fun ) @ ti ) ) )
=> ( ( D @ ( C @ ( A @ insert @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) )
= ( B @ ( C @ ( A @ insert @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) ) ) )
& ( ( ( D @ ( C @ ( A @ insert @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) )
= ( B @ ( C @ ( A @ insert @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) ) )
=> ( ( D @ ( bool @ ( A @ fun ) @ ti ) )
= ( B @ ( bool @ ( A @ fun ) @ ti ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(49,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( D @ ( B @ member @ ( bool @ ( bool @ ( B @ fun ) @ fun ) @ ( B @ hAPP ) ) ) @ ( bool @ ( bool @ ( B @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( ( E @ ( C @ ( A @ ( B @ image ) @ ( bool @ ( A @ fun ) @ ( bool @ ( B @ fun ) @ fun ) @ ( A @ ( B @ fun ) @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( B @ fun ) @ hAPP ) ) ) @ ( D @ ( C @ ( A @ ( B @ hAPP ) ) ) @ ( A @ insert @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) )
= ( E @ ( C @ ( A @ ( B @ image ) @ ( bool @ ( A @ fun ) @ ( bool @ ( B @ fun ) @ fun ) @ ( A @ ( B @ fun ) @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( B @ fun ) @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_89_insert__image) ).
thf(312,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( D @ ( B @ member @ ( bool @ ( bool @ ( B @ fun ) @ fun ) @ ( B @ hAPP ) ) ) @ ( bool @ ( bool @ ( B @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( ( E @ ( C @ ( A @ ( B @ image ) @ ( bool @ ( A @ fun ) @ ( bool @ ( B @ fun ) @ fun ) @ ( A @ ( B @ fun ) @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( B @ fun ) @ hAPP ) ) ) @ ( D @ ( C @ ( A @ ( B @ hAPP ) ) ) @ ( A @ insert @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) )
= ( E @ ( C @ ( A @ ( B @ image ) @ ( bool @ ( A @ fun ) @ ( bool @ ( B @ fun ) @ fun ) @ ( A @ ( B @ fun ) @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( B @ fun ) @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(44,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ finite_finite @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( bool @ ( A @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ combc ) ) @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ collect @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ finite_finite @ ( bool @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_1_finite__Collect__subsets) ).
thf(292,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ finite_finite @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( bool @ ( A @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ combc ) ) @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ collect @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ finite_finite @ ( bool @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ hAPP ) ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(98,axiom,
! [A: $i] :
( ( A @ insert @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ fun ) @ ti ) )
= ( A @ insert ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Set_Oinsert_res) ).
thf(452,plain,
! [A: $i] :
( ( A @ insert @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ fun ) @ ti ) )
= ( A @ insert ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(74,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ combi @ ( A @ ( A @ hAPP ) ) ) )
= ( B @ ( A @ ti ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBI_1_1_U) ).
thf(380,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ combi @ ( A @ ( A @ hAPP ) ) ) )
= ( B @ ( A @ ti ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(117,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( A @ finite_finite @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( C @ ( B @ ( A @ insert @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( A @ finite_finite @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_3_finite_OinsertI) ).
thf(512,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( A @ finite_finite @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( C @ ( B @ ( A @ insert @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( A @ finite_finite @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(125,axiom,
( ( suc @ ( nat @ ( nat @ fun ) @ ti ) )
= suc ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Nat_OSuc_res) ).
thf(534,plain,
( ( suc @ ( nat @ ( nat @ fun ) @ ti ) )
= suc ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(36,axiom,
! [A: $i,B: $i] :
( ( B @ preorder )
=> ( B @ ( A @ fun ) @ preorder ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun___Orderings_Opreorder) ).
thf(270,plain,
! [A: $i,B: $i] :
( ( B @ preorder )
=> ( B @ ( A @ fun ) @ preorder ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(124,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( D @ ( C @ ( A @ member @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( ( C @ ( A @ ti ) )
= ( B @ ( A @ ti ) ) ) )
=> ( D @ ( B @ ( A @ insert @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( C @ ( A @ member @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_53_insertCI) ).
thf(529,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( D @ ( C @ ( A @ member @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( ( C @ ( A @ ti ) )
= ( B @ ( A @ ti ) ) ) )
=> ( D @ ( B @ ( A @ insert @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( C @ ( A @ member @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(32,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( A @ finite_finite @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( ( C @ ( B @ ( bool @ ( A @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( C @ ( A @ finite_card @ ( nat @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( B @ ( A @ finite_card @ ( nat @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_5_card__mono) ).
thf(260,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( A @ finite_finite @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( ( C @ ( B @ ( bool @ ( A @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( C @ ( A @ finite_card @ ( nat @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( B @ ( A @ finite_card @ ( nat @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(79,axiom,
! [A: $i] :
( ( A @ ( bool @ ti ) @ hBOOL )
<=> ( A @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_hBOOL_arg1) ).
thf(392,plain,
! [A: $i] :
( ( ( A @ hBOOL )
=> ( A @ ( bool @ ti ) @ hBOOL ) )
& ( ( A @ ( bool @ ti ) @ hBOOL )
=> ( A @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(46,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( D @ ( A @ ( B @ image ) @ ( bool @ ( A @ fun ) @ ( bool @ ( B @ fun ) @ fun ) @ ( A @ ( B @ fun ) @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( B @ fun ) @ hAPP ) ) ) @ ( C @ ( bool @ ( A @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
<=> ? [F: $i] :
( ( ( C @ ( bool @ ( A @ fun ) @ ti ) )
= ( F @ ( D @ ( A @ ( B @ image ) @ ( bool @ ( A @ fun ) @ ( bool @ ( B @ fun ) @ fun ) @ ( A @ ( B @ fun ) @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( B @ fun ) @ hAPP ) ) ) ) )
& ( E @ ( F @ ( bool @ ( B @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( B @ fun ) @ fun ) @ ( bool @ ( B @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( B @ fun ) @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_90_subset__image__iff) ).
thf(297,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ? [F: $i] :
( ( ( C @ ( bool @ ( A @ fun ) @ ti ) )
= ( F @ ( D @ ( A @ ( B @ image ) @ ( bool @ ( A @ fun ) @ ( bool @ ( B @ fun ) @ fun ) @ ( A @ ( B @ fun ) @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( B @ fun ) @ hAPP ) ) ) ) )
& ( E @ ( F @ ( bool @ ( B @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( B @ fun ) @ fun ) @ ( bool @ ( B @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( B @ fun ) @ hAPP ) ) ) @ hBOOL ) )
=> ( E @ ( D @ ( A @ ( B @ image ) @ ( bool @ ( A @ fun ) @ ( bool @ ( B @ fun ) @ fun ) @ ( A @ ( B @ fun ) @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( B @ fun ) @ hAPP ) ) ) @ ( C @ ( bool @ ( A @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL ) )
& ( ( E @ ( D @ ( A @ ( B @ image ) @ ( bool @ ( A @ fun ) @ ( bool @ ( B @ fun ) @ fun ) @ ( A @ ( B @ fun ) @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( B @ fun ) @ hAPP ) ) ) @ ( C @ ( bool @ ( A @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ? [F: $i] :
( ( ( C @ ( bool @ ( A @ fun ) @ ti ) )
= ( F @ ( D @ ( A @ ( B @ image ) @ ( bool @ ( A @ fun ) @ ( bool @ ( B @ fun ) @ fun ) @ ( A @ ( B @ fun ) @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( B @ fun ) @ hAPP ) ) ) ) )
& ( E @ ( F @ ( bool @ ( B @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( B @ fun ) @ fun ) @ ( bool @ ( B @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( B @ fun ) @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(89,axiom,
! [A: $i] :
( A
!= ( A @ ( suc @ ( nat @ ( nat @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_19_n__not__Suc__n) ).
thf(429,plain,
! [A: $i] :
( A
!= ( A @ ( suc @ ( nat @ ( nat @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(12,axiom,
( ( fNot @ ( bool @ ( bool @ fun ) @ ti ) )
= fNot ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_fNot_res) ).
thf(192,plain,
( ( fNot @ ( bool @ ( bool @ fun ) @ ti ) )
= fNot ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(153,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ insert @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
<=> ( ( D @ ( C @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
| ( ( B @ ( A @ ti ) )
= ( D @ ( A @ ti ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_61_insert__code) ).
thf(630,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( D @ ( C @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
| ( ( B @ ( A @ ti ) )
= ( D @ ( A @ ti ) ) ) )
=> ( D @ ( C @ ( B @ ( A @ insert @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) )
& ( ( D @ ( C @ ( B @ ( A @ insert @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( D @ ( C @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
| ( ( B @ ( A @ ti ) )
= ( D @ ( A @ ti ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(103,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( ( A @ ( B @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( A @ ( nat @ minus_minus @ ( nat @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( B @ ( C @ ( nat @ minus_minus @ ( nat @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
<=> ( A @ ( C @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_39_le__diff__iff) ).
thf(467,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( ( A @ ( B @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( ( ( A @ ( C @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( A @ ( nat @ minus_minus @ ( nat @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( B @ ( C @ ( nat @ minus_minus @ ( nat @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) )
& ( ( B @ ( A @ ( nat @ minus_minus @ ( nat @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( B @ ( C @ ( nat @ minus_minus @ ( nat @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( A @ ( C @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(151,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( A @ insert @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( B @ ( A @ insert @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) )
= ( D @ ( B @ ( A @ insert @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( C @ ( A @ insert @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_59_insert__commute) ).
thf(625,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( A @ insert @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( B @ ( A @ insert @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) )
= ( D @ ( B @ ( A @ insert @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( C @ ( A @ insert @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(101,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ insert @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) )
= ( C @ ( A @ member @ ( bool @ ( bool @ ( A @ fun ) @ ( A @ combc ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( B @ ( A @ fequal @ ( bool @ ( A @ ( A @ combc ) ) @ ( bool @ ( A @ fun ) @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( fdisj @ ( A @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) @ ( bool @ ( bool @ fun ) @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ ( bool @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ fun ) @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ combs ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( A @ collect @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_insert__compr__raw) ).
thf(461,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ insert @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) )
= ( C @ ( A @ member @ ( bool @ ( bool @ ( A @ fun ) @ ( A @ combc ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( B @ ( A @ fequal @ ( bool @ ( A @ ( A @ combc ) ) @ ( bool @ ( A @ fun ) @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( fdisj @ ( A @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) @ ( bool @ ( bool @ fun ) @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ ( bool @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ fun ) @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ combs ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( A @ collect @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(53,axiom,
( ( nat @ minus_minus @ ( nat @ ( nat @ fun ) @ ( nat @ fun ) @ ti ) )
= ( nat @ minus_minus ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Groups_Ominus__class_Ominus_res) ).
thf(323,plain,
( ( nat @ minus_minus @ ( nat @ ( nat @ fun ) @ ( nat @ fun ) @ ti ) )
= ( nat @ minus_minus ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(324,plain,
( ( nat @ minus_minus @ ( nat @ ( nat @ fun ) @ ( nat @ fun ) @ ti ) )
= ( nat @ minus_minus ) ),
inference(lifteq,[status(thm)],[323]) ).
thf(158,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( fimplies @ ( bool @ ( bool @ fun ) @ ( bool @ hAPP ) ) ) @ ( bool @ ( bool @ hAPP ) ) ) @ hBOOL )
| ~ ( B @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fimplies_2_1_U) ).
thf(650,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( fimplies @ ( bool @ ( bool @ fun ) @ ( bool @ hAPP ) ) ) @ ( bool @ ( bool @ hAPP ) ) ) @ hBOOL )
| ~ ( B @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(77,axiom,
! [A: $i,B: $i] :
( ( B @ order )
=> ( B @ ( A @ fun ) @ order ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun___Orderings_Oorder) ).
thf(388,plain,
! [A: $i,B: $i] :
( ( B @ order )
=> ( B @ ( A @ fun ) @ order ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(4,axiom,
! [A: $i] :
( ( A @ undefined @ ( A @ ti ) )
= ( A @ undefined ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_HOL_Oundefined_res) ).
thf(167,plain,
! [A: $i] :
( ( A @ undefined @ ( A @ ti ) )
= ( A @ undefined ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(168,plain,
! [A: $i] :
( ( A @ undefined @ ( A @ ti ) )
= ( A @ undefined ) ),
inference(cnf,[status(esa)],[167]) ).
thf(169,plain,
! [A: $i] :
( ( A @ undefined @ ( A @ ti ) )
= ( A @ undefined ) ),
inference(lifteq,[status(thm)],[168]) ).
thf(114,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ ( nat @ minus_minus @ ( nat @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( nat @ minus_minus @ ( nat @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( nat @ ( nat @ hAPP ) ) ) )
= ( B @ ( C @ ( A @ ( nat @ minus_minus @ ( nat @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( nat @ minus_minus @ ( nat @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( nat @ ( nat @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_25_diff__commute) ).
thf(499,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ ( nat @ minus_minus @ ( nat @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( nat @ minus_minus @ ( nat @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( nat @ ( nat @ hAPP ) ) ) )
= ( B @ ( C @ ( A @ ( nat @ minus_minus @ ( nat @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( nat @ minus_minus @ ( nat @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( nat @ ( nat @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(104,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( bool @ ( A @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( ( C @ ( B @ ( A @ member @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( D @ ( B @ ( A @ member @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_69_in__mono) ).
thf(471,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( bool @ ( A @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( ( C @ ( B @ ( A @ member @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( D @ ( B @ ( A @ member @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(24,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( bool @ ( A @ fun ) @ ti ) )
= ( C @ ( bool @ ( A @ fun ) @ ti ) ) )
=> ~ ( ( C @ ( B @ ( bool @ ( A @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ~ ( B @ ( C @ ( bool @ ( A @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_73_equalityE) ).
thf(225,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( bool @ ( A @ fun ) @ ti ) )
= ( C @ ( bool @ ( A @ fun ) @ ti ) ) )
=> ~ ( ( C @ ( B @ ( bool @ ( A @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ~ ( B @ ( C @ ( bool @ ( A @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(59,axiom,
! [A: $i,B: $i] :
( ( B @ hBOOL )
| ~ ( A @ hBOOL )
| ~ ( B @ ( A @ ( fimplies @ ( bool @ ( bool @ fun ) @ ( bool @ hAPP ) ) ) @ ( bool @ ( bool @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fimplies_3_1_U) ).
thf(339,plain,
! [A: $i,B: $i] :
( ( B @ hBOOL )
| ~ ( A @ hBOOL )
| ~ ( B @ ( A @ ( fimplies @ ( bool @ ( bool @ fun ) @ ( bool @ hAPP ) ) ) @ ( bool @ ( bool @ hAPP ) ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(130,axiom,
! [A: $i] :
( ( A @ ( nat @ ord_less_eq @ ( bool @ ( nat @ ( nat @ combc ) ) @ ( bool @ ( nat @ fun ) @ ( nat @ fun ) @ ( bool @ ( nat @ fun ) @ ( nat @ fun ) @ hAPP ) ) ) @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( nat @ collect @ ( bool @ ( nat @ fun ) @ ( bool @ ( nat @ fun ) @ hAPP ) ) ) @ ( nat @ finite_card @ ( nat @ ( bool @ ( nat @ fun ) @ hAPP ) ) ) )
= ( A @ ( suc @ ( nat @ ( nat @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_13_card__Collect__le__nat) ).
thf(554,plain,
! [A: $i] :
( ( A @ ( nat @ ord_less_eq @ ( bool @ ( nat @ ( nat @ combc ) ) @ ( bool @ ( nat @ fun ) @ ( nat @ fun ) @ ( bool @ ( nat @ fun ) @ ( nat @ fun ) @ hAPP ) ) ) @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( nat @ collect @ ( bool @ ( nat @ fun ) @ ( bool @ ( nat @ fun ) @ hAPP ) ) ) @ ( nat @ finite_card @ ( nat @ ( bool @ ( nat @ fun ) @ hAPP ) ) ) )
= ( A @ ( suc @ ( nat @ ( nat @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(193,plain,
( ( fNot @ ( bool @ ( bool @ fun ) @ ti ) )
= fNot ),
inference(lifteq,[status(thm)],[192]) ).
thf(123,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( suc @ ( nat @ ( nat @ hAPP ) ) ) @ ( B @ ( A @ ( suc @ ( nat @ ( nat @ hAPP ) ) ) @ ( nat @ minus_minus @ ( nat @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( nat @ minus_minus @ ( nat @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( nat @ ( nat @ hAPP ) ) ) )
= ( C @ ( B @ ( A @ ( nat @ minus_minus @ ( nat @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( nat @ minus_minus @ ( nat @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( nat @ ( nat @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_37_Suc__diff__diff) ).
thf(526,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( suc @ ( nat @ ( nat @ hAPP ) ) ) @ ( B @ ( A @ ( suc @ ( nat @ ( nat @ hAPP ) ) ) @ ( nat @ minus_minus @ ( nat @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( nat @ minus_minus @ ( nat @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( nat @ ( nat @ hAPP ) ) ) )
= ( C @ ( B @ ( A @ ( nat @ minus_minus @ ( nat @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( nat @ minus_minus @ ( nat @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( nat @ ( nat @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(110,axiom,
! [A: $i,B: $i] :
( ( ( A @ finite_finite_1 )
& ( B @ finite_finite_1 ) )
=> ( B @ ( A @ fun ) @ finite_finite_1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_fun___Finite__Set_Ofinite) ).
thf(489,plain,
! [A: $i,B: $i] :
( ( ( A @ finite_finite_1 )
& ( B @ finite_finite_1 ) )
=> ( B @ ( A @ fun ) @ finite_finite_1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(70,axiom,
! [A: $i] :
( ~ ( A @ hBOOL )
| ~ ( A @ ( fNot @ ( bool @ ( bool @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fNot_1_1_U) ).
thf(368,plain,
! [A: $i] :
( ~ ( A @ hBOOL )
| ~ ( A @ ( fNot @ ( bool @ ( bool @ hAPP ) ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(369,plain,
! [A: $i] :
( ~ ( A @ hBOOL )
| ~ ( A @ ( fNot @ ( bool @ ( bool @ hAPP ) ) ) @ hBOOL ) ),
inference(cnf,[status(esa)],[368]) ).
thf(748,plain,
! [A: $i] :
( ~ $true
| ( ( A @ ( fNot @ ( bool @ ( bool @ hAPP ) ) ) @ hBOOL )
!= ( A @ hBOOL ) )
| ~ ( A @ hBOOL ) ),
inference(eqfactor_ordered,[status(thm)],[369]) ).
thf(750,plain,
! [A: $i] :
( ( ( A @ ( fNot @ ( bool @ ( bool @ hAPP ) ) ) )
!= A )
| ~ ( A @ hBOOL ) ),
inference(simp,[status(thm)],[748]) ).
thf(1005,plain,
! [A: $i] :
( ( ( u @ ( pname @ finite_finite @ ( bool @ ( bool @ ( pname @ fun ) @ hAPP ) ) ) @ hBOOL )
!= ( A @ hBOOL ) )
| ( ( A @ ( fNot @ ( bool @ ( bool @ hAPP ) ) ) )
!= A )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[289,750]) ).
thf(1006,plain,
! [A: $i] :
( ( ( u @ ( pname @ finite_finite @ ( bool @ ( bool @ ( pname @ fun ) @ hAPP ) ) ) @ hBOOL )
!= ( A @ hBOOL ) )
| ( ( A @ ( fNot @ ( bool @ ( bool @ hAPP ) ) ) )
!= A ) ),
inference(simp,[status(thm)],[1005]) ).
thf(1007,plain,
( ( u @ ( pname @ finite_finite @ ( bool @ ( bool @ ( pname @ fun ) @ hAPP ) ) ) @ ( fNot @ ( bool @ ( bool @ hAPP ) ) ) )
!= ( u @ ( pname @ finite_finite @ ( bool @ ( bool @ ( pname @ fun ) @ hAPP ) ) ) ) ),
inference(pattern_uni,[status(thm)],[1006:[bind(A,$thf( u @ ( pname @ finite_finite @ ( bool @ ( bool @ ( pname @ fun ) @ hAPP ) ) ) ))]]) ).
thf(1074,plain,
( ( ( u @ ( pname @ finite_finite @ ( bool @ ( bool @ ( pname @ fun ) @ hAPP ) ) ) )
!= u )
| ( ( pname @ finite_finite )
!= fNot )
| ( bool != bool )
| ( ( bool @ ( pname @ fun ) )
!= bool ) ),
inference(simp,[status(thm)],[1007]) ).
thf(1075,plain,
( ( ( u @ ( pname @ finite_finite @ ( bool @ ( bool @ ( pname @ fun ) @ hAPP ) ) ) )
!= u )
| ( ( pname @ finite_finite )
!= fNot )
| ( ( bool @ ( pname @ fun ) )
!= bool ) ),
inference(simp,[status(thm)],[1074]) ).
thf(106,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( D @ ( B @ finite_finite @ ( bool @ ( bool @ ( B @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( ( D @ ( C @ ( A @ ( B @ image ) @ ( bool @ ( A @ fun ) @ ( bool @ ( B @ fun ) @ fun ) @ ( A @ ( B @ fun ) @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( B @ fun ) @ hAPP ) ) ) @ ( A @ finite_finite @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ? [E: $i] :
( ~ ( E @ ( C @ ( A @ ( B @ hAPP ) ) ) @ ( C @ ( A @ fequal @ ( B @ ( bool @ ( A @ fun ) @ ( A @ combb ) ) @ ( bool @ ( A @ fun ) @ ( B @ fun ) @ ( A @ ( B @ fun ) @ fun ) @ ( bool @ ( A @ fun ) @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( B @ fun ) @ ( A @ ( B @ fun ) @ hAPP ) ) ) @ ( bool @ ( A @ ( B @ combc ) ) @ ( bool @ ( B @ fun ) @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ ( B @ fun ) @ hAPP ) ) ) @ ( bool @ ( B @ fun ) @ ( A @ hAPP ) ) ) @ ( D @ ( B @ member @ ( bool @ ( bool @ ( B @ fun ) @ ( B @ combc ) ) @ ( bool @ ( B @ fun ) @ ( bool @ ( B @ fun ) @ fun ) @ ( bool @ ( bool @ ( B @ fun ) @ fun ) @ ( B @ fun ) @ hAPP ) ) ) @ ( bool @ ( B @ fun ) @ ( bool @ ( B @ fun ) @ hAPP ) ) ) @ ( fconj @ ( B @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) @ ( bool @ ( bool @ fun ) @ ( B @ fun ) @ ( bool @ ( B @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ ( bool @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ fun ) @ ( B @ fun ) @ ( bool @ ( B @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( B @ combs ) ) @ ( bool @ ( B @ fun ) @ ( bool @ ( B @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ ( B @ fun ) @ hAPP ) ) ) @ ( bool @ ( B @ fun ) @ ( bool @ ( B @ fun ) @ hAPP ) ) ) @ ( B @ collect @ ( bool @ ( B @ fun ) @ ( bool @ ( B @ fun ) @ hAPP ) ) ) @ ( B @ finite_finite @ ( bool @ ( bool @ ( B @ fun ) @ hAPP ) ) ) @ hBOOL )
& ( D @ ( E @ ( B @ member @ ( bool @ ( bool @ ( B @ fun ) @ fun ) @ ( B @ hAPP ) ) ) @ ( bool @ ( bool @ ( B @ fun ) @ hAPP ) ) ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_49_pigeonhole__infinite) ).
thf(476,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( D @ ( B @ finite_finite @ ( bool @ ( bool @ ( B @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( ( D @ ( C @ ( A @ ( B @ image ) @ ( bool @ ( A @ fun ) @ ( bool @ ( B @ fun ) @ fun ) @ ( A @ ( B @ fun ) @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( B @ fun ) @ hAPP ) ) ) @ ( A @ finite_finite @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ? [E: $i] :
( ~ ( E @ ( C @ ( A @ ( B @ hAPP ) ) ) @ ( C @ ( A @ fequal @ ( B @ ( bool @ ( A @ fun ) @ ( A @ combb ) ) @ ( bool @ ( A @ fun ) @ ( B @ fun ) @ ( A @ ( B @ fun ) @ fun ) @ ( bool @ ( A @ fun ) @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( B @ fun ) @ ( A @ ( B @ fun ) @ hAPP ) ) ) @ ( bool @ ( A @ ( B @ combc ) ) @ ( bool @ ( B @ fun ) @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ ( B @ fun ) @ hAPP ) ) ) @ ( bool @ ( B @ fun ) @ ( A @ hAPP ) ) ) @ ( D @ ( B @ member @ ( bool @ ( bool @ ( B @ fun ) @ ( B @ combc ) ) @ ( bool @ ( B @ fun ) @ ( bool @ ( B @ fun ) @ fun ) @ ( bool @ ( bool @ ( B @ fun ) @ fun ) @ ( B @ fun ) @ hAPP ) ) ) @ ( bool @ ( B @ fun ) @ ( bool @ ( B @ fun ) @ hAPP ) ) ) @ ( fconj @ ( B @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) @ ( bool @ ( bool @ fun ) @ ( B @ fun ) @ ( bool @ ( B @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ ( bool @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ fun ) @ ( B @ fun ) @ ( bool @ ( B @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( B @ combs ) ) @ ( bool @ ( B @ fun ) @ ( bool @ ( B @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ ( B @ fun ) @ hAPP ) ) ) @ ( bool @ ( B @ fun ) @ ( bool @ ( B @ fun ) @ hAPP ) ) ) @ ( B @ collect @ ( bool @ ( B @ fun ) @ ( bool @ ( B @ fun ) @ hAPP ) ) ) @ ( B @ finite_finite @ ( bool @ ( bool @ ( B @ fun ) @ hAPP ) ) ) @ hBOOL )
& ( D @ ( E @ ( B @ member @ ( bool @ ( bool @ ( B @ fun ) @ fun ) @ ( B @ hAPP ) ) ) @ ( bool @ ( bool @ ( B @ fun ) @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(100,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( ! [D: $i] :
( ( D @ ( suc @ ( nat @ ( nat @ hAPP ) ) ) @ ( B @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( D @ ( B @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) )
=> ( A @ ( C @ ( nat @ minus_minus @ ( nat @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( B @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_94_zero__induct__lemma) ).
thf(457,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( ! [D: $i] :
( ( D @ ( suc @ ( nat @ ( nat @ hAPP ) ) ) @ ( B @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( D @ ( B @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) )
=> ( A @ ( C @ ( nat @ minus_minus @ ( nat @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( B @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(7,axiom,
( ( na @ ( nat @ ti ) )
= na ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_v_na_res) ).
thf(172,plain,
( ( na @ ( nat @ ti ) )
= na ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(173,plain,
( ( na @ ( nat @ ti ) )
= na ),
inference(lifteq,[status(thm)],[172]) ).
thf(135,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( A @ ti ) )
= ( F @ ( E @ ( A @ ( B @ hAPP ) ) ) ) )
=> ( ( C @ ( F @ ( B @ member @ ( bool @ ( bool @ ( B @ fun ) @ fun ) @ ( B @ hAPP ) ) ) @ ( bool @ ( bool @ ( B @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( C @ ( E @ ( A @ ( B @ image ) @ ( bool @ ( A @ fun ) @ ( bool @ ( B @ fun ) @ fun ) @ ( A @ ( B @ fun ) @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( B @ fun ) @ hAPP ) ) ) @ ( D @ ( A @ member @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_50_image__eqI) ).
thf(569,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( D @ ( A @ ti ) )
= ( F @ ( E @ ( A @ ( B @ hAPP ) ) ) ) )
=> ( ( C @ ( F @ ( B @ member @ ( bool @ ( bool @ ( B @ fun ) @ fun ) @ ( B @ hAPP ) ) ) @ ( bool @ ( bool @ ( B @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( C @ ( E @ ( A @ ( B @ image ) @ ( bool @ ( A @ fun ) @ ( bool @ ( B @ fun ) @ fun ) @ ( A @ ( B @ fun ) @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( B @ fun ) @ hAPP ) ) ) @ ( D @ ( A @ member @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(29,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( ( A @ ( B @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( A @ ( nat @ minus_minus @ ( nat @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( B @ ( C @ ( nat @ minus_minus @ ( nat @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( nat @ minus_minus @ ( nat @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( nat @ ( nat @ hAPP ) ) ) )
= ( A @ ( C @ ( nat @ minus_minus @ ( nat @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( nat @ ( nat @ hAPP ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_Nat_Odiff__diff__eq) ).
thf(244,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( ( A @ ( B @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( A @ ( nat @ minus_minus @ ( nat @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( B @ ( C @ ( nat @ minus_minus @ ( nat @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( nat @ minus_minus @ ( nat @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( nat @ ( nat @ hAPP ) ) ) )
= ( A @ ( C @ ( nat @ minus_minus @ ( nat @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( nat @ ( nat @ hAPP ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(68,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ insert @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
<=> ( ( D @ ( C @ ( bool @ ( A @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
& ( D @ ( B @ ( A @ member @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_insert__subset) ).
thf(360,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( D @ ( C @ ( bool @ ( A @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
& ( D @ ( B @ ( A @ member @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL ) )
=> ( D @ ( C @ ( B @ ( A @ insert @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL ) )
& ( ( D @ ( C @ ( B @ ( A @ insert @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( ( D @ ( C @ ( bool @ ( A @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
& ( D @ ( B @ ( A @ member @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( bool @ ( x_a @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( x_a @ fun ) @ fun ) @ ( bool @ ( x_a @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( x_a @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( A @ ( B @ ( p @ ( bool @ ( bool @ ( x_a @ fun ) @ fun ) @ ( bool @ ( x_a @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( x_a @ fun ) @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0_assms_I1_J) ).
thf(205,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( bool @ ( x_a @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( x_a @ fun ) @ fun ) @ ( bool @ ( x_a @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( x_a @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( A @ ( B @ ( p @ ( bool @ ( bool @ ( x_a @ fun ) @ fun ) @ ( bool @ ( x_a @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( x_a @ fun ) @ hAPP ) ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(309,plain,
~ ? [A: $i] :
( ( A @ ( suc @ ( nat @ ( nat @ hAPP ) ) ) )
= A ),
inference(miniscope,[status(thm)],[308]) ).
thf(310,plain,
! [A: $i] :
( ( A @ ( suc @ ( nat @ ( nat @ hAPP ) ) ) )
!= A ),
inference(cnf,[status(esa)],[309]) ).
thf(311,plain,
! [A: $i] :
( ( A @ ( suc @ ( nat @ ( nat @ hAPP ) ) ) )
!= A ),
inference(lifteq,[status(thm)],[310]) ).
thf(80,axiom,
! [A: $i,B: $i] :
( ( A @ hBOOL )
| ~ ( B @ ( A @ ( fconj @ ( bool @ ( bool @ fun ) @ ( bool @ hAPP ) ) ) @ ( bool @ ( bool @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fconj_2_1_U) ).
thf(398,plain,
! [A: $i,B: $i] :
( ( A @ hBOOL )
| ~ ( B @ ( A @ ( fconj @ ( bool @ ( bool @ fun ) @ ( bool @ hAPP ) ) ) @ ( bool @ ( bool @ hAPP ) ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(1,conjecture,
u @ ( mgt_call @ ( x_a @ ( pname @ image ) @ ( bool @ ( x_a @ fun ) @ ( bool @ ( pname @ fun ) @ fun ) @ ( x_a @ ( pname @ fun ) @ hAPP ) ) ) @ ( bool @ ( x_a @ fun ) @ ( bool @ ( pname @ fun ) @ hAPP ) ) ) @ ( g @ ( pn @ ( mgt_call @ ( x_a @ ( pname @ hAPP ) ) ) @ ( x_a @ insert @ ( bool @ ( x_a @ fun ) @ ( bool @ ( x_a @ fun ) @ fun ) @ ( x_a @ hAPP ) ) ) @ ( bool @ ( x_a @ fun ) @ ( bool @ ( x_a @ fun ) @ hAPP ) ) ) @ ( bool @ ( x_a @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( x_a @ fun ) @ fun ) @ ( bool @ ( x_a @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( x_a @ fun ) @ hAPP ) ) ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_6) ).
thf(2,negated_conjecture,
~ ( u @ ( mgt_call @ ( x_a @ ( pname @ image ) @ ( bool @ ( x_a @ fun ) @ ( bool @ ( pname @ fun ) @ fun ) @ ( x_a @ ( pname @ fun ) @ hAPP ) ) ) @ ( bool @ ( x_a @ fun ) @ ( bool @ ( pname @ fun ) @ hAPP ) ) ) @ ( g @ ( pn @ ( mgt_call @ ( x_a @ ( pname @ hAPP ) ) ) @ ( x_a @ insert @ ( bool @ ( x_a @ fun ) @ ( bool @ ( x_a @ fun ) @ fun ) @ ( x_a @ hAPP ) ) ) @ ( bool @ ( x_a @ fun ) @ ( bool @ ( x_a @ fun ) @ hAPP ) ) ) @ ( bool @ ( x_a @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( x_a @ fun ) @ fun ) @ ( bool @ ( x_a @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( x_a @ fun ) @ hAPP ) ) ) @ hBOOL ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(163,plain,
~ ( u @ ( mgt_call @ ( x_a @ ( pname @ image ) @ ( bool @ ( x_a @ fun ) @ ( bool @ ( pname @ fun ) @ fun ) @ ( x_a @ ( pname @ fun ) @ hAPP ) ) ) @ ( bool @ ( x_a @ fun ) @ ( bool @ ( pname @ fun ) @ hAPP ) ) ) @ ( g @ ( pn @ ( mgt_call @ ( x_a @ ( pname @ hAPP ) ) ) @ ( x_a @ insert @ ( bool @ ( x_a @ fun ) @ ( bool @ ( x_a @ fun ) @ fun ) @ ( x_a @ hAPP ) ) ) @ ( bool @ ( x_a @ fun ) @ ( bool @ ( x_a @ fun ) @ hAPP ) ) ) @ ( bool @ ( x_a @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( x_a @ fun ) @ fun ) @ ( bool @ ( x_a @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( x_a @ fun ) @ hAPP ) ) ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(1008,plain,
( ( ( u @ ( pname @ finite_finite @ ( bool @ ( bool @ ( pname @ fun ) @ hAPP ) ) ) @ hBOOL )
!= ( u @ ( mgt_call @ ( x_a @ ( pname @ image ) @ ( bool @ ( x_a @ fun ) @ ( bool @ ( pname @ fun ) @ fun ) @ ( x_a @ ( pname @ fun ) @ hAPP ) ) ) @ ( bool @ ( x_a @ fun ) @ ( bool @ ( pname @ fun ) @ hAPP ) ) ) @ ( g @ ( pn @ ( mgt_call @ ( x_a @ ( pname @ hAPP ) ) ) @ ( x_a @ insert @ ( bool @ ( x_a @ fun ) @ ( bool @ ( x_a @ fun ) @ fun ) @ ( x_a @ hAPP ) ) ) @ ( bool @ ( x_a @ fun ) @ ( bool @ ( x_a @ fun ) @ hAPP ) ) ) @ ( bool @ ( x_a @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( x_a @ fun ) @ fun ) @ ( bool @ ( x_a @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( x_a @ fun ) @ hAPP ) ) ) @ hBOOL ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[289,163]) ).
thf(1009,plain,
( ( u @ ( pname @ finite_finite @ ( bool @ ( bool @ ( pname @ fun ) @ hAPP ) ) ) @ hBOOL )
!= ( u @ ( mgt_call @ ( x_a @ ( pname @ image ) @ ( bool @ ( x_a @ fun ) @ ( bool @ ( pname @ fun ) @ fun ) @ ( x_a @ ( pname @ fun ) @ hAPP ) ) ) @ ( bool @ ( x_a @ fun ) @ ( bool @ ( pname @ fun ) @ hAPP ) ) ) @ ( g @ ( pn @ ( mgt_call @ ( x_a @ ( pname @ hAPP ) ) ) @ ( x_a @ insert @ ( bool @ ( x_a @ fun ) @ ( bool @ ( x_a @ fun ) @ fun ) @ ( x_a @ hAPP ) ) ) @ ( bool @ ( x_a @ fun ) @ ( bool @ ( x_a @ fun ) @ hAPP ) ) ) @ ( bool @ ( x_a @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( x_a @ fun ) @ fun ) @ ( bool @ ( x_a @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( x_a @ fun ) @ hAPP ) ) ) @ hBOOL ) ),
inference(simp,[status(thm)],[1008]) ).
thf(1015,plain,
( ( u @ ( pname @ finite_finite @ ( bool @ ( bool @ ( pname @ fun ) @ hAPP ) ) ) )
!= ( u @ ( mgt_call @ ( x_a @ ( pname @ image ) @ ( bool @ ( x_a @ fun ) @ ( bool @ ( pname @ fun ) @ fun ) @ ( x_a @ ( pname @ fun ) @ hAPP ) ) ) @ ( bool @ ( x_a @ fun ) @ ( bool @ ( pname @ fun ) @ hAPP ) ) ) @ ( g @ ( pn @ ( mgt_call @ ( x_a @ ( pname @ hAPP ) ) ) @ ( x_a @ insert @ ( bool @ ( x_a @ fun ) @ ( bool @ ( x_a @ fun ) @ fun ) @ ( x_a @ hAPP ) ) ) @ ( bool @ ( x_a @ fun ) @ ( bool @ ( x_a @ fun ) @ hAPP ) ) ) @ ( bool @ ( x_a @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( x_a @ fun ) @ fun ) @ ( bool @ ( x_a @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( x_a @ fun ) @ hAPP ) ) ) ) ),
inference(simp,[status(thm)],[1009]) ).
thf(1134,plain,
( ( ( u @ ( mgt_call @ ( x_a @ ( pname @ image ) @ ( bool @ ( x_a @ fun ) @ ( bool @ ( pname @ fun ) @ fun ) @ ( x_a @ ( pname @ fun ) @ hAPP ) ) ) @ ( bool @ ( x_a @ fun ) @ ( bool @ ( pname @ fun ) @ hAPP ) ) ) )
!= u )
| ( ( g @ ( pn @ ( mgt_call @ ( x_a @ ( pname @ hAPP ) ) ) @ ( x_a @ insert @ ( bool @ ( x_a @ fun ) @ ( bool @ ( x_a @ fun ) @ fun ) @ ( x_a @ hAPP ) ) ) @ ( bool @ ( x_a @ fun ) @ ( bool @ ( x_a @ fun ) @ hAPP ) ) ) @ ( bool @ ( x_a @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( x_a @ fun ) @ fun ) @ ( bool @ ( x_a @ fun ) @ hAPP ) ) ) )
!= ( pname @ finite_finite ) )
| ( bool != bool )
| ( ( bool @ ( pname @ fun ) )
!= ( bool @ ( x_a @ fun ) ) ) ),
inference(simp,[status(thm)],[1015]) ).
thf(1135,plain,
( ( ( u @ ( mgt_call @ ( x_a @ ( pname @ image ) @ ( bool @ ( x_a @ fun ) @ ( bool @ ( pname @ fun ) @ fun ) @ ( x_a @ ( pname @ fun ) @ hAPP ) ) ) @ ( bool @ ( x_a @ fun ) @ ( bool @ ( pname @ fun ) @ hAPP ) ) ) )
!= u )
| ( ( g @ ( pn @ ( mgt_call @ ( x_a @ ( pname @ hAPP ) ) ) @ ( x_a @ insert @ ( bool @ ( x_a @ fun ) @ ( bool @ ( x_a @ fun ) @ fun ) @ ( x_a @ hAPP ) ) ) @ ( bool @ ( x_a @ fun ) @ ( bool @ ( x_a @ fun ) @ hAPP ) ) ) @ ( bool @ ( x_a @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( x_a @ fun ) @ fun ) @ ( bool @ ( x_a @ fun ) @ hAPP ) ) ) )
!= ( pname @ finite_finite ) )
| ( ( bool @ ( pname @ fun ) )
!= ( bool @ ( x_a @ fun ) ) ) ),
inference(simp,[status(thm)],[1134]) ).
thf(87,axiom,
! [A: $i,B: $i,C: $i] : ( B @ ( C @ ( A @ insert @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( B @ ( bool @ ( A @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_83_subset__insertI) ).
thf(425,plain,
! [A: $i,B: $i,C: $i] : ( B @ ( C @ ( A @ insert @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( B @ ( bool @ ( A @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(165,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ti ) @ ( A @ ti ) )
= ( B @ ( A @ ti ) ) ),
inference(cnf,[status(esa)],[164]) ).
thf(166,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ ti ) @ ( A @ ti ) )
= ( B @ ( A @ ti ) ) ),
inference(lifteq,[status(thm)],[165]) ).
thf(34,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( D @ ( A @ ( B @ ( C @ combb ) ) @ ( B @ ( A @ fun ) @ ( C @ ( A @ fun ) @ fun ) @ ( B @ ( C @ fun ) @ hAPP ) ) ) @ ( B @ ( A @ fun ) @ ( C @ ( A @ fun ) @ hAPP ) ) ) @ ( B @ ( A @ hAPP ) ) ) )
= ( F @ ( E @ ( C @ ( A @ hAPP ) ) ) @ ( D @ ( B @ ( C @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBB_1_1_U) ).
thf(264,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( D @ ( A @ ( B @ ( C @ combb ) ) @ ( B @ ( A @ fun ) @ ( C @ ( A @ fun ) @ fun ) @ ( B @ ( C @ fun ) @ hAPP ) ) ) @ ( B @ ( A @ fun ) @ ( C @ ( A @ fun ) @ hAPP ) ) ) @ ( B @ ( A @ hAPP ) ) ) )
= ( F @ ( E @ ( C @ ( A @ hAPP ) ) ) @ ( D @ ( B @ ( C @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(10,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( D @ ( A @ ( B @ image ) @ ( bool @ ( A @ fun ) @ ( bool @ ( B @ fun ) @ fun ) @ ( A @ ( B @ fun ) @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( B @ fun ) @ hAPP ) ) ) @ ( C @ ( A @ member @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
<=> ? [F: $i] :
( ( ( C @ ( A @ ti ) )
= ( F @ ( D @ ( A @ ( B @ hAPP ) ) ) ) )
& ( E @ ( F @ ( B @ member @ ( bool @ ( bool @ ( B @ fun ) @ fun ) @ ( B @ hAPP ) ) ) @ ( bool @ ( bool @ ( B @ fun ) @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_image__iff) ).
thf(180,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ? [F: $i] :
( ( ( C @ ( A @ ti ) )
= ( F @ ( D @ ( A @ ( B @ hAPP ) ) ) ) )
& ( E @ ( F @ ( B @ member @ ( bool @ ( bool @ ( B @ fun ) @ fun ) @ ( B @ hAPP ) ) ) @ ( bool @ ( bool @ ( B @ fun ) @ hAPP ) ) ) @ hBOOL ) )
=> ( E @ ( D @ ( A @ ( B @ image ) @ ( bool @ ( A @ fun ) @ ( bool @ ( B @ fun ) @ fun ) @ ( A @ ( B @ fun ) @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( B @ fun ) @ hAPP ) ) ) @ ( C @ ( A @ member @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL ) )
& ( ( E @ ( D @ ( A @ ( B @ image ) @ ( bool @ ( A @ fun ) @ ( bool @ ( B @ fun ) @ fun ) @ ( A @ ( B @ fun ) @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( B @ fun ) @ hAPP ) ) ) @ ( C @ ( A @ member @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ? [F: $i] :
( ( ( C @ ( A @ ti ) )
= ( F @ ( D @ ( A @ ( B @ hAPP ) ) ) ) )
& ( E @ ( F @ ( B @ member @ ( bool @ ( bool @ ( B @ fun ) @ fun ) @ ( B @ hAPP ) ) ) @ ( bool @ ( bool @ ( B @ fun ) @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(45,axiom,
! [A: $i] :
( ( A @ finite_card @ ( nat @ ( bool @ ( A @ fun ) @ fun ) @ ti ) )
= ( A @ finite_card ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Finite__Set_Ocard_res) ).
thf(294,plain,
! [A: $i] :
( ( A @ finite_card @ ( nat @ ( bool @ ( A @ fun ) @ fun ) @ ti ) )
= ( A @ finite_card ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(295,plain,
! [A: $i] :
( ( A @ finite_card @ ( nat @ ( bool @ ( A @ fun ) @ fun ) @ ti ) )
= ( A @ finite_card ) ),
inference(cnf,[status(esa)],[294]) ).
thf(296,plain,
! [A: $i] :
( ( A @ finite_card @ ( nat @ ( bool @ ( A @ fun ) @ fun ) @ ti ) )
= ( A @ finite_card ) ),
inference(lifteq,[status(thm)],[295]) ).
thf(141,axiom,
u @ ( mgt_call @ ( x_a @ ( pname @ image ) @ ( bool @ ( x_a @ fun ) @ ( bool @ ( pname @ fun ) @ fun ) @ ( x_a @ ( pname @ fun ) @ hAPP ) ) ) @ ( bool @ ( x_a @ fun ) @ ( bool @ ( pname @ fun ) @ hAPP ) ) ) @ ( g @ ( bool @ ( x_a @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( x_a @ fun ) @ fun ) @ ( bool @ ( x_a @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( x_a @ fun ) @ hAPP ) ) ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_1) ).
thf(584,plain,
u @ ( mgt_call @ ( x_a @ ( pname @ image ) @ ( bool @ ( x_a @ fun ) @ ( bool @ ( pname @ fun ) @ fun ) @ ( x_a @ ( pname @ fun ) @ hAPP ) ) ) @ ( bool @ ( x_a @ fun ) @ ( bool @ ( pname @ fun ) @ hAPP ) ) ) @ ( g @ ( bool @ ( x_a @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( x_a @ fun ) @ fun ) @ ( bool @ ( x_a @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( x_a @ fun ) @ hAPP ) ) ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] :
( ( C @ ( D @ ( A @ member @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( D @ ( A @ member @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL ) )
=> ( B @ ( C @ ( bool @ ( A @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_93_subsetI) ).
thf(176,plain,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] :
( ( C @ ( D @ ( A @ member @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( D @ ( A @ member @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL ) )
=> ( B @ ( C @ ( bool @ ( A @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(138,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( fimplies @ ( bool @ ( bool @ fun ) @ ( bool @ hAPP ) ) ) @ ( bool @ ( bool @ hAPP ) ) ) @ hBOOL )
| ( B @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fimplies_1_1_U) ).
thf(577,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( fimplies @ ( bool @ ( bool @ fun ) @ ( bool @ hAPP ) ) ) @ ( bool @ ( bool @ hAPP ) ) ) @ hBOOL )
| ( B @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(139,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( A @ ( nat @ minus_minus @ ( nat @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( C @ ( A @ ( nat @ minus_minus @ ( nat @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_diff__le__mono2) ).
thf(579,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( A @ ( nat @ minus_minus @ ( nat @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( C @ ( A @ ( nat @ minus_minus @ ( nat @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(17,axiom,
( ( pn @ ( pname @ ti ) )
= pn ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_v_pn_res) ).
thf(203,plain,
( ( pn @ ( pname @ ti ) )
= pn ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(204,plain,
( ( pn @ ( pname @ ti ) )
= pn ),
inference(lifteq,[status(thm)],[203]) ).
thf(95,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/sandbox2/benchmark/theBenchmark.p',tsy_c_hAPP_arg1) ).
thf(445,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)],[95]) ).
thf(136,axiom,
! [A: $i] :
~ ( A @ ( A @ ( suc @ ( nat @ ( nat @ hAPP ) ) ) @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_Suc__n__not__le__n) ).
thf(572,plain,
! [A: $i] :
~ ( A @ ( A @ ( suc @ ( nat @ ( nat @ hAPP ) ) ) @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(57,axiom,
! [A: $i] :
( ( A @ preorder )
=> ! [B: $i] : ( B @ ( B @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_97_order__refl) ).
thf(335,plain,
! [A: $i] :
( ( A @ preorder )
=> ! [B: $i] : ( B @ ( B @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(22,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ insert @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) )
= ( C @ ( A @ member @ ( bool @ ( bool @ ( A @ fun ) @ ( A @ combc ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( B @ ( A @ fequal @ ( bool @ ( A @ ( A @ combc ) ) @ ( bool @ ( A @ fun ) @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( fdisj @ ( A @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) @ ( bool @ ( bool @ fun ) @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ ( bool @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ fun ) @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ combs ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( A @ collect @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_56_insert__compr) ).
thf(219,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ insert @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) )
= ( C @ ( A @ member @ ( bool @ ( bool @ ( A @ fun ) @ ( A @ combc ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( B @ ( A @ fequal @ ( bool @ ( A @ ( A @ combc ) ) @ ( bool @ ( A @ fun ) @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( fdisj @ ( A @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) @ ( bool @ ( bool @ fun ) @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ ( bool @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ fun ) @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ combs ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( A @ collect @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(38,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( D @ ( C @ ( A @ member @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( C @ ( A @ insert @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( D @ ( bool @ ( A @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
<=> ( B @ ( D @ ( bool @ ( A @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_85_subset__insert) ).
thf(274,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( D @ ( C @ ( A @ member @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( ( ( B @ ( D @ ( bool @ ( A @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( C @ ( A @ insert @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( D @ ( bool @ ( A @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL ) )
& ( ( B @ ( C @ ( A @ insert @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( D @ ( bool @ ( A @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( D @ ( bool @ ( A @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(85,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( bool @ ( A @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( C @ ( bool @ ( A @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( bool @ ( A @ fun ) @ ti ) )
= ( C @ ( bool @ ( A @ fun ) @ ti ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_51_equalityI) ).
thf(419,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( bool @ ( A @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( C @ ( bool @ ( A @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( bool @ ( A @ fun ) @ ti ) )
= ( C @ ( bool @ ( A @ fun ) @ ti ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(51,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( D @ ( bool @ ( B @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( B @ fun ) @ fun ) @ ( bool @ ( B @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( B @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( E @ ( C @ ( A @ ( B @ image ) @ ( bool @ ( A @ fun ) @ ( bool @ ( B @ fun ) @ fun ) @ ( A @ ( B @ fun ) @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( B @ fun ) @ hAPP ) ) ) @ ( D @ ( C @ ( A @ ( B @ image ) @ ( bool @ ( A @ fun ) @ ( bool @ ( B @ fun ) @ fun ) @ ( A @ ( B @ fun ) @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( B @ fun ) @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_image__mono) ).
thf(318,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( D @ ( bool @ ( B @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( B @ fun ) @ fun ) @ ( bool @ ( B @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( B @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( E @ ( C @ ( A @ ( B @ image ) @ ( bool @ ( A @ fun ) @ ( bool @ ( B @ fun ) @ fun ) @ ( A @ ( B @ fun ) @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( B @ fun ) @ hAPP ) ) ) @ ( D @ ( C @ ( A @ ( B @ image ) @ ( bool @ ( A @ fun ) @ ( bool @ ( B @ fun ) @ fun ) @ ( A @ ( B @ fun ) @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( B @ fun ) @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(91,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( suc @ ( nat @ ( nat @ hAPP ) ) ) )
= ( B @ ( suc @ ( nat @ ( nat @ hAPP ) ) ) ) )
=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_16_Suc__inject) ).
thf(434,plain,
! [A: $i,B: $i] :
( ( ( A @ ( suc @ ( nat @ ( nat @ hAPP ) ) ) )
= ( B @ ( suc @ ( nat @ ( nat @ hAPP ) ) ) ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(97,axiom,
( ( mgt_call @ ( x_a @ ( pname @ fun ) @ ti ) )
= mgt_call ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_v_mgt__call_res) ).
thf(450,plain,
( ( mgt_call @ ( x_a @ ( pname @ fun ) @ ti ) )
= mgt_call ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(451,plain,
( ( mgt_call @ ( x_a @ ( pname @ fun ) @ ti ) )
= mgt_call ),
inference(lifteq,[status(thm)],[450]) ).
thf(134,axiom,
! [A: $i] : ( A @ ( nat @ ord_less_eq @ ( bool @ ( nat @ ( nat @ combc ) ) @ ( bool @ ( nat @ fun ) @ ( nat @ fun ) @ ( bool @ ( nat @ fun ) @ ( nat @ fun ) @ hAPP ) ) ) @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( nat @ collect @ ( bool @ ( nat @ fun ) @ ( bool @ ( nat @ fun ) @ hAPP ) ) ) @ ( nat @ finite_finite @ ( bool @ ( bool @ ( nat @ fun ) @ hAPP ) ) ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_12_finite__Collect__le__nat) ).
thf(567,plain,
! [A: $i] : ( A @ ( nat @ ord_less_eq @ ( bool @ ( nat @ ( nat @ combc ) ) @ ( bool @ ( nat @ fun ) @ ( nat @ fun ) @ ( bool @ ( nat @ fun ) @ ( nat @ fun ) @ hAPP ) ) ) @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( nat @ collect @ ( bool @ ( nat @ fun ) @ ( bool @ ( nat @ fun ) @ hAPP ) ) ) @ ( nat @ finite_finite @ ( bool @ ( bool @ ( nat @ fun ) @ hAPP ) ) ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(112,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/sandbox2/benchmark/theBenchmark.p',help_fequal_2_1_T) ).
thf(494,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)],[112]) ).
thf(535,plain,
( ( suc @ ( nat @ ( nat @ fun ) @ ti ) )
= suc ),
inference(lifteq,[status(thm)],[534]) ).
thf(144,axiom,
( ( g @ ( bool @ ( x_a @ fun ) @ ti ) )
= g ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_v_G_res) ).
thf(594,plain,
( ( g @ ( bool @ ( x_a @ fun ) @ ti ) )
= g ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(21,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ insert @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( A @ finite_finite @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
<=> ( C @ ( A @ finite_finite @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_finite__insert) ).
thf(213,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( A @ finite_finite @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( C @ ( B @ ( A @ insert @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( A @ finite_finite @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL ) )
& ( ( C @ ( B @ ( A @ insert @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( A @ finite_finite @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( C @ ( A @ finite_finite @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(108,axiom,
! [A: $i,B: $i] :
( ( B @ ( suc @ ( nat @ ( nat @ hAPP ) ) ) @ ( A @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( ~ ( B @ ( A @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( A
= ( B @ ( suc @ ( nat @ ( nat @ hAPP ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_31_le__SucE) ).
thf(483,plain,
! [A: $i,B: $i] :
( ( B @ ( suc @ ( nat @ ( nat @ hAPP ) ) ) @ ( A @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( ~ ( B @ ( A @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( A
= ( B @ ( suc @ ( nat @ ( nat @ hAPP ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(15,axiom,
( ( fdisj @ ( bool @ ( bool @ fun ) @ ( bool @ fun ) @ ti ) )
= fdisj ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_fdisj_res) ).
thf(198,plain,
( ( fdisj @ ( bool @ ( bool @ fun ) @ ( bool @ fun ) @ ti ) )
= fdisj ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(55,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ member @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( ( C @ ( B @ ( A @ insert @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) )
= ( C @ ( bool @ ( A @ fun ) @ ti ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_64_insert__absorb) ).
thf(330,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ member @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( ( C @ ( B @ ( A @ insert @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) )
= ( C @ ( bool @ ( A @ fun ) @ ti ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(69,axiom,
u @ ( pn @ ( pname @ member @ ( bool @ ( bool @ ( pname @ fun ) @ fun ) @ ( pname @ hAPP ) ) ) @ ( bool @ ( bool @ ( pname @ fun ) @ hAPP ) ) ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_4) ).
thf(367,plain,
u @ ( pn @ ( pname @ member @ ( bool @ ( bool @ ( pname @ fun ) @ fun ) @ ( pname @ hAPP ) ) ) @ ( bool @ ( bool @ ( pname @ fun ) @ hAPP ) ) ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(129,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( ( A @ ( C @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( A @ ( B @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_21_le__trans) ).
thf(552,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( ( A @ ( C @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( A @ ( B @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(121,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( suc @ ( nat @ ( nat @ hAPP ) ) ) @ ( A @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_le__SucI) ).
thf(521,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( suc @ ( nat @ ( nat @ hAPP ) ) ) @ ( A @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(39,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( A @ finite_finite @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( ( ~ ( C @ ( B @ ( A @ member @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( ( C @ ( B @ ( A @ insert @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( A @ finite_card @ ( nat @ ( bool @ ( A @ fun ) @ hAPP ) ) ) )
= ( C @ ( A @ finite_card @ ( nat @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( suc @ ( nat @ ( nat @ hAPP ) ) ) ) ) )
& ( ( C @ ( B @ ( A @ member @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( ( C @ ( B @ ( A @ insert @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( A @ finite_card @ ( nat @ ( bool @ ( A @ fun ) @ hAPP ) ) ) )
= ( C @ ( A @ finite_card @ ( nat @ ( bool @ ( A @ fun ) @ hAPP ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_card__insert__if) ).
thf(278,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( A @ finite_finite @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( ( ~ ( C @ ( B @ ( A @ member @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( ( C @ ( B @ ( A @ insert @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( A @ finite_card @ ( nat @ ( bool @ ( A @ fun ) @ hAPP ) ) ) )
= ( C @ ( A @ finite_card @ ( nat @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( suc @ ( nat @ ( nat @ hAPP ) ) ) ) ) )
& ( ( C @ ( B @ ( A @ member @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( ( C @ ( B @ ( A @ insert @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( A @ finite_card @ ( nat @ ( bool @ ( A @ fun ) @ hAPP ) ) ) )
= ( C @ ( A @ finite_card @ ( nat @ ( bool @ ( A @ fun ) @ hAPP ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(99,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( fdisj @ ( bool @ ( bool @ fun ) @ ( bool @ hAPP ) ) ) @ ( bool @ ( bool @ hAPP ) ) ) @ hBOOL )
| ~ ( B @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fdisj_1_1_U) ).
thf(455,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( fdisj @ ( bool @ ( bool @ fun ) @ ( bool @ hAPP ) ) ) @ ( bool @ ( bool @ hAPP ) ) ) @ hBOOL )
| ~ ( B @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(47,axiom,
! [A: $i] : ( A @ ( A @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_24_le__refl) ).
thf(306,plain,
! [A: $i] : ( A @ ( A @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(35,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( A @ collect @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( B @ ( A @ insert @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) )
= ( C @ ( B @ ( A @ fequal @ ( bool @ ( A @ ( A @ combc ) ) @ ( bool @ ( A @ fun ) @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( fNot @ ( A @ ( bool @ ( bool @ combb ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( fimplies @ ( A @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) @ ( bool @ ( bool @ fun ) @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ ( bool @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ fun ) @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ combs ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( A @ collect @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_57_insert__Collect) ).
thf(267,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( A @ collect @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( B @ ( A @ insert @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) )
= ( C @ ( B @ ( A @ fequal @ ( bool @ ( A @ ( A @ combc ) ) @ ( bool @ ( A @ fun ) @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( fNot @ ( A @ ( bool @ ( bool @ combb ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( fimplies @ ( A @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) @ ( bool @ ( bool @ fun ) @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ ( bool @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ fun ) @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ combs ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( A @ collect @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(28,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( ( A @ ( B @ ( suc @ ( nat @ ( nat @ hAPP ) ) ) @ ( nat @ minus_minus @ ( nat @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( nat @ ( nat @ hAPP ) ) ) )
= ( A @ ( B @ ( nat @ minus_minus @ ( nat @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( suc @ ( nat @ ( nat @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_11_Suc__diff__le) ).
thf(241,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( ( A @ ( B @ ( suc @ ( nat @ ( nat @ hAPP ) ) ) @ ( nat @ minus_minus @ ( nat @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( nat @ ( nat @ hAPP ) ) ) )
= ( A @ ( B @ ( nat @ minus_minus @ ( nat @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( suc @ ( nat @ ( nat @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(161,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( B @ finite_finite @ ( bool @ ( bool @ ( B @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( ( E @ ( D @ ( A @ ( B @ image ) @ ( bool @ ( A @ fun ) @ ( bool @ ( B @ fun ) @ fun ) @ ( A @ ( B @ fun ) @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( B @ fun ) @ hAPP ) ) ) @ ( C @ ( bool @ ( A @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( C @ ( A @ finite_finite @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_finite__surj) ).
thf(658,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( B @ finite_finite @ ( bool @ ( bool @ ( B @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( ( E @ ( D @ ( A @ ( B @ image ) @ ( bool @ ( A @ fun ) @ ( bool @ ( B @ fun ) @ fun ) @ ( A @ ( B @ fun ) @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( B @ fun ) @ hAPP ) ) ) @ ( C @ ( bool @ ( A @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( C @ ( A @ finite_finite @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(105,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( suc @ ( nat @ ( nat @ hAPP ) ) ) @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ? [C: $i] :
( B
= ( C @ ( suc @ ( nat @ ( nat @ hAPP ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_95_Suc__le__D) ).
thf(473,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( suc @ ( nat @ ( nat @ hAPP ) ) ) @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ? [C: $i] :
( B
= ( C @ ( suc @ ( nat @ ( nat @ hAPP ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(157,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( B @ finite_finite @ ( bool @ ( bool @ ( B @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( D @ ( B @ finite_card @ ( nat @ ( bool @ ( B @ fun ) @ hAPP ) ) ) @ ( D @ ( C @ ( A @ ( B @ image ) @ ( bool @ ( A @ fun ) @ ( bool @ ( B @ fun ) @ fun ) @ ( A @ ( B @ fun ) @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( B @ fun ) @ hAPP ) ) ) @ ( A @ finite_card @ ( nat @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_card__image__le) ).
thf(648,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( B @ finite_finite @ ( bool @ ( bool @ ( B @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( D @ ( B @ finite_card @ ( nat @ ( bool @ ( B @ fun ) @ hAPP ) ) ) @ ( D @ ( C @ ( A @ ( B @ image ) @ ( bool @ ( A @ fun ) @ ( bool @ ( B @ fun ) @ fun ) @ ( A @ ( B @ fun ) @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( B @ fun ) @ hAPP ) ) ) @ ( A @ finite_card @ ( nat @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(66,axiom,
~ ( g @ ( pn @ ( mgt_call @ ( x_a @ ( pname @ hAPP ) ) ) @ ( x_a @ member @ ( bool @ ( bool @ ( x_a @ fun ) @ fun ) @ ( x_a @ hAPP ) ) ) @ ( bool @ ( bool @ ( x_a @ fun ) @ hAPP ) ) ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_5) ).
thf(355,plain,
~ ( g @ ( pn @ ( mgt_call @ ( x_a @ ( pname @ hAPP ) ) ) @ ( x_a @ member @ ( bool @ ( bool @ ( x_a @ fun ) @ fun ) @ ( x_a @ hAPP ) ) ) @ ( bool @ ( bool @ ( x_a @ fun ) @ hAPP ) ) ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( A @ member @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( D @ ( bool @ ( A @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( C @ ( A @ member @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_70_set__rev__mp) ).
thf(194,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( A @ member @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( D @ ( bool @ ( A @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( C @ ( A @ member @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(148,axiom,
! [A: $i,B: $i] : ( A @ ( B @ ( A @ ( nat @ minus_minus @ ( nat @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_45_diff__le__self) ).
thf(617,plain,
! [A: $i,B: $i] : ( A @ ( B @ ( A @ ( nat @ minus_minus @ ( nat @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(119,axiom,
! [A: $i] :
( ( A @ ( fNot @ ( bool @ ( bool @ hAPP ) ) ) @ hBOOL )
| ( A @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fNot_2_1_U) ).
thf(516,plain,
! [A: $i] :
( ( A @ ( fNot @ ( bool @ ( bool @ hAPP ) ) ) @ hBOOL )
| ( A @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(131,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ ( fconj @ ( bool @ ( bool @ fun ) @ ( bool @ hAPP ) ) ) @ ( bool @ ( bool @ hAPP ) ) ) @ hBOOL )
| ~ ( A @ hBOOL )
| ~ ( B @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fconj_1_1_U) ).
thf(557,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ ( fconj @ ( bool @ ( bool @ fun ) @ ( bool @ hAPP ) ) ) @ ( bool @ ( bool @ hAPP ) ) ) @ hBOOL )
| ~ ( A @ hBOOL )
| ~ ( B @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(154,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( A @ ti ) @ ( C @ ( B @ ( A @ hAPP ) ) ) )
= ( D @ ( C @ ( B @ ( A @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_hAPP_arg2) ).
thf(640,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)],[154]) ).
thf(83,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( bool @ ( A @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( D @ ( bool @ ( A @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( C @ ( bool @ ( A @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_subset__trans) ).
thf(414,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( bool @ ( A @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( D @ ( bool @ ( A @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( C @ ( bool @ ( A @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(199,plain,
( ( fdisj @ ( bool @ ( bool @ fun ) @ ( bool @ fun ) @ ti ) )
= fdisj ),
inference(lifteq,[status(thm)],[198]) ).
thf(93,axiom,
( ( fimplies @ ( bool @ ( bool @ fun ) @ ( bool @ fun ) @ ti ) )
= fimplies ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_fimplies_res) ).
thf(441,plain,
( ( fimplies @ ( bool @ ( bool @ fun ) @ ( bool @ fun ) @ ti ) )
= fimplies ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(115,axiom,
! [A: $i,B: $i] :
( ( ( A @ ( suc @ ( nat @ ( nat @ hAPP ) ) ) )
= ( B @ ( suc @ ( nat @ ( nat @ hAPP ) ) ) ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_17_nat_Oinject) ).
thf(502,plain,
! [A: $i,B: $i] :
( ( ( A = B )
=> ( ( A @ ( suc @ ( nat @ ( nat @ hAPP ) ) ) )
= ( B @ ( suc @ ( nat @ ( nat @ hAPP ) ) ) ) ) )
& ( ( ( A @ ( suc @ ( nat @ ( nat @ hAPP ) ) ) )
= ( B @ ( suc @ ( nat @ ( nat @ hAPP ) ) ) ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(358,plain,
! [A: $i] :
( ( A @ combi @ ( A @ ( A @ fun ) @ ti ) )
= ( A @ combi ) ),
inference(cnf,[status(esa)],[357]) ).
thf(359,plain,
! [A: $i] :
( ( A @ combi @ ( A @ ( A @ fun ) @ ti ) )
= ( A @ combi ) ),
inference(lifteq,[status(thm)],[358]) ).
thf(155,axiom,
( ( fconj @ ( bool @ ( bool @ fun ) @ ( bool @ fun ) @ ti ) )
= fconj ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_fconj_res) ).
thf(643,plain,
( ( fconj @ ( bool @ ( bool @ fun ) @ ( bool @ fun ) @ ti ) )
= fconj ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(142,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( ( A @ ( B @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( ( ( B @ ( C @ ( nat @ minus_minus @ ( nat @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( nat @ ( nat @ hAPP ) ) ) )
= ( B @ ( A @ ( nat @ minus_minus @ ( nat @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( nat @ ( nat @ hAPP ) ) ) ) )
<=> ( C = A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_41_eq__diff__iff) ).
thf(585,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( ( A @ ( B @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( ( ( C = A )
=> ( ( B @ ( C @ ( nat @ minus_minus @ ( nat @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( nat @ ( nat @ hAPP ) ) ) )
= ( B @ ( A @ ( nat @ minus_minus @ ( nat @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( nat @ ( nat @ hAPP ) ) ) ) ) )
& ( ( ( B @ ( C @ ( nat @ minus_minus @ ( nat @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( nat @ ( nat @ hAPP ) ) ) )
= ( B @ ( A @ ( nat @ minus_minus @ ( nat @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( nat @ ( nat @ hAPP ) ) ) ) )
=> ( C = A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(71,axiom,
! [A: $i,B: $i] :
( ( B @ ( suc @ ( nat @ ( nat @ hAPP ) ) ) @ ( A @ ( suc @ ( nat @ ( nat @ hAPP ) ) ) @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
<=> ( B @ ( A @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_33_Suc__le__mono) ).
thf(370,plain,
! [A: $i,B: $i] :
( ( ( B @ ( A @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( suc @ ( nat @ ( nat @ hAPP ) ) ) @ ( A @ ( suc @ ( nat @ ( nat @ hAPP ) ) ) @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) )
& ( ( B @ ( suc @ ( nat @ ( nat @ hAPP ) ) ) @ ( A @ ( suc @ ( nat @ ( nat @ hAPP ) ) ) @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( A @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(175,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( 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 )
| ~ ( D @ ( C @ ( bool @ ( A @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL ) ),
inference(cnf,[status(esa)],[174]) ).
thf(595,plain,
( ( g @ ( bool @ ( x_a @ fun ) @ ti ) )
= g ),
inference(lifteq,[status(thm)],[594]) ).
thf(113,axiom,
! [A: $i] :
( ( A @ order )
=> ! [B: $i,C: $i,D: $i] :
( ! [E: $i] : ( E @ ( suc @ ( nat @ ( nat @ hAPP ) ) ) @ ( D @ ( A @ ( nat @ hAPP ) ) ) @ ( E @ ( D @ ( A @ ( nat @ hAPP ) ) ) @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( C @ ( B @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( C @ ( D @ ( A @ ( nat @ hAPP ) ) ) @ ( B @ ( D @ ( A @ ( nat @ hAPP ) ) ) @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_48_lift__Suc__mono__le) ).
thf(497,plain,
! [A: $i] :
( ( A @ order )
=> ! [B: $i,C: $i,D: $i] :
( ! [E: $i] : ( E @ ( suc @ ( nat @ ( nat @ hAPP ) ) ) @ ( D @ ( A @ ( nat @ hAPP ) ) ) @ ( E @ ( D @ ( A @ ( nat @ hAPP ) ) ) @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL )
=> ( ( C @ ( B @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( C @ ( D @ ( A @ ( nat @ hAPP ) ) ) @ ( B @ ( D @ ( A @ ( nat @ hAPP ) ) ) @ ( A @ ord_less_eq @ ( bool @ ( A @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(25,axiom,
u @ ( mgt_call @ ( x_a @ ( pname @ image ) @ ( bool @ ( x_a @ fun ) @ ( bool @ ( pname @ fun ) @ fun ) @ ( x_a @ ( pname @ fun ) @ hAPP ) ) ) @ ( bool @ ( x_a @ fun ) @ ( bool @ ( pname @ fun ) @ hAPP ) ) ) @ ( x_a @ finite_card @ ( nat @ ( bool @ ( x_a @ fun ) @ hAPP ) ) ) @ ( na @ ( suc @ ( nat @ ( nat @ hAPP ) ) ) @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_2) ).
thf(231,plain,
u @ ( mgt_call @ ( x_a @ ( pname @ image ) @ ( bool @ ( x_a @ fun ) @ ( bool @ ( pname @ fun ) @ fun ) @ ( x_a @ ( pname @ fun ) @ hAPP ) ) ) @ ( bool @ ( x_a @ fun ) @ ( bool @ ( pname @ fun ) @ hAPP ) ) ) @ ( x_a @ finite_card @ ( nat @ ( bool @ ( x_a @ fun ) @ hAPP ) ) ) @ ( na @ ( suc @ ( nat @ ( nat @ hAPP ) ) ) @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(127,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( bool @ ( A @ fun ) @ ti ) )
= ( C @ ( bool @ ( A @ fun ) @ ti ) ) )
<=> ( ( B @ ( C @ ( bool @ ( A @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
& ( C @ ( B @ ( bool @ ( A @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_set__eq__subset) ).
thf(539,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( B @ ( C @ ( bool @ ( A @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
& ( C @ ( B @ ( bool @ ( A @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL ) )
=> ( ( B @ ( bool @ ( A @ fun ) @ ti ) )
= ( C @ ( bool @ ( A @ fun ) @ ti ) ) ) )
& ( ( ( B @ ( bool @ ( A @ fun ) @ ti ) )
= ( C @ ( bool @ ( A @ fun ) @ ti ) ) )
=> ( ( B @ ( C @ ( bool @ ( A @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
& ( C @ ( B @ ( bool @ ( A @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(140,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( A @ ( B @ hAPP ) ) ) @ ( A @ ti ) )
= ( D @ ( C @ ( A @ ( B @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_hAPP_res) ).
thf(581,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)],[140]) ).
thf(517,plain,
! [A: $i] :
( ( A @ ( fNot @ ( bool @ ( bool @ hAPP ) ) ) @ hBOOL )
| ( A @ hBOOL ) ),
inference(cnf,[status(esa)],[516]) ).
thf(159,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ combi @ ( A @ ( A @ image ) @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) )
= ( B @ ( bool @ ( A @ fun ) @ ti ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_82_image__ident) ).
thf(652,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ combi @ ( A @ ( A @ image ) @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) )
= ( B @ ( bool @ ( A @ fun ) @ ti ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(78,axiom,
! [A: $i,B: $i] :
( ( B @ hBOOL )
| ( A @ hBOOL )
| ~ ( B @ ( A @ ( fdisj @ ( bool @ ( bool @ fun ) @ ( bool @ hAPP ) ) ) @ ( bool @ ( bool @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fdisj_3_1_U) ).
thf(390,plain,
! [A: $i,B: $i] :
( ( B @ hBOOL )
| ( A @ hBOOL )
| ~ ( B @ ( A @ ( fdisj @ ( bool @ ( bool @ fun ) @ ( bool @ hAPP ) ) ) @ ( bool @ ( bool @ hAPP ) ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(81,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( fdisj @ ( A @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) @ ( bool @ ( bool @ fun ) @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ ( bool @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ fun ) @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ combs ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( A @ collect @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( A @ finite_finite @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
<=> ( ( C @ ( A @ collect @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( A @ finite_finite @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
& ( B @ ( A @ collect @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( A @ finite_finite @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_26_finite__Collect__disjI) ).
thf(401,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( C @ ( A @ collect @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( A @ finite_finite @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
& ( B @ ( A @ collect @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( A @ finite_finite @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL ) )
=> ( C @ ( B @ ( fdisj @ ( A @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) @ ( bool @ ( bool @ fun ) @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ ( bool @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ fun ) @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ combs ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( A @ collect @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( A @ finite_finite @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL ) )
& ( ( C @ ( B @ ( fdisj @ ( A @ ( bool @ ( bool @ fun ) @ ( bool @ combb ) ) @ ( bool @ ( bool @ fun ) @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ ( bool @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ fun ) @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ combs ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( bool @ ( bool @ fun ) @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( A @ collect @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( A @ finite_finite @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( ( C @ ( A @ collect @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( A @ finite_finite @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
& ( B @ ( A @ collect @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( A @ finite_finite @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(6,axiom,
nat @ preorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Opreorder) ).
thf(171,plain,
nat @ preorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(27,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/sandbox2/benchmark/theBenchmark.p',fact_75_mem__def) ).
thf(235,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)],[27]) ).
thf(19,axiom,
! [A: $i] :
( ( A @ collect @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ti ) )
= ( A @ collect ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_Set_OCollect_res) ).
thf(207,plain,
! [A: $i] :
( ( A @ collect @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ti ) )
= ( A @ collect ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(37,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( A @ member @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( D @ ( B @ ( A @ insert @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( C @ ( A @ member @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_63_insertI2) ).
thf(272,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( A @ member @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( D @ ( B @ ( A @ insert @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( C @ ( A @ member @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(75,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( B @ finite_finite @ ( bool @ ( bool @ ( B @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( D @ ( C @ ( A @ ( B @ image ) @ ( bool @ ( A @ fun ) @ ( bool @ ( B @ fun ) @ fun ) @ ( A @ ( B @ fun ) @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( B @ fun ) @ hAPP ) ) ) @ ( A @ finite_finite @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_2_finite__imageI) ).
thf(383,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( B @ finite_finite @ ( bool @ ( bool @ ( B @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( D @ ( C @ ( A @ ( B @ image ) @ ( bool @ ( A @ fun ) @ ( bool @ ( B @ fun ) @ fun ) @ ( A @ ( B @ fun ) @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( B @ fun ) @ hAPP ) ) ) @ ( A @ finite_finite @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(345,plain,
! [A: $i] :
( ( A @ finite_finite @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ti ) )
= ( A @ finite_finite ) ),
inference(cnf,[status(esa)],[344]) ).
thf(346,plain,
! [A: $i] :
( ( A @ finite_finite @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ti ) )
= ( A @ finite_finite ) ),
inference(lifteq,[status(thm)],[345]) ).
thf(128,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( A @ finite_finite @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( ~ ( C @ ( B @ ( A @ member @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( ( C @ ( B @ ( A @ insert @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( A @ finite_card @ ( nat @ ( bool @ ( A @ fun ) @ hAPP ) ) ) )
= ( C @ ( A @ finite_card @ ( nat @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( suc @ ( nat @ ( nat @ hAPP ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_card__insert__disjoint) ).
thf(549,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( A @ finite_finite @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( ~ ( C @ ( B @ ( A @ member @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( ( C @ ( B @ ( A @ insert @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( A @ finite_card @ ( nat @ ( bool @ ( A @ fun ) @ hAPP ) ) ) )
= ( C @ ( A @ finite_card @ ( nat @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( suc @ ( nat @ ( nat @ hAPP ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(126,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ combc ) ) @ ( C @ ( A @ fun ) @ ( B @ fun ) @ ( C @ ( B @ fun ) @ ( A @ fun ) @ fun ) @ ti ) )
= ( C @ ( B @ ( A @ combc ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_COMBC_res) ).
thf(536,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ combc ) ) @ ( C @ ( A @ fun ) @ ( B @ fun ) @ ( C @ ( B @ fun ) @ ( A @ fun ) @ fun ) @ ti ) )
= ( C @ ( B @ ( A @ combc ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(43,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( bool @ ( A @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( D @ ( B @ ( A @ insert @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( C @ ( B @ ( A @ insert @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_87_insert__mono) ).
thf(290,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( bool @ ( A @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( D @ ( B @ ( A @ insert @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( C @ ( B @ ( A @ insert @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(73,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( D @ ( B @ member @ ( bool @ ( bool @ ( B @ fun ) @ fun ) @ ( B @ hAPP ) ) ) @ ( bool @ ( bool @ ( B @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( E @ ( C @ ( A @ ( B @ image ) @ ( bool @ ( A @ fun ) @ ( bool @ ( B @ fun ) @ fun ) @ ( A @ ( B @ fun ) @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( B @ fun ) @ hAPP ) ) ) @ ( D @ ( C @ ( A @ ( B @ hAPP ) ) ) @ ( A @ member @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_imageI) ).
thf(378,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( D @ ( B @ member @ ( bool @ ( bool @ ( B @ fun ) @ fun ) @ ( B @ hAPP ) ) ) @ ( bool @ ( bool @ ( B @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( E @ ( C @ ( A @ ( B @ image ) @ ( bool @ ( A @ fun ) @ ( bool @ ( B @ fun ) @ fun ) @ ( A @ ( B @ fun ) @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( B @ fun ) @ hAPP ) ) ) @ ( D @ ( C @ ( 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)],[73]) ).
thf(90,axiom,
bool @ preorder,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Opreorder) ).
thf(433,plain,
bool @ preorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(116,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( A @ finite_finite @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( ( C @ ( B @ ( bool @ ( A @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( A @ finite_finite @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_rev__finite__subset) ).
thf(510,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( A @ finite_finite @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( ( C @ ( B @ ( bool @ ( A @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( B @ ( A @ finite_finite @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(50,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/sandbox2/benchmark/theBenchmark.p',fact_74_ext) ).
thf(315,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)],[50]) ).
thf(33,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( bool @ ( A @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( ( C @ ( B @ ( A @ member @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( D @ ( B @ ( A @ member @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_subsetD) ).
thf(262,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( bool @ ( A @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( ( C @ ( B @ ( A @ member @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( D @ ( B @ ( 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(86,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ combb ) ) @ ( B @ ( C @ fun ) @ ( A @ ( C @ fun ) @ fun ) @ ( B @ ( A @ fun ) @ fun ) @ ti ) )
= ( C @ ( B @ ( A @ combb ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_COMBB_res) ).
thf(422,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ combb ) ) @ ( B @ ( C @ fun ) @ ( A @ ( C @ fun ) @ fun ) @ ( B @ ( A @ fun ) @ fun ) @ ti ) )
= ( C @ ( B @ ( A @ combb ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(20,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( bool @ ( A @ fun ) @ ti ) )
= ( C @ ( bool @ ( A @ fun ) @ ti ) ) )
=> ( B @ ( C @ ( bool @ ( A @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_equalityD2) ).
thf(210,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( bool @ ( A @ fun ) @ ti ) )
= ( C @ ( bool @ ( A @ fun ) @ ti ) ) )
=> ( B @ ( C @ ( bool @ ( A @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(60,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( D @ ( A @ insert @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( C @ ( B @ ( A @ image ) @ ( bool @ ( B @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( B @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( B @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) )
= ( E @ ( C @ ( B @ ( A @ image ) @ ( bool @ ( B @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( B @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( B @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( D @ ( C @ ( B @ ( A @ hAPP ) ) ) @ ( B @ insert @ ( bool @ ( B @ fun ) @ ( bool @ ( B @ fun ) @ fun ) @ ( B @ hAPP ) ) ) @ ( bool @ ( B @ fun ) @ ( bool @ ( B @ fun ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_88_image__insert) ).
thf(341,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( D @ ( A @ insert @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( C @ ( B @ ( A @ image ) @ ( bool @ ( B @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( B @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( B @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) )
= ( E @ ( C @ ( B @ ( A @ image ) @ ( bool @ ( B @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( B @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( B @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( D @ ( C @ ( B @ ( A @ hAPP ) ) ) @ ( B @ insert @ ( bool @ ( B @ fun ) @ ( bool @ ( B @ fun ) @ fun ) @ ( B @ hAPP ) ) ) @ ( bool @ ( B @ fun ) @ ( bool @ ( B @ fun ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(92,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i] :
( ( E @ ( F @ ( B @ member @ ( bool @ ( bool @ ( B @ fun ) @ fun ) @ ( B @ hAPP ) ) ) @ ( bool @ ( bool @ ( B @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( D @ ( F @ ( C @ ( A @ ( B @ hAPP ) ) ) @ ( A @ member @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL ) )
=> ( D @ ( E @ ( C @ ( A @ ( B @ image ) @ ( bool @ ( A @ fun ) @ ( bool @ ( B @ fun ) @ fun ) @ ( A @ ( B @ fun ) @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( B @ fun ) @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_96_image__subsetI) ).
thf(437,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i] :
( ( E @ ( F @ ( B @ member @ ( bool @ ( bool @ ( B @ fun ) @ fun ) @ ( B @ hAPP ) ) ) @ ( bool @ ( bool @ ( B @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( D @ ( F @ ( C @ ( A @ ( B @ hAPP ) ) ) @ ( A @ member @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL ) )
=> ( D @ ( E @ ( C @ ( A @ ( B @ image ) @ ( bool @ ( A @ fun ) @ ( bool @ ( B @ fun ) @ fun ) @ ( A @ ( B @ fun ) @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( B @ fun ) @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(102,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( D @ ( B @ ( C @ ( A @ combs ) ) @ ( B @ ( A @ fun ) @ ( C @ ( A @ fun ) @ fun ) @ ( B @ ( C @ fun ) @ ( A @ fun ) @ hAPP ) ) ) @ ( B @ ( A @ fun ) @ ( C @ ( A @ fun ) @ hAPP ) ) ) @ ( B @ ( A @ hAPP ) ) ) )
= ( F @ ( E @ ( C @ ( A @ hAPP ) ) ) @ ( F @ ( D @ ( B @ ( C @ fun ) @ ( A @ hAPP ) ) ) @ ( B @ ( C @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBS_1_1_U) ).
thf(464,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( D @ ( B @ ( C @ ( A @ combs ) ) @ ( B @ ( A @ fun ) @ ( C @ ( A @ fun ) @ fun ) @ ( B @ ( C @ fun ) @ ( A @ fun ) @ hAPP ) ) ) @ ( B @ ( A @ fun ) @ ( C @ ( A @ fun ) @ hAPP ) ) ) @ ( B @ ( A @ hAPP ) ) ) )
= ( F @ ( E @ ( C @ ( A @ hAPP ) ) ) @ ( F @ ( D @ ( B @ ( C @ fun ) @ ( A @ hAPP ) ) ) @ ( B @ ( C @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(137,axiom,
! [A: $i,B: $i,C: $i] : ( C @ ( B @ ( A @ insert @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( B @ ( A @ member @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_insertI1) ).
thf(575,plain,
! [A: $i,B: $i,C: $i] : ( C @ ( B @ ( A @ insert @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( B @ ( A @ member @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(88,axiom,
! [A: $i,B: $i] :
( ( B @ hBOOL )
| ~ ( B @ ( A @ ( fconj @ ( bool @ ( bool @ fun ) @ ( bool @ hAPP ) ) ) @ ( bool @ ( bool @ hAPP ) ) ) @ hBOOL ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_fconj_3_1_U) ).
thf(427,plain,
! [A: $i,B: $i] :
( ( B @ hBOOL )
| ~ ( B @ ( A @ ( fconj @ ( bool @ ( bool @ fun ) @ ( bool @ hAPP ) ) ) @ ( bool @ ( bool @ hAPP ) ) ) @ hBOOL ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(145,axiom,
! [A: $i,B: $i] :
( ( B @ ( suc @ ( nat @ ( nat @ hAPP ) ) ) @ ( A @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
<=> ( ( A
= ( B @ ( suc @ ( nat @ ( nat @ hAPP ) ) ) ) )
| ( B @ ( A @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_le__Suc__eq) ).
thf(596,plain,
! [A: $i,B: $i] :
( ( ( ( A
= ( B @ ( suc @ ( nat @ ( nat @ hAPP ) ) ) ) )
| ( B @ ( A @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) )
=> ( B @ ( suc @ ( nat @ ( nat @ hAPP ) ) ) @ ( A @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) )
& ( ( B @ ( suc @ ( nat @ ( nat @ hAPP ) ) ) @ ( A @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( ( A
= ( B @ ( suc @ ( nat @ ( nat @ hAPP ) ) ) ) )
| ( B @ ( A @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(644,plain,
( ( fconj @ ( bool @ ( bool @ fun ) @ ( bool @ fun ) @ ti ) )
= fconj ),
inference(lifteq,[status(thm)],[643]) ).
thf(442,plain,
( ( fimplies @ ( bool @ ( bool @ fun ) @ ( bool @ fun ) @ ti ) )
= fimplies ),
inference(lifteq,[status(thm)],[441]) ).
thf(16,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( A @ ( C @ image ) @ ( bool @ ( A @ fun ) @ ( bool @ ( C @ fun ) @ fun ) @ ( A @ ( C @ fun ) @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( C @ fun ) @ hAPP ) ) ) @ ( D @ ( B @ ( A @ image ) @ ( bool @ ( B @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( B @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( B @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) )
= ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ combb ) ) @ ( B @ ( C @ fun ) @ ( A @ ( C @ fun ) @ fun ) @ ( B @ ( A @ fun ) @ hAPP ) ) ) @ ( B @ ( C @ fun ) @ ( A @ ( C @ fun ) @ hAPP ) ) ) @ ( B @ ( C @ image ) @ ( bool @ ( B @ fun ) @ ( bool @ ( C @ fun ) @ fun ) @ ( B @ ( C @ fun ) @ hAPP ) ) ) @ ( bool @ ( B @ fun ) @ ( bool @ ( C @ fun ) @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_image__image) ).
thf(200,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( A @ ( C @ image ) @ ( bool @ ( A @ fun ) @ ( bool @ ( C @ fun ) @ fun ) @ ( A @ ( C @ fun ) @ hAPP ) ) ) @ ( bool @ ( A @ fun ) @ ( bool @ ( C @ fun ) @ hAPP ) ) ) @ ( D @ ( B @ ( A @ image ) @ ( bool @ ( B @ fun ) @ ( bool @ ( A @ fun ) @ fun ) @ ( B @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( B @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) )
= ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ combb ) ) @ ( B @ ( C @ fun ) @ ( A @ ( C @ fun ) @ fun ) @ ( B @ ( A @ fun ) @ hAPP ) ) ) @ ( B @ ( C @ fun ) @ ( A @ ( C @ fun ) @ hAPP ) ) ) @ ( B @ ( C @ image ) @ ( bool @ ( B @ fun ) @ ( bool @ ( C @ fun ) @ fun ) @ ( B @ ( C @ fun ) @ hAPP ) ) ) @ ( bool @ ( B @ fun ) @ ( bool @ ( C @ fun ) @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(109,axiom,
! [A: $i] :
( ( A @ member @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ fun ) @ ti ) )
= ( A @ member ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',tsy_c_member_res) ).
thf(486,plain,
! [A: $i] :
( ( A @ member @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( A @ fun ) @ ti ) )
= ( A @ member ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(58,axiom,
! [A: $i,B: $i] : ( B @ ( B @ ( bool @ ( A @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_65_subset__refl) ).
thf(337,plain,
! [A: $i,B: $i] : ( B @ ( B @ ( bool @ ( A @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(111,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( D @ ( B @ ( C @ ( A @ combc ) ) @ ( B @ ( A @ fun ) @ ( C @ fun ) @ ( B @ ( C @ fun ) @ ( A @ fun ) @ hAPP ) ) ) @ ( B @ ( A @ fun ) @ ( C @ hAPP ) ) ) @ ( B @ ( A @ hAPP ) ) ) )
= ( E @ ( F @ ( D @ ( B @ ( C @ fun ) @ ( A @ hAPP ) ) ) @ ( B @ ( C @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',help_COMBC_1_1_U) ).
thf(491,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( D @ ( B @ ( C @ ( A @ combc ) ) @ ( B @ ( A @ fun ) @ ( C @ fun ) @ ( B @ ( C @ fun ) @ ( A @ fun ) @ hAPP ) ) ) @ ( B @ ( A @ fun ) @ ( C @ hAPP ) ) ) @ ( B @ ( A @ hAPP ) ) ) )
= ( E @ ( F @ ( D @ ( B @ ( C @ fun ) @ ( A @ hAPP ) ) ) @ ( B @ ( C @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(23,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( A @ finite_finite @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( ( C @ ( B @ ( bool @ ( A @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( A @ finite_card @ ( nat @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( C @ ( A @ finite_card @ ( nat @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( bool @ ( A @ fun ) @ ti ) )
= ( C @ ( bool @ ( A @ fun ) @ ti ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_card__seteq) ).
thf(222,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( A @ finite_finite @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( ( C @ ( B @ ( bool @ ( A @ fun ) @ ord_less_eq @ ( bool @ ( bool @ ( A @ fun ) @ fun ) @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( bool @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( A @ finite_card @ ( nat @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( C @ ( A @ finite_card @ ( nat @ ( bool @ ( A @ fun ) @ hAPP ) ) ) @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( ( B @ ( bool @ ( A @ fun ) @ ti ) )
= ( C @ ( bool @ ( A @ fun ) @ ti ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(143,axiom,
( ( g @ ( x_a @ finite_card @ ( nat @ ( bool @ ( x_a @ fun ) @ hAPP ) ) ) )
= ( na @ ( suc @ ( nat @ ( nat @ hAPP ) ) ) @ ( u @ ( mgt_call @ ( x_a @ ( pname @ image ) @ ( bool @ ( x_a @ fun ) @ ( bool @ ( pname @ fun ) @ fun ) @ ( x_a @ ( pname @ fun ) @ hAPP ) ) ) @ ( bool @ ( x_a @ fun ) @ ( bool @ ( pname @ fun ) @ hAPP ) ) ) @ ( x_a @ finite_card @ ( nat @ ( bool @ ( x_a @ fun ) @ hAPP ) ) ) @ ( nat @ minus_minus @ ( nat @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( nat @ ( nat @ hAPP ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_3) ).
thf(592,plain,
( ( g @ ( x_a @ finite_card @ ( nat @ ( bool @ ( x_a @ fun ) @ hAPP ) ) ) )
= ( na @ ( suc @ ( nat @ ( nat @ hAPP ) ) ) @ ( u @ ( mgt_call @ ( x_a @ ( pname @ image ) @ ( bool @ ( x_a @ fun ) @ ( bool @ ( pname @ fun ) @ fun ) @ ( x_a @ ( pname @ fun ) @ hAPP ) ) ) @ ( bool @ ( x_a @ fun ) @ ( bool @ ( pname @ fun ) @ hAPP ) ) ) @ ( x_a @ finite_card @ ( nat @ ( bool @ ( x_a @ fun ) @ hAPP ) ) ) @ ( nat @ minus_minus @ ( nat @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( nat @ ( nat @ hAPP ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(26,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( ( A @ ( B @ ( nat @ minus_minus @ ( nat @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( B @ ( nat @ minus_minus @ ( nat @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( nat @ ( nat @ hAPP ) ) ) )
= A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_diff__diff__cancel) ).
thf(232,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( nat @ ord_less_eq @ ( bool @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( bool @ ( nat @ hAPP ) ) ) @ hBOOL )
=> ( ( A @ ( B @ ( nat @ minus_minus @ ( nat @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( nat @ ( nat @ hAPP ) ) ) @ ( B @ ( nat @ minus_minus @ ( nat @ ( nat @ fun ) @ ( nat @ hAPP ) ) ) @ ( nat @ ( nat @ hAPP ) ) ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(1012,plain,
! [A: $i] :
( ( ( u @ ( pname @ finite_finite @ ( bool @ ( bool @ ( pname @ fun ) @ hAPP ) ) ) @ hBOOL )
!= ( A @ hBOOL ) )
| ~ $true
| ~ ( A @ ( fNot @ ( bool @ ( bool @ hAPP ) ) ) @ hBOOL ) ),
inference(paramod_ordered,[status(thm)],[289,369]) ).
thf(1013,plain,
! [A: $i] :
( ( ( u @ ( pname @ finite_finite @ ( bool @ ( bool @ ( pname @ fun ) @ hAPP ) ) ) @ hBOOL )
!= ( A @ hBOOL ) )
| ~ ( A @ ( fNot @ ( bool @ ( bool @ hAPP ) ) ) @ hBOOL ) ),
inference(simp,[status(thm)],[1012]) ).
thf(1014,plain,
~ ( u @ ( pname @ finite_finite @ ( bool @ ( bool @ ( pname @ fun ) @ hAPP ) ) ) @ ( fNot @ ( bool @ ( bool @ hAPP ) ) ) @ hBOOL ),
inference(pattern_uni,[status(thm)],[1013:[bind(A,$thf( u @ ( pname @ finite_finite @ ( bool @ ( bool @ ( pname @ fun ) @ hAPP ) ) ) ))]]) ).
thf(1567,plain,
$false,
inference(e,[status(thm)],[385,645,629,347,518,352,333,628,523,308,247,655,614,408,170,174,288,257,320,565,619,344,357,196,559,189,606,284,416,325,289,448,164,443,376,623,514,348,353,480,660,312,292,452,380,512,534,270,529,260,392,297,429,192,630,467,625,461,324,650,388,169,499,471,225,339,554,193,526,489,1075,476,457,173,569,244,360,205,311,398,1135,750,425,166,264,180,296,584,176,1007,577,579,204,445,572,335,172,219,274,419,318,434,451,567,494,535,323,594,213,483,198,330,367,552,521,278,455,1015,306,267,241,167,658,473,648,355,194,617,516,557,640,414,199,441,502,359,643,585,370,175,595,497,231,450,539,203,581,368,517,652,390,401,171,235,207,272,383,346,549,536,287,290,378,433,510,315,262,422,210,294,341,437,464,575,427,596,644,442,369,163,200,486,337,491,222,592,232,1014]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWW473+5 : TPTP v9.3.1. Released v5.3.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.15/5.42 % Computer : n004.cluster.edu
% 0.15/5.42 % Model : x86_64 x86_64
% 0.15/5.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/5.42 % Memory : 8046.5625MB
% 0.15/5.42 % OS : Linux 6.8.0-71-generic
% 0.15/5.43 % CPULimit : 300
% 0.15/5.43 % WCLimit : 300
% 0.15/5.43 % DateTime : Sat Sep 26 16:01:42 UTC 2026
% 0.15/5.43 % CPUTime :
% 0.15/5.43 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 1.24/6.27 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.16/6.69 % [INFO] Parsing done (412ms).
% 2.59/6.71 % [INFO] Running in sequential loop mode.
% 4.08/7.28 % [INFO] eprover registered as external prover.
% 4.08/7.29 % [INFO] Scanning for conjecture ...
% 5.08/7.55 % [INFO] Found a conjecture (or negated_conjecture) and 160 axioms. Running axiom selection ...
% 5.91/7.79 % [INFO] Axiom selection finished. Selected 160 axioms (removed 0 axioms).
% 8.06/8.30 % [INFO] Problem is first-order (TPTP FOF).
% 8.42/8.33 % [INFO] Type checking passed.
% 8.42/8.34 % [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 ...
% 27.16/12.59 % External prover 'e' found a proof!
% 27.16/12.59 % [INFO] Killing All external provers ...
% 27.16/12.59 % Time passed: 6962ms (effective reasoning time: 5875ms)
% 27.16/12.59 % 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)>
% 27.16/12.59 % Axioms used in derivation (160): tsy_c_Finite__Set_Ocard_res, fact_44_diff__le__mono2, fact_88_image__insert, help_fimplies_2_1_U, fact_48_lift__Suc__mono__le, tsy_c_fconj_res, arity_HOL_Obool___Finite__Set_Ofinite, fact_79_rev__image__eqI, arity_HOL_Obool___Orderings_Oorder, help_COMBS_1_1_U, fact_47_finite__subset__image, tsy_v_na_res, tsy_c_Nat_OSuc_res, fact_58_insert__absorb2, help_fconj_3_1_U, fact_72_subset__trans, fact_13_card__Collect__le__nat, fact_67_equalityD1, arity_HOL_Obool___Orderings_Opreorder, fact_60_insert__iff, fact_80_insert__compr__raw, fact_38_diff__Suc__Suc, tsy_c_member_res, fact_15_finite, tsy_c_fimplies_res, fact_5_card__mono, conj_3, fact_39_le__diff__iff, fact_53_insertCI, fact_37_Suc__diff__diff, help_COMBI_1_1_U, arity_Nat_Onat___Orderings_Opreorder, fact_96_image__subsetI, fact_18_Suc__n__not__n, fact_71_set__mp, fact_2_finite__imageI, fact_19_n__not__Suc__n, fact_85_subset__insert, fact_75_mem__def, fact_29_rev__finite__subset, fact_63_insertI2, tsy_c_hAPP_res, tsy_c_Set_OCollect_res, fact_30_Suc__leD, fact_97_order__refl, fact_46_finite__surj, tsy_c_hAPP_arg1, tsy_c_Orderings_Oord__class_Oless__eq_res, fact_68_equalityD2, help_fNot_2_1_U, fact_31_le__SucE, fact_22_eq__imp__le, tsy_c_COMBC_res, fact_64_insert__absorb, help_fNot_1_1_U, tsy_c_COMBS_res, tsy_v_U_res, fact_41_eq__diff__iff, fact_54_insertE, fact_59_insert__commute, fact_74_ext, tsy_c_hBOOL_arg1, fact_93_subsetI, fact_36_Suc__n__not__le__n, fact_10_finite__Collect__conjI, fact_69_in__mono, fact_78_imageI, tsy_c_Finite__Set_Ofinite_res, help_COMBB_1_1_U, fact_89_insert__image, fact_83_subset__insertI, conj_2, fact_7_card__insert__le, fact_81_image__image, arity_fun___Orderings_Oorder, fact_23_nat__le__linear, help_fdisj_1_1_U, fact_70_set__rev__mp, tsy_c_hAPP_arg2, fact_95_Suc__le__D, fact_76_Collect__def, tsy_c_Set_Oimage_res, fact_66_set__eq__subset, help_fconj_2_1_U, arity_fun___Orderings_Opreorder, fact_61_insert__code, tsy_c_COMBB_res, tsy_c_fNot_res, fact_12_finite__Collect__le__nat, fact_42_diff__diff__cancel, fact_27_finite__insert, fact_98_finite__nat__set__iff__bounded__le, fact_90_subset__image__iff, tsy_c_HOL_Oundefined_res, fact_21_le__trans, fact_94_zero__induct__lemma, help_ti_idem, fact_43_diff__le__mono, fact_20_le__antisym, help_fequal_1_1_T, arity_fun___Finite__Set_Ofinite, fact_87_insert__mono, fact_82_image__ident, fact_52_subsetD, tsy_c_fequal_res, fact_25_diff__commute, tsy_v_P_res, fact_56_insert__compr, fact_14_finite__code, help_fdisj_2_1_U, tsy_c_Set_Oinsert_res, fact_9_card__insert__disjoint, fact_16_Suc__inject, tsy_v_pn_res, fact_33_Suc__le__mono, fact_45_diff__le__self, fact_8_card__insert__if, help_COMBC_1_1_U, fact_57_insert__Collect, fact_34_le__Suc__eq, fact_17_nat_Oinject, fact_51_equalityI, fact_92_imageE, tsy_v_mgt__call_res, conj_1, help_fequal_2_1_T, fact_1_finite__Collect__subsets, fact_50_image__eqI, fact_49_pigeonhole__infinite, help_fconj_1_1_U, help_fdisj_3_1_U, fact_86_subset__insertI2, tsy_v_G_res, fact_65_subset__refl, fact_73_equalityE, fact_6_card__seteq, fact_55_insertI1, fact_28_finite__subset, arity_Nat_Onat___Orderings_Oorder, fact_4_card__image__le, fact_91_image__mono, fact_40_Nat_Odiff__diff__eq, fact_24_le__refl, fact_84_insert__subset, fact_35_not__less__eq__eq, tsy_c_COMBI_res, fact_26_finite__Collect__disjI, conj_4, fact_77_image__iff, tsy_c_Groups_Ominus__class_Ominus_res, fact_11_Suc__diff__le, fact_0_assms_I1_J, help_fimplies_1_1_U, fact_32_le__SucI, conj_5, help_fimplies_3_1_U, conj_0, fact_62_insert__ident, tsy_c_fdisj_res, fact_3_finite_OinsertI
% 27.16/12.59 % No. of inferences in proof: 367
% 27.16/12.60 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 6962 ms resp. 5875 ms w/o parsing
% 27.48/12.82 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 27.48/12.83 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------