TSTP Solution File: SWW473+5 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SWW473+5 : TPTP v8.1.2. Released v5.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n010.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 12:24:09 EDT 2023
% Result : Theorem 10.92s 3.57s
% Output : Refutation 12.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 197
% Syntax : Number of formulae : 360 ( 134 unt; 36 typ; 0 def)
% Number of atoms : 677 ( 192 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 13020 ( 69 ~; 45 |; 44 &;12598 @)
% ( 19 <=>; 245 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 11 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 33 ( 33 >; 0 *; 0 +; 0 <<)
% Number of symbols : 38 ( 36 usr; 16 con; 0-4 aty)
% Number of variables : 822 ( 0 ^; 807 !; 15 ?; 822 :)
% Comments :
%------------------------------------------------------------------------------
thf(hBOOL_type,type,
hBOOL: $i > $o ).
thf(hAPP_type,type,
hAPP: $i > $i > $i > $i > $i ).
thf(fun_type,type,
fun: $i > $i > $i ).
thf(x_a_type,type,
x_a: $i ).
thf(bool_type,type,
bool: $i ).
thf(ord_less_eq_type,type,
ord_less_eq: $i > $i ).
thf(insert_type,type,
insert: $i > $i ).
thf(pname_type,type,
pname: $i ).
thf(mgt_call_type,type,
mgt_call: $i ).
thf(pn_type,type,
pn: $i ).
thf(g_type,type,
g: $i ).
thf(image_type,type,
image: $i > $i > $i ).
thf(u_type,type,
u: $i ).
thf(ti_type,type,
ti: $i > $i > $i ).
thf(undefined_type,type,
undefined: $i > $i ).
thf(order_type,type,
order: $i > $o ).
thf(nat_type,type,
nat: $i ).
thf(preorder_type,type,
preorder: $i > $o ).
thf(na_type,type,
na: $i ).
thf(member_type,type,
member: $i > $i ).
thf(fNot_type,type,
fNot: $i ).
thf(fdisj_type,type,
fdisj: $i ).
thf(combb_type,type,
combb: $i > $i > $i > $i ).
thf(p_type,type,
p: $i ).
thf(collect_type,type,
collect: $i > $i ).
thf(finite_finite_type,type,
finite_finite: $i > $i ).
thf(combs_type,type,
combs: $i > $i > $i > $i ).
thf(combc_type,type,
combc: $i > $i > $i > $i ).
thf(fequal_type,type,
fequal: $i > $i ).
thf(finite_card_type,type,
finite_card: $i > $i ).
thf(suc_type,type,
suc: $i ).
thf(minus_minus_type,type,
minus_minus: $i > $i ).
thf(fimplies_type,type,
fimplies: $i ).
thf(finite_finite_1_type,type,
finite_finite_1: $i > $o ).
thf(fconj_type,type,
fconj: $i ).
thf(combi_type,type,
combi: $i > $i ).
thf(73,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ B @ bool ) @ bool @ ( hAPP @ B @ ( fun @ ( fun @ B @ bool ) @ bool ) @ ( member @ B ) @ D ) @ E ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ ( hAPP @ B @ A @ C @ D ) ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) ) @ ( image @ B @ A ) @ C ) @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_imageI) ).
thf(365,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ B @ bool ) @ bool @ ( hAPP @ B @ ( fun @ ( fun @ B @ bool ) @ bool ) @ ( member @ B ) @ D ) @ E ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ ( hAPP @ B @ A @ C @ D ) ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) ) @ ( image @ B @ A ) @ C ) @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(114,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ nat @ nat @ ( hAPP @ nat @ ( fun @ nat @ nat ) @ ( minus_minus @ nat ) @ ( hAPP @ nat @ nat @ ( hAPP @ nat @ ( fun @ nat @ nat ) @ ( minus_minus @ nat ) @ A ) @ B ) ) @ C )
= ( hAPP @ nat @ nat @ ( hAPP @ nat @ ( fun @ nat @ nat ) @ ( minus_minus @ nat ) @ ( hAPP @ nat @ nat @ ( hAPP @ nat @ ( fun @ nat @ nat ) @ ( minus_minus @ nat ) @ A ) @ C ) ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_diff__commute) ).
thf(479,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ nat @ nat @ ( hAPP @ nat @ ( fun @ nat @ nat ) @ ( minus_minus @ nat ) @ ( hAPP @ nat @ nat @ ( hAPP @ nat @ ( fun @ nat @ nat ) @ ( minus_minus @ nat ) @ A ) @ B ) ) @ C )
= ( hAPP @ nat @ nat @ ( hAPP @ nat @ ( fun @ nat @ nat ) @ ( minus_minus @ nat ) @ ( hAPP @ nat @ nat @ ( hAPP @ nat @ ( fun @ nat @ nat ) @ ( minus_minus @ nat ) @ A ) @ C ) ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(139,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less_eq @ nat ) @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less_eq @ nat ) @ ( hAPP @ nat @ nat @ ( hAPP @ nat @ ( fun @ nat @ nat ) @ ( minus_minus @ nat ) @ A ) @ C ) ) @ ( hAPP @ nat @ nat @ ( hAPP @ nat @ ( fun @ nat @ nat ) @ ( minus_minus @ nat ) @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_diff__le__mono2) ).
thf(555,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less_eq @ nat ) @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less_eq @ nat ) @ ( hAPP @ nat @ nat @ ( hAPP @ nat @ ( fun @ nat @ nat ) @ ( minus_minus @ nat ) @ A ) @ C ) ) @ ( hAPP @ nat @ nat @ ( hAPP @ nat @ ( fun @ nat @ nat ) @ ( minus_minus @ nat ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(5,axiom,
order @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Oorder) ).
thf(170,plain,
order @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(40,axiom,
! [A: $i] :
( ( ti @ ( fun @ A @ ( fun @ A @ bool ) ) @ ( fequal @ A ) )
= ( fequal @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_fequal_res) ).
thf(276,plain,
! [A: $i] :
( ( ti @ ( fun @ A @ ( fun @ A @ bool ) ) @ ( fequal @ A ) )
= ( fequal @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(103,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less_eq @ nat ) @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less_eq @ nat ) @ B ) @ A ) )
=> ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less_eq @ nat ) @ ( hAPP @ nat @ nat @ ( hAPP @ nat @ ( fun @ nat @ nat ) @ ( minus_minus @ nat ) @ C ) @ B ) ) @ ( hAPP @ nat @ nat @ ( hAPP @ nat @ ( fun @ nat @ nat ) @ ( minus_minus @ nat ) @ A ) @ B ) ) )
<=> ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less_eq @ nat ) @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_le__diff__iff) ).
thf(449,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less_eq @ nat ) @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less_eq @ nat ) @ B ) @ A ) )
=> ( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less_eq @ nat ) @ ( hAPP @ nat @ nat @ ( hAPP @ nat @ ( fun @ nat @ nat ) @ ( minus_minus @ nat ) @ C ) @ B ) ) @ ( hAPP @ nat @ nat @ ( hAPP @ nat @ ( fun @ nat @ nat ) @ ( minus_minus @ nat ) @ A ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less_eq @ nat ) @ C ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less_eq @ nat ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less_eq @ nat ) @ ( hAPP @ nat @ nat @ ( hAPP @ nat @ ( fun @ nat @ nat ) @ ( minus_minus @ nat ) @ C ) @ B ) ) @ ( hAPP @ nat @ nat @ ( hAPP @ nat @ ( fun @ nat @ nat ) @ ( minus_minus @ nat ) @ A ) @ B ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(79,axiom,
! [A: $i] :
( ( hBOOL @ ( ti @ bool @ A ) )
<=> ( hBOOL @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_hBOOL_arg1) ).
thf(379,plain,
! [A: $i] :
( ( ( hBOOL @ ( ti @ bool @ A ) )
=> ( hBOOL @ A ) )
& ( ( hBOOL @ A )
=> ( hBOOL @ ( ti @ bool @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(100,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ B @ C ) )
=> ( ! [D: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ B @ ( hAPP @ nat @ nat @ suc @ D ) ) )
=> ( hBOOL @ ( hAPP @ nat @ bool @ B @ D ) ) )
=> ( hBOOL @ ( hAPP @ nat @ bool @ B @ ( hAPP @ nat @ nat @ ( hAPP @ nat @ ( fun @ nat @ nat ) @ ( minus_minus @ nat ) @ C ) @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_zero__induct__lemma) ).
thf(440,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ B @ C ) )
=> ( ! [D: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ B @ ( hAPP @ nat @ nat @ suc @ D ) ) )
=> ( hBOOL @ ( hAPP @ nat @ bool @ B @ D ) ) )
=> ( hBOOL @ ( hAPP @ nat @ bool @ B @ ( hAPP @ nat @ nat @ ( hAPP @ nat @ ( fun @ nat @ nat ) @ ( minus_minus @ nat ) @ C ) @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(80,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ bool @ bool @ ( hAPP @ bool @ ( fun @ bool @ bool ) @ fconj @ A ) @ B ) )
| ( hBOOL @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_2_1_U) ).
thf(384,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ bool @ bool @ ( hAPP @ bool @ ( fun @ bool @ bool ) @ fconj @ A ) @ B ) )
| ( hBOOL @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(121,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less_eq @ nat ) @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less_eq @ nat ) @ A ) @ ( hAPP @ nat @ nat @ suc @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_le__SucI) ).
thf(500,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less_eq @ nat ) @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less_eq @ nat ) @ A ) @ ( hAPP @ nat @ nat @ suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(8,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_set__mp) ).
thf(174,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(90,axiom,
preorder @ bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Opreorder) ).
thf(417,plain,
preorder @ bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(55,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ C ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ C )
= ( ti @ ( fun @ A @ bool ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_insert__absorb) ).
thf(320,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ C ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ C )
= ( ti @ ( fun @ A @ bool ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(76,axiom,
! [A: $i,B: $i,C: $i] :
( ( ti @ ( fun @ ( fun @ A @ ( fun @ B @ C ) ) @ ( fun @ ( fun @ A @ B ) @ ( fun @ A @ C ) ) ) @ ( combs @ A @ B @ C ) )
= ( combs @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_COMBS_res) ).
thf(372,plain,
! [A: $i,B: $i,C: $i] :
( ( ti @ ( fun @ ( fun @ A @ ( fun @ B @ C ) ) @ ( fun @ ( fun @ A @ B ) @ ( fun @ A @ C ) ) ) @ ( combs @ A @ B @ C ) )
= ( combs @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(147,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ B )
= ( ti @ ( fun @ A @ bool ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_Collect__def) ).
thf(587,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ B )
= ( ti @ ( fun @ A @ bool ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(66,axiom,
~ ( hBOOL @ ( hAPP @ ( fun @ x_a @ bool ) @ bool @ ( hAPP @ x_a @ ( fun @ ( fun @ x_a @ bool ) @ bool ) @ ( member @ x_a ) @ ( hAPP @ pname @ x_a @ mgt_call @ pn ) ) @ g ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_5) ).
thf(344,plain,
~ ( hBOOL @ ( hAPP @ ( fun @ x_a @ bool ) @ bool @ ( hAPP @ x_a @ ( fun @ ( fun @ x_a @ bool ) @ bool ) @ ( member @ x_a ) @ ( hAPP @ pname @ x_a @ mgt_call @ pn ) ) @ g ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(15,axiom,
( ( ti @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ fdisj )
= fdisj ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_fdisj_res) ).
thf(196,plain,
( ( ti @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ fdisj )
= fdisj ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(107,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ D ) ) )
=> ( ( ( ti @ A @ B )
!= ( ti @ A @ C ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_insertE) ).
thf(460,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ D ) ) )
=> ( ( ( ti @ A @ B )
!= ( ti @ A @ C ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(92,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ B @ bool ) @ bool @ ( hAPP @ B @ ( fun @ ( fun @ B @ bool ) @ bool ) @ ( member @ B ) @ F ) @ E ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ ( hAPP @ B @ A @ C @ F ) ) @ D ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) ) @ ( image @ B @ A ) @ C ) @ E ) ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_image__subsetI) ).
thf(421,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ B @ bool ) @ bool @ ( hAPP @ B @ ( fun @ ( fun @ B @ bool ) @ bool ) @ ( member @ B ) @ F ) @ E ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ ( hAPP @ B @ A @ C @ F ) ) @ D ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) ) @ ( image @ B @ A ) @ C ) @ E ) ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(44,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( fun @ ( fun @ A @ bool ) @ bool ) @ bool @ ( finite_finite @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( collect @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( hAPP @ ( fun @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) ) @ ( combc @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1_finite__Collect__subsets) ).
thf(284,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( fun @ ( fun @ A @ bool ) @ bool ) @ bool @ ( finite_finite @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( collect @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( hAPP @ ( fun @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) ) @ ( combc @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(57,axiom,
! [A: $i] :
( ( preorder @ A )
=> ! [B: $i] : ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ B ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_order__refl) ).
thf(325,plain,
! [A: $i] :
( ( preorder @ A )
=> ! [B: $i] : ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ B ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(26,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less_eq @ nat ) @ A ) @ B ) )
=> ( ( hAPP @ nat @ nat @ ( hAPP @ nat @ ( fun @ nat @ nat ) @ ( minus_minus @ nat ) @ B ) @ ( hAPP @ nat @ nat @ ( hAPP @ nat @ ( fun @ nat @ nat ) @ ( minus_minus @ nat ) @ B ) @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_diff__diff__cancel) ).
thf(228,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less_eq @ nat ) @ A ) @ B ) )
=> ( ( hAPP @ nat @ nat @ ( hAPP @ nat @ ( fun @ nat @ nat ) @ ( minus_minus @ nat ) @ B ) @ ( hAPP @ nat @ nat @ ( hAPP @ nat @ ( fun @ nat @ nat ) @ ( minus_minus @ nat ) @ B ) @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(46,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ C ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) ) @ ( image @ B @ A ) @ D ) @ E ) ) )
<=> ? [F: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ B @ bool ) @ bool @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ ( fun @ B @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ B @ bool ) ) @ F ) @ E ) )
& ( ( ti @ ( fun @ A @ bool ) @ C )
= ( hAPP @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) ) @ ( image @ B @ A ) @ D ) @ F ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_subset__image__iff) ).
thf(289,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ C ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) ) @ ( image @ B @ A ) @ D ) @ E ) ) )
=> ? [F: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ B @ bool ) @ bool @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ ( fun @ B @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ B @ bool ) ) @ F ) @ E ) )
& ( ( ti @ ( fun @ A @ bool ) @ C )
= ( hAPP @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) ) @ ( image @ B @ A ) @ D ) @ F ) ) ) )
& ( ? [F: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ B @ bool ) @ bool @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ ( fun @ B @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ B @ bool ) ) @ F ) @ E ) )
& ( ( ti @ ( fun @ A @ bool ) @ C )
= ( hAPP @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) ) @ ( image @ B @ A ) @ D ) @ F ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ C ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) ) @ ( image @ B @ A ) @ D ) @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(54,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) ) @ ( image @ B @ A ) @ D ) @ E ) ) )
=> ~ ! [F: $i] :
( ( ( ti @ A @ C )
= ( hAPP @ B @ A @ D @ F ) )
=> ~ ( hBOOL @ ( hAPP @ ( fun @ B @ bool ) @ bool @ ( hAPP @ B @ ( fun @ ( fun @ B @ bool ) @ bool ) @ ( member @ B ) @ F ) @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_imageE) ).
thf(316,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) ) @ ( image @ B @ A ) @ D ) @ E ) ) )
=> ~ ! [F: $i] :
( ( ( ti @ A @ C )
= ( hAPP @ B @ A @ D @ F ) )
=> ~ ( hBOOL @ ( hAPP @ ( fun @ B @ bool ) @ bool @ ( hAPP @ B @ ( fun @ ( fun @ B @ bool ) @ bool ) @ ( member @ B ) @ F ) @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(35,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ C ) )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( combs @ A @ bool @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ ( fun @ bool @ bool ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ A ) @ fimplies ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ bool @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( combb @ bool @ bool @ A ) @ fNot ) @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ A @ bool ) ) @ ( fun @ A @ ( fun @ A @ bool ) ) @ ( combc @ A @ A @ bool ) @ ( fequal @ A ) ) @ B ) ) ) ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_insert__Collect) ).
thf(261,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ C ) )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( combs @ A @ bool @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ ( fun @ bool @ bool ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ A ) @ fimplies ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ bool @ bool ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( combb @ bool @ bool @ A ) @ fNot ) @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ A @ bool ) ) @ ( fun @ A @ ( fun @ A @ bool ) ) @ ( combc @ A @ A @ bool ) @ ( fequal @ A ) ) @ B ) ) ) ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(22,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ C )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( combs @ A @ bool @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ ( fun @ bool @ bool ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ A ) @ fdisj ) @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ A @ bool ) ) @ ( fun @ A @ ( fun @ A @ bool ) ) @ ( combc @ A @ A @ bool ) @ ( fequal @ A ) ) @ B ) ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( combc @ A @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_insert__compr) ).
thf(216,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ C )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( combs @ A @ bool @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ ( fun @ bool @ bool ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ A ) @ fdisj ) @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ A @ bool ) ) @ ( fun @ A @ ( fun @ A @ bool ) ) @ ( combc @ A @ A @ bool ) @ ( fequal @ A ) ) @ B ) ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( combc @ A @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( ti @ A @ ( ti @ A @ B ) )
= ( ti @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_ti_idem) ).
thf(164,plain,
! [A: $i,B: $i] :
( ( ti @ A @ ( ti @ A @ B ) )
= ( ti @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(10,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) ) @ ( image @ B @ A ) @ D ) @ E ) ) )
<=> ? [F: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ B @ bool ) @ bool @ ( hAPP @ B @ ( fun @ ( fun @ B @ bool ) @ bool ) @ ( member @ B ) @ F ) @ E ) )
& ( ( ti @ A @ C )
= ( hAPP @ B @ A @ D @ F ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_image__iff) ).
thf(179,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) ) @ ( image @ B @ A ) @ D ) @ E ) ) )
=> ? [F: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ B @ bool ) @ bool @ ( hAPP @ B @ ( fun @ ( fun @ B @ bool ) @ bool ) @ ( member @ B ) @ F ) @ E ) )
& ( ( ti @ A @ C )
= ( hAPP @ B @ A @ D @ F ) ) ) )
& ( ? [F: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ B @ bool ) @ bool @ ( hAPP @ B @ ( fun @ ( fun @ B @ bool ) @ bool ) @ ( member @ B ) @ F ) @ E ) )
& ( ( ti @ A @ C )
= ( hAPP @ B @ A @ D @ F ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) ) @ ( image @ B @ A ) @ D ) @ E ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(101,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ C )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( combs @ A @ bool @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ ( fun @ bool @ bool ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ A ) @ fdisj ) @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ A @ bool ) ) @ ( fun @ A @ ( fun @ A @ bool ) ) @ ( combc @ A @ A @ bool ) @ ( fequal @ A ) ) @ B ) ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( combc @ A @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_insert__compr__raw) ).
thf(443,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ C )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( combs @ A @ bool @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ ( fun @ bool @ bool ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ A ) @ fdisj ) @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ A @ bool ) ) @ ( fun @ A @ ( fun @ A @ bool ) ) @ ( combc @ A @ A @ bool ) @ ( fequal @ A ) ) @ B ) ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( combc @ A @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(21,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ C ) ) )
<=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_finite__insert) ).
thf(211,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ C ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ C ) ) )
& ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(126,axiom,
! [A: $i,B: $i,C: $i] :
( ( ti @ ( fun @ ( fun @ A @ ( fun @ B @ C ) ) @ ( fun @ B @ ( fun @ A @ C ) ) ) @ ( combc @ A @ B @ C ) )
= ( combc @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_COMBC_res) ).
thf(514,plain,
! [A: $i,B: $i,C: $i] :
( ( ti @ ( fun @ ( fun @ A @ ( fun @ B @ C ) ) @ ( fun @ B @ ( fun @ A @ C ) ) ) @ ( combc @ A @ B @ C ) )
= ( combc @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(88,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ bool @ bool @ ( hAPP @ bool @ ( fun @ bool @ bool ) @ fconj @ A ) @ B ) )
| ( hBOOL @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_3_1_U) ).
thf(411,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ bool @ bool @ ( hAPP @ bool @ ( fun @ bool @ bool ) @ fconj @ A ) @ B ) )
| ( hBOOL @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(95,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ A @ B @ ( ti @ ( fun @ A @ B ) @ C ) @ D )
= ( hAPP @ A @ B @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_hAPP_arg1) ).
thf(428,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ A @ B @ ( ti @ ( fun @ A @ B ) @ C ) @ D )
= ( hAPP @ A @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(104,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_in__mono) ).
thf(452,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(125,axiom,
( ( ti @ ( fun @ nat @ nat ) @ suc )
= suc ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Nat_OSuc_res) ).
thf(512,plain,
( ( ti @ ( fun @ nat @ nat ) @ suc )
= suc ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(129,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less_eq @ nat ) @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less_eq @ nat ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less_eq @ nat ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_le__trans) ).
thf(529,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less_eq @ nat ) @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less_eq @ nat ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less_eq @ nat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(17,axiom,
( ( ti @ pname @ pn )
= pn ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_v_pn_res) ).
thf(201,plain,
( ( ti @ pname @ pn )
= pn ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(131,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ B )
| ~ ( hBOOL @ A )
| ( hBOOL @ ( hAPP @ bool @ bool @ ( hAPP @ bool @ ( fun @ bool @ bool ) @ fconj @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fconj_1_1_U) ).
thf(534,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ B )
| ~ ( hBOOL @ A )
| ( hBOOL @ ( hAPP @ bool @ bool @ ( hAPP @ bool @ ( fun @ bool @ bool ) @ fconj @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(61,axiom,
! [A: $i] :
( ( ti @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( finite_finite @ A ) )
= ( finite_finite @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Finite__Set_Ofinite_res) ).
thf(334,plain,
! [A: $i] :
( ( ti @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( finite_finite @ A ) )
= ( finite_finite @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(68,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ C ) ) @ D ) )
<=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ D ) )
& ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_insert__subset) ).
thf(349,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ C ) ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ D ) )
& ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ C ) @ D ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ D ) )
& ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ C ) @ D ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ C ) ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(151,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ D ) )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_insert__commute) ).
thf(598,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ D ) )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(142,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less_eq @ nat ) @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less_eq @ nat ) @ B ) @ A ) )
=> ( ( ( hAPP @ nat @ nat @ ( hAPP @ nat @ ( fun @ nat @ nat ) @ ( minus_minus @ nat ) @ C ) @ B )
= ( hAPP @ nat @ nat @ ( hAPP @ nat @ ( fun @ nat @ nat ) @ ( minus_minus @ nat ) @ A ) @ B ) )
<=> ( C = A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_eq__diff__iff) ).
thf(561,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less_eq @ nat ) @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less_eq @ nat ) @ B ) @ A ) )
=> ( ( ( ( hAPP @ nat @ nat @ ( hAPP @ nat @ ( fun @ nat @ nat ) @ ( minus_minus @ nat ) @ C ) @ B )
= ( hAPP @ nat @ nat @ ( hAPP @ nat @ ( fun @ nat @ nat ) @ ( minus_minus @ nat ) @ A ) @ B ) )
=> ( C = A ) )
& ( ( C = A )
=> ( ( hAPP @ nat @ nat @ ( hAPP @ nat @ ( fun @ nat @ nat ) @ ( minus_minus @ nat ) @ C ) @ B )
= ( hAPP @ nat @ nat @ ( hAPP @ nat @ ( fun @ nat @ nat ) @ ( minus_minus @ nat ) @ A ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(47,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less_eq @ nat ) @ A ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_le__refl) ).
thf(297,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less_eq @ nat ) @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(93,axiom,
( ( ti @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ fimplies )
= fimplies ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_fimplies_res) ).
thf(424,plain,
( ( ti @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ fimplies )
= fimplies ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ D ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_set__rev__mp) ).
thf(192,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ D ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(161,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ B @ bool ) @ bool @ ( finite_finite @ B ) @ E ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ C ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) ) @ ( image @ B @ A ) @ D ) @ E ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_finite__surj) ).
thf(630,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ B @ bool ) @ bool @ ( finite_finite @ B ) @ E ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ C ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) ) @ ( image @ B @ A ) @ D ) @ E ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(98,axiom,
! [A: $i] :
( ( ti @ ( fun @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) ) @ ( insert @ A ) )
= ( insert @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Set_Oinsert_res) ).
thf(435,plain,
! [A: $i] :
( ( ti @ ( fun @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) ) @ ( insert @ A ) )
= ( insert @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(59,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ bool @ bool @ ( hAPP @ bool @ ( fun @ bool @ bool ) @ fimplies @ A ) @ B ) )
| ~ ( hBOOL @ A )
| ( hBOOL @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fimplies_3_1_U) ).
thf(329,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ bool @ bool @ ( hAPP @ bool @ ( fun @ bool @ bool ) @ fimplies @ A ) @ B ) )
| ~ ( hBOOL @ A )
| ( hBOOL @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(118,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less_eq @ nat ) @ A ) @ B ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less_eq @ nat ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_nat__le__linear) ).
thf(493,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less_eq @ nat ) @ A ) @ B ) )
| ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less_eq @ nat ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(137,axiom,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_insertI1) ).
thf(551,plain,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(155,axiom,
( ( ti @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ fconj )
= fconj ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_fconj_res) ).
thf(615,plain,
( ( ti @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ fconj )
= fconj ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(85,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ C ) @ B ) )
=> ( ( ti @ ( fun @ A @ bool ) @ B )
= ( ti @ ( fun @ A @ bool ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_equalityI) ).
thf(403,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ C ) @ B ) )
=> ( ( ti @ ( fun @ A @ bool ) @ B )
= ( ti @ ( fun @ A @ bool ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(70,axiom,
! [A: $i] :
( ~ ( hBOOL @ ( hAPP @ bool @ bool @ fNot @ A ) )
| ~ ( hBOOL @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fNot_1_1_U) ).
thf(356,plain,
! [A: $i] :
( ~ ( hBOOL @ ( hAPP @ bool @ bool @ fNot @ A ) )
| ~ ( hBOOL @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(128,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ C ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ C ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ nat @ ( finite_card @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ C ) )
= ( hAPP @ nat @ nat @ suc @ ( hAPP @ ( fun @ A @ bool ) @ nat @ ( finite_card @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_card__insert__disjoint) ).
thf(526,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ C ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ C ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ nat @ ( finite_card @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ C ) )
= ( hAPP @ nat @ nat @ suc @ ( hAPP @ ( fun @ A @ bool ) @ nat @ ( finite_card @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(116,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_rev__finite__subset) ).
thf(489,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(148,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less_eq @ nat ) @ ( hAPP @ nat @ nat @ ( hAPP @ nat @ ( fun @ nat @ nat ) @ ( minus_minus @ nat ) @ A ) @ B ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_diff__le__self) ).
thf(590,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less_eq @ nat ) @ ( hAPP @ nat @ nat @ ( hAPP @ nat @ ( fun @ nat @ nat ) @ ( minus_minus @ nat ) @ A ) @ B ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(111,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ A @ B @ ( hAPP @ C @ ( fun @ A @ B ) @ ( hAPP @ ( fun @ A @ ( fun @ C @ B ) ) @ ( fun @ C @ ( fun @ A @ B ) ) @ ( combc @ A @ C @ B ) @ D ) @ E ) @ F )
= ( hAPP @ C @ B @ ( hAPP @ A @ ( fun @ C @ B ) @ D @ F ) @ E ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBC_1_1_U) ).
thf(471,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ A @ B @ ( hAPP @ C @ ( fun @ A @ B ) @ ( hAPP @ ( fun @ A @ ( fun @ C @ B ) ) @ ( fun @ C @ ( fun @ A @ B ) ) @ ( combc @ A @ C @ B ) @ D ) @ E ) @ F )
= ( hAPP @ C @ B @ ( hAPP @ A @ ( fun @ C @ B ) @ D @ F ) @ E ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(33,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_subsetD) ).
thf(256,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(158,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ B )
| ( hBOOL @ ( hAPP @ bool @ bool @ ( hAPP @ bool @ ( fun @ bool @ bool ) @ fimplies @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fimplies_2_1_U) ).
thf(622,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ B )
| ( hBOOL @ ( hAPP @ bool @ bool @ ( hAPP @ bool @ ( fun @ bool @ bool ) @ fimplies @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(82,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less_eq @ nat ) @ A ) @ B ) )
<=> ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less_eq @ nat ) @ ( hAPP @ nat @ nat @ suc @ B ) ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_not__less__eq__eq) ).
thf(393,plain,
! [A: $i,B: $i] :
( ( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less_eq @ nat ) @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less_eq @ nat ) @ ( hAPP @ nat @ nat @ suc @ B ) ) @ A ) ) )
& ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less_eq @ nat ) @ ( hAPP @ nat @ nat @ suc @ B ) ) @ A ) )
=> ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less_eq @ nat ) @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(106,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ B @ bool ) @ bool @ ( finite_finite @ B ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) ) @ ( image @ B @ A ) @ C ) @ D ) ) )
=> ? [E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ B @ bool ) @ bool @ ( hAPP @ B @ ( fun @ ( fun @ B @ bool ) @ bool ) @ ( member @ B ) @ E ) @ D ) )
& ~ ( hBOOL @ ( hAPP @ ( fun @ B @ bool ) @ bool @ ( finite_finite @ B ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ B @ bool ) @ ( collect @ B ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ B @ bool ) @ ( hAPP @ ( fun @ B @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ B @ bool ) ) @ ( combs @ B @ bool @ bool ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ B @ ( fun @ bool @ bool ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ B @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ B ) @ fconj ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ B @ bool ) @ ( hAPP @ ( fun @ B @ ( fun @ ( fun @ B @ bool ) @ bool ) ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ B @ bool ) ) @ ( combc @ B @ ( fun @ B @ bool ) @ bool ) @ ( member @ B ) ) @ D ) ) ) @ ( hAPP @ A @ ( fun @ B @ bool ) @ ( hAPP @ ( fun @ B @ ( fun @ A @ bool ) ) @ ( fun @ A @ ( fun @ B @ bool ) ) @ ( combc @ B @ A @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ B @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ ( fun @ A @ bool ) ) @ ( fun @ ( fun @ B @ A ) @ ( fun @ B @ ( fun @ A @ bool ) ) ) @ ( combb @ A @ ( fun @ A @ bool ) @ B ) @ ( fequal @ A ) ) @ C ) ) @ ( hAPP @ B @ A @ C @ E ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_pigeonhole__infinite) ).
thf(457,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ B @ bool ) @ bool @ ( finite_finite @ B ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) ) @ ( image @ B @ A ) @ C ) @ D ) ) )
=> ? [E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ B @ bool ) @ bool @ ( hAPP @ B @ ( fun @ ( fun @ B @ bool ) @ bool ) @ ( member @ B ) @ E ) @ D ) )
& ~ ( hBOOL @ ( hAPP @ ( fun @ B @ bool ) @ bool @ ( finite_finite @ B ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ B @ bool ) @ ( collect @ B ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ B @ bool ) @ ( hAPP @ ( fun @ B @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ B @ bool ) ) @ ( combs @ B @ bool @ bool ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ B @ ( fun @ bool @ bool ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ B @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ B ) @ fconj ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ B @ bool ) @ ( hAPP @ ( fun @ B @ ( fun @ ( fun @ B @ bool ) @ bool ) ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ B @ bool ) ) @ ( combc @ B @ ( fun @ B @ bool ) @ bool ) @ ( member @ B ) ) @ D ) ) ) @ ( hAPP @ A @ ( fun @ B @ bool ) @ ( hAPP @ ( fun @ B @ ( fun @ A @ bool ) ) @ ( fun @ A @ ( fun @ B @ bool ) ) @ ( combc @ B @ A @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ B @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ ( fun @ A @ bool ) ) @ ( fun @ ( fun @ B @ A ) @ ( fun @ B @ ( fun @ A @ bool ) ) ) @ ( combb @ A @ ( fun @ A @ bool ) @ B ) @ ( fequal @ A ) ) @ C ) ) @ ( hAPP @ B @ A @ C @ E ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(144,axiom,
( ( ti @ ( fun @ x_a @ bool ) @ g )
= g ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_v_G_res) ).
thf(569,plain,
( ( ti @ ( fun @ x_a @ bool ) @ g )
= g ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(37,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_insertI2) ).
thf(266,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(19,axiom,
! [A: $i] :
( ( ti @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( collect @ A ) )
= ( collect @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Set_OCollect_res) ).
thf(205,plain,
! [A: $i] :
( ( ti @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( collect @ A ) )
= ( collect @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(124,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ D ) )
=> ( ( ti @ A @ C )
= ( ti @ A @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_insertCI) ).
thf(508,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ~ ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ D ) )
=> ( ( ti @ A @ C )
= ( ti @ A @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(52,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( fequal @ A ) @ B ) @ C ) )
| ( ( ti @ A @ B )
= ( ti @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_1_1_T) ).
thf(311,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( fequal @ A ) @ B ) @ C ) )
| ( ( ti @ A @ B )
= ( ti @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(133,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less_eq @ nat ) @ ( hAPP @ nat @ nat @ suc @ A ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less_eq @ nat ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_Suc__leD) ).
thf(541,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less_eq @ nat ) @ ( hAPP @ nat @ nat @ suc @ A ) ) @ B ) )
=> ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less_eq @ nat ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(83,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ D ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_subset__trans) ).
thf(398,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ D ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(36,axiom,
! [A: $i,B: $i] :
( ( preorder @ B )
=> ( preorder @ ( fun @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Orderings_Opreorder) ).
thf(264,plain,
! [A: $i,B: $i] :
( ( preorder @ B )
=> ( preorder @ ( fun @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(41,axiom,
( ( ti @ ( fun @ ( fun @ x_a @ bool ) @ ( fun @ ( fun @ x_a @ bool ) @ bool ) ) @ p )
= p ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_v_P_res) ).
thf(279,plain,
( ( ti @ ( fun @ ( fun @ x_a @ bool ) @ ( fun @ ( fun @ x_a @ bool ) @ bool ) ) @ p )
= p ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(77,axiom,
! [A: $i,B: $i] :
( ( order @ B )
=> ( order @ ( fun @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Orderings_Oorder) ).
thf(375,plain,
! [A: $i,B: $i] :
( ( order @ B )
=> ( order @ ( fun @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(152,axiom,
( ( ti @ ( fun @ pname @ bool ) @ u )
= u ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_v_U_res) ).
thf(601,plain,
( ( ti @ ( fun @ pname @ bool ) @ u )
= u ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ D ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ D ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_subsetI) ).
thf(176,plain,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ D ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ D ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(45,axiom,
! [A: $i] :
( ( ti @ ( fun @ ( fun @ A @ bool ) @ nat ) @ ( finite_card @ A ) )
= ( finite_card @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Finite__Set_Ocard_res) ).
thf(286,plain,
! [A: $i] :
( ( ti @ ( fun @ ( fun @ A @ bool ) @ nat ) @ ( finite_card @ A ) )
= ( finite_card @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(42,axiom,
hBOOL @ ( hAPP @ ( fun @ pname @ bool ) @ bool @ ( finite_finite @ pname ) @ u ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(281,plain,
hBOOL @ ( hAPP @ ( fun @ pname @ bool ) @ bool @ ( finite_finite @ pname ) @ u ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(135,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ti @ A @ D )
= ( hAPP @ B @ A @ E @ F ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ B @ bool ) @ bool @ ( hAPP @ B @ ( fun @ ( fun @ B @ bool ) @ bool ) @ ( member @ B ) @ F ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ D ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) ) @ ( image @ B @ A ) @ E ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_image__eqI) ).
thf(545,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ti @ A @ D )
= ( hAPP @ B @ A @ E @ F ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ B @ bool ) @ bool @ ( hAPP @ B @ ( fun @ ( fun @ B @ bool ) @ bool ) @ ( member @ B ) @ F ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ D ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) ) @ ( image @ B @ A ) @ E ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(89,axiom,
! [A: $i] :
( A
!= ( hAPP @ nat @ nat @ suc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_n__not__Suc__n) ).
thf(413,plain,
! [A: $i] :
( A
!= ( hAPP @ nat @ nat @ suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(109,axiom,
! [A: $i] :
( ( ti @ ( fun @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) ) @ ( member @ A ) )
= ( member @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_member_res) ).
thf(466,plain,
! [A: $i] :
( ( ti @ ( fun @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) ) @ ( member @ A ) )
= ( member @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(28,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less_eq @ nat ) @ A ) @ B ) )
=> ( ( hAPP @ nat @ nat @ ( hAPP @ nat @ ( fun @ nat @ nat ) @ ( minus_minus @ nat ) @ ( hAPP @ nat @ nat @ suc @ B ) ) @ A )
= ( hAPP @ nat @ nat @ suc @ ( hAPP @ nat @ nat @ ( hAPP @ nat @ ( fun @ nat @ nat ) @ ( minus_minus @ nat ) @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_Suc__diff__le) ).
thf(236,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less_eq @ nat ) @ A ) @ B ) )
=> ( ( hAPP @ nat @ nat @ ( hAPP @ nat @ ( fun @ nat @ nat ) @ ( minus_minus @ nat ) @ ( hAPP @ nat @ nat @ suc @ B ) ) @ A )
= ( hAPP @ nat @ nat @ suc @ ( hAPP @ nat @ nat @ ( hAPP @ nat @ ( fun @ nat @ nat ) @ ( minus_minus @ nat ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( ti @ ( fun @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) ) ) @ ( image @ A @ B ) )
= ( image @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Set_Oimage_res) ).
thf(187,plain,
! [A: $i,B: $i] :
( ( ti @ ( fun @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) ) ) @ ( image @ A @ B ) )
= ( image @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(86,axiom,
! [A: $i,B: $i,C: $i] :
( ( ti @ ( fun @ ( fun @ A @ B ) @ ( fun @ ( fun @ C @ A ) @ ( fun @ C @ B ) ) ) @ ( combb @ A @ B @ C ) )
= ( combb @ A @ B @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_COMBB_res) ).
thf(406,plain,
! [A: $i,B: $i,C: $i] :
( ( ti @ ( fun @ ( fun @ A @ B ) @ ( fun @ ( fun @ C @ A ) @ ( fun @ C @ B ) ) ) @ ( combb @ A @ B @ C ) )
= ( combb @ A @ B @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(7,axiom,
( ( ti @ nat @ na )
= na ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_v_na_res) ).
thf(172,plain,
( ( ti @ nat @ na )
= na ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(23,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less_eq @ nat ) @ ( hAPP @ ( fun @ A @ bool ) @ nat @ ( finite_card @ A ) @ C ) ) @ ( hAPP @ ( fun @ A @ bool ) @ nat @ ( finite_card @ A ) @ B ) ) )
=> ( ( ti @ ( fun @ A @ bool ) @ B )
= ( ti @ ( fun @ A @ bool ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_card__seteq) ).
thf(219,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less_eq @ nat ) @ ( hAPP @ ( fun @ A @ bool ) @ nat @ ( finite_card @ A ) @ C ) ) @ ( hAPP @ ( fun @ A @ bool ) @ nat @ ( finite_card @ A ) @ B ) ) )
=> ( ( ti @ ( fun @ A @ bool ) @ B )
= ( ti @ ( fun @ A @ bool ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(78,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ bool @ bool @ ( hAPP @ bool @ ( fun @ bool @ bool ) @ fdisj @ A ) @ B ) )
| ( hBOOL @ A )
| ( hBOOL @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fdisj_3_1_U) ).
thf(377,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ ( hAPP @ bool @ bool @ ( hAPP @ bool @ ( fun @ bool @ bool ) @ fdisj @ A ) @ B ) )
| ( hBOOL @ A )
| ( hBOOL @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(143,axiom,
( ( hAPP @ ( fun @ x_a @ bool ) @ nat @ ( finite_card @ x_a ) @ g )
= ( hAPP @ nat @ nat @ ( hAPP @ nat @ ( fun @ nat @ nat ) @ ( minus_minus @ nat ) @ ( hAPP @ ( fun @ x_a @ bool ) @ nat @ ( finite_card @ x_a ) @ ( hAPP @ ( fun @ pname @ bool ) @ ( fun @ x_a @ bool ) @ ( hAPP @ ( fun @ pname @ x_a ) @ ( fun @ ( fun @ pname @ bool ) @ ( fun @ x_a @ bool ) ) @ ( image @ pname @ x_a ) @ mgt_call ) @ u ) ) ) @ ( hAPP @ nat @ nat @ suc @ na ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_3) ).
thf(567,plain,
( ( hAPP @ ( fun @ x_a @ bool ) @ nat @ ( finite_card @ x_a ) @ g )
= ( hAPP @ nat @ nat @ ( hAPP @ nat @ ( fun @ nat @ nat ) @ ( minus_minus @ nat ) @ ( hAPP @ ( fun @ x_a @ bool ) @ nat @ ( finite_card @ x_a ) @ ( hAPP @ ( fun @ pname @ bool ) @ ( fun @ x_a @ bool ) @ ( hAPP @ ( fun @ pname @ x_a ) @ ( fun @ ( fun @ pname @ bool ) @ ( fun @ x_a @ bool ) ) @ ( image @ pname @ x_a ) @ mgt_call ) @ u ) ) ) @ ( hAPP @ nat @ nat @ suc @ na ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(49,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ B @ bool ) @ bool @ ( hAPP @ B @ ( fun @ ( fun @ B @ bool ) @ bool ) @ ( member @ B ) @ D ) @ E ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ ( hAPP @ B @ A @ C @ D ) ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) ) @ ( image @ B @ A ) @ C ) @ E ) )
= ( hAPP @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) ) @ ( image @ B @ A ) @ C ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_insert__image) ).
thf(303,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ B @ bool ) @ bool @ ( hAPP @ B @ ( fun @ ( fun @ B @ bool ) @ bool ) @ ( member @ B ) @ D ) @ E ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ ( hAPP @ B @ A @ C @ D ) ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) ) @ ( image @ B @ A ) @ C ) @ E ) )
= ( hAPP @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) ) @ ( image @ B @ A ) @ C ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(39,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ C ) )
=> ( ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ C ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ nat @ ( finite_card @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ C ) )
= ( hAPP @ ( fun @ A @ bool ) @ nat @ ( finite_card @ A ) @ C ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ C ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ nat @ ( finite_card @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ C ) )
= ( hAPP @ nat @ nat @ suc @ ( hAPP @ ( fun @ A @ bool ) @ nat @ ( finite_card @ A ) @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_card__insert__if) ).
thf(271,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ C ) )
=> ( ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ C ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ nat @ ( finite_card @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ C ) )
= ( hAPP @ ( fun @ A @ bool ) @ nat @ ( finite_card @ A ) @ C ) ) )
& ( ~ ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ C ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ nat @ ( finite_card @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ C ) )
= ( hAPP @ nat @ nat @ suc @ ( hAPP @ ( fun @ A @ bool ) @ nat @ ( finite_card @ A ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(20,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( ti @ ( fun @ A @ bool ) @ B )
= ( ti @ ( fun @ A @ bool ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_equalityD2) ).
thf(208,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ti @ ( fun @ A @ bool ) @ B )
= ( ti @ ( fun @ A @ bool ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(113,axiom,
! [A: $i] :
( ( order @ A )
=> ! [B: $i,C: $i,D: $i] :
( ! [E: $i] : ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ ( hAPP @ nat @ A @ D @ E ) ) @ ( hAPP @ nat @ A @ D @ ( hAPP @ nat @ nat @ suc @ E ) ) ) )
=> ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less_eq @ nat ) @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ ( hAPP @ nat @ A @ D @ B ) ) @ ( hAPP @ nat @ A @ D @ C ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_lift__Suc__mono__le) ).
thf(477,plain,
! [A: $i] :
( ( order @ A )
=> ! [B: $i,C: $i,D: $i] :
( ! [E: $i] : ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ ( hAPP @ nat @ A @ D @ E ) ) @ ( hAPP @ nat @ A @ D @ ( hAPP @ nat @ nat @ suc @ E ) ) ) )
=> ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less_eq @ nat ) @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( ord_less_eq @ A ) @ ( hAPP @ nat @ A @ D @ B ) ) @ ( hAPP @ nat @ A @ D @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(81,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( combs @ A @ bool @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ ( fun @ bool @ bool ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ A ) @ fdisj ) @ B ) ) @ C ) ) ) )
<=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ B ) ) )
& ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_finite__Collect__disjI) ).
thf(387,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( combs @ A @ bool @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ ( fun @ bool @ bool ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ A ) @ fdisj ) @ B ) ) @ C ) ) ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ B ) ) )
& ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ C ) ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ B ) ) )
& ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ C ) ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( combs @ A @ bool @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ ( fun @ bool @ bool ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ A ) @ fdisj ) @ B ) ) @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(74,axiom,
! [A: $i,B: $i] :
( ( hAPP @ A @ A @ ( combi @ A ) @ B )
= ( ti @ A @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBI_1_1_U) ).
thf(367,plain,
! [A: $i,B: $i] :
( ( hAPP @ A @ A @ ( combi @ A ) @ B )
= ( ti @ A @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(56,axiom,
! [A: $i] :
( ( finite_finite_1 @ A )
=> ! [B: $i] : ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_finite) ).
thf(323,plain,
! [A: $i] :
( ( finite_finite_1 @ A )
=> ! [B: $i] : ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(31,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less_eq @ nat ) @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less_eq @ nat ) @ B ) @ A ) )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_le__antisym) ).
thf(251,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less_eq @ nat ) @ A ) @ B ) )
=> ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less_eq @ nat ) @ B ) @ A ) )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(16,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) ) @ ( image @ A @ B ) @ D ) @ ( hAPP @ ( fun @ C @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ C @ A ) @ ( fun @ ( fun @ C @ bool ) @ ( fun @ A @ bool ) ) @ ( image @ C @ A ) @ E ) @ F ) )
= ( hAPP @ ( fun @ C @ bool ) @ ( fun @ B @ bool ) @ ( hAPP @ ( fun @ C @ B ) @ ( fun @ ( fun @ C @ bool ) @ ( fun @ B @ bool ) ) @ ( image @ C @ B ) @ ( hAPP @ ( fun @ C @ A ) @ ( fun @ C @ B ) @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ C @ A ) @ ( fun @ C @ B ) ) @ ( combb @ A @ B @ C ) @ D ) @ E ) ) @ F ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_image__image) ).
thf(198,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) ) @ ( image @ A @ B ) @ D ) @ ( hAPP @ ( fun @ C @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ C @ A ) @ ( fun @ ( fun @ C @ bool ) @ ( fun @ A @ bool ) ) @ ( image @ C @ A ) @ E ) @ F ) )
= ( hAPP @ ( fun @ C @ bool ) @ ( fun @ B @ bool ) @ ( hAPP @ ( fun @ C @ B ) @ ( fun @ ( fun @ C @ bool ) @ ( fun @ B @ bool ) ) @ ( image @ C @ B ) @ ( hAPP @ ( fun @ C @ A ) @ ( fun @ C @ B ) @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ C @ A ) @ ( fun @ C @ B ) ) @ ( combb @ A @ B @ C ) @ D ) @ E ) ) @ F ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(50,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i] :
( ( hAPP @ A @ B @ C @ E )
= ( hAPP @ A @ B @ D @ E ) )
=> ( ( ti @ ( fun @ A @ B ) @ C )
= ( ti @ ( fun @ A @ B ) @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_ext) ).
thf(306,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i] :
( ( hAPP @ A @ B @ C @ E )
= ( hAPP @ A @ B @ D @ E ) )
=> ( ( ti @ ( fun @ A @ B ) @ C )
= ( ti @ ( fun @ A @ B ) @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(48,axiom,
! [A: $i] :
( ( hAPP @ nat @ nat @ suc @ A )
!= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_Suc__n__not__n) ).
thf(299,plain,
! [A: $i] :
( ( hAPP @ nat @ nat @ suc @ A )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(96,axiom,
! [A: $i] :
( ( finite_finite_1 @ A )
=> ! [B: $i] : ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_finite__code) ).
thf(431,plain,
! [A: $i] :
( ( finite_finite_1 @ A )
=> ! [B: $i] : ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(4,axiom,
! [A: $i] :
( ( ti @ A @ ( undefined @ A ) )
= ( undefined @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_HOL_Oundefined_res) ).
thf(167,plain,
! [A: $i] :
( ( ti @ A @ ( undefined @ A ) )
= ( undefined @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(123,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ nat @ nat @ ( hAPP @ nat @ ( fun @ nat @ nat ) @ ( minus_minus @ nat ) @ ( hAPP @ nat @ nat @ ( hAPP @ nat @ ( fun @ nat @ nat ) @ ( minus_minus @ nat ) @ ( hAPP @ nat @ nat @ suc @ A ) ) @ B ) ) @ ( hAPP @ nat @ nat @ suc @ C ) )
= ( hAPP @ nat @ nat @ ( hAPP @ nat @ ( fun @ nat @ nat ) @ ( minus_minus @ nat ) @ ( hAPP @ nat @ nat @ ( hAPP @ nat @ ( fun @ nat @ nat ) @ ( minus_minus @ nat ) @ A ) @ B ) ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_Suc__diff__diff) ).
thf(505,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ nat @ nat @ ( hAPP @ nat @ ( fun @ nat @ nat ) @ ( minus_minus @ nat ) @ ( hAPP @ nat @ nat @ ( hAPP @ nat @ ( fun @ nat @ nat ) @ ( minus_minus @ nat ) @ ( hAPP @ nat @ nat @ suc @ A ) ) @ B ) ) @ ( hAPP @ nat @ nat @ suc @ C ) )
= ( hAPP @ nat @ nat @ ( hAPP @ nat @ ( fun @ nat @ nat ) @ ( minus_minus @ nat ) @ ( hAPP @ nat @ nat @ ( hAPP @ nat @ ( fun @ nat @ nat ) @ ( minus_minus @ nat ) @ A ) @ B ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(99,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ B )
| ( hBOOL @ ( hAPP @ bool @ bool @ ( hAPP @ bool @ ( fun @ bool @ bool ) @ fdisj @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fdisj_1_1_U) ).
thf(438,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ B )
| ( hBOOL @ ( hAPP @ bool @ bool @ ( hAPP @ bool @ ( fun @ bool @ bool ) @ fdisj @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(94,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less_eq @ nat ) @ ( hAPP @ ( fun @ A @ bool ) @ nat @ ( finite_card @ A ) @ C ) ) @ ( hAPP @ ( fun @ A @ bool ) @ nat @ ( finite_card @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_card__insert__le) ).
thf(426,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less_eq @ nat ) @ ( hAPP @ ( fun @ A @ bool ) @ nat @ ( finite_card @ A ) @ C ) ) @ ( hAPP @ ( fun @ A @ bool ) @ nat @ ( finite_card @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(130,axiom,
! [A: $i] :
( ( hAPP @ ( fun @ nat @ bool ) @ nat @ ( finite_card @ nat ) @ ( hAPP @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) @ ( collect @ nat ) @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( hAPP @ ( fun @ nat @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ ( fun @ nat @ bool ) ) @ ( combc @ nat @ nat @ bool ) @ ( ord_less_eq @ nat ) ) @ A ) ) )
= ( hAPP @ nat @ nat @ suc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_card__Collect__le__nat) ).
thf(531,plain,
! [A: $i] :
( ( hAPP @ ( fun @ nat @ bool ) @ nat @ ( finite_card @ nat ) @ ( hAPP @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) @ ( collect @ nat ) @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( hAPP @ ( fun @ nat @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ ( fun @ nat @ bool ) ) @ ( combc @ nat @ nat @ bool ) @ ( ord_less_eq @ nat ) ) @ A ) ) )
= ( hAPP @ nat @ nat @ suc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(136,axiom,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less_eq @ nat ) @ ( hAPP @ nat @ nat @ suc @ A ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_Suc__n__not__le__n) ).
thf(548,plain,
! [A: $i] :
~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less_eq @ nat ) @ ( hAPP @ nat @ nat @ suc @ A ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(156,axiom,
! [A: $i] :
( ( preorder @ A )
=> ( ( ti @ ( fun @ A @ ( fun @ A @ bool ) ) @ ( ord_less_eq @ A ) )
= ( ord_less_eq @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Orderings_Oord__class_Oless__eq_res) ).
thf(617,plain,
! [A: $i] :
( ( preorder @ A )
=> ( ( ti @ ( fun @ A @ ( fun @ A @ bool ) ) @ ( ord_less_eq @ A ) )
= ( ord_less_eq @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(65,axiom,
! [A: $i,B: $i] :
( ~ ( hBOOL @ B )
| ( hBOOL @ ( hAPP @ bool @ bool @ ( hAPP @ bool @ ( fun @ bool @ bool ) @ fdisj @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fdisj_2_1_U) ).
thf(342,plain,
! [A: $i,B: $i] :
( ~ ( hBOOL @ B )
| ( hBOOL @ ( hAPP @ bool @ bool @ ( hAPP @ bool @ ( fun @ bool @ bool ) @ fdisj @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(69,axiom,
hBOOL @ ( hAPP @ ( fun @ pname @ bool ) @ bool @ ( hAPP @ pname @ ( fun @ ( fun @ pname @ bool ) @ bool ) @ ( member @ pname ) @ pn ) @ u ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_4) ).
thf(355,plain,
hBOOL @ ( hAPP @ ( fun @ pname @ bool ) @ bool @ ( hAPP @ pname @ ( fun @ ( fun @ pname @ bool ) @ bool ) @ ( member @ pname ) @ pn ) @ u ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(138,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ B )
| ( hBOOL @ ( hAPP @ bool @ bool @ ( hAPP @ bool @ ( fun @ bool @ bool ) @ fimplies @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fimplies_1_1_U) ).
thf(553,plain,
! [A: $i,B: $i] :
( ( hBOOL @ B )
| ( hBOOL @ ( hAPP @ bool @ bool @ ( hAPP @ bool @ ( fun @ bool @ bool ) @ fimplies @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(14,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ C ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ C ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_subset__insertI2) ).
thf(194,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ C ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ C ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(140,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ti @ A @ ( hAPP @ B @ A @ C @ D ) )
= ( hAPP @ B @ A @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_hAPP_res) ).
thf(557,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ti @ A @ ( hAPP @ B @ A @ C @ D ) )
= ( hAPP @ B @ A @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(146,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ nat @ bool ) @ bool @ ( finite_finite @ nat ) @ A ) )
<=> ? [B: $i] :
! [C: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ nat @ bool ) @ bool @ ( hAPP @ nat @ ( fun @ ( fun @ nat @ bool ) @ bool ) @ ( member @ nat ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less_eq @ nat ) @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_98_finite__nat__set__iff__bounded__le) ).
thf(580,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ nat @ bool ) @ bool @ ( finite_finite @ nat ) @ A ) )
=> ? [B: $i] :
! [C: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ nat @ bool ) @ bool @ ( hAPP @ nat @ ( fun @ ( fun @ nat @ bool ) @ bool ) @ ( member @ nat ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less_eq @ nat ) @ C ) @ B ) ) ) )
& ( ? [B: $i] :
! [C: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ nat @ bool ) @ bool @ ( hAPP @ nat @ ( fun @ ( fun @ nat @ bool ) @ bool ) @ ( member @ nat ) @ C ) @ A ) )
=> ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less_eq @ nat ) @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ nat @ bool ) @ bool @ ( finite_finite @ nat ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(43,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ C ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ C ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_insert__mono) ).
thf(282,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ C ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ C ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(58,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ B ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_subset__refl) ).
thf(327,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ B ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(87,axiom,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_subset__insertI) ).
thf(409,plain,
! [A: $i,B: $i,C: $i] : ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(60,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) ) @ ( image @ A @ B ) @ C ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ D ) @ E ) )
= ( hAPP @ ( fun @ B @ bool ) @ ( fun @ B @ bool ) @ ( hAPP @ B @ ( fun @ ( fun @ B @ bool ) @ ( fun @ B @ bool ) ) @ ( insert @ B ) @ ( hAPP @ A @ B @ C @ D ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) ) @ ( image @ A @ B ) @ C ) @ E ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_image__insert) ).
thf(331,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) ) @ ( image @ A @ B ) @ C ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ D ) @ E ) )
= ( hAPP @ ( fun @ B @ bool ) @ ( fun @ B @ bool ) @ ( hAPP @ B @ ( fun @ ( fun @ B @ bool ) @ ( fun @ B @ bool ) ) @ ( insert @ B ) @ ( hAPP @ A @ B @ C @ D ) ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) ) @ ( image @ A @ B ) @ C ) @ E ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(75,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ B @ bool ) @ bool @ ( finite_finite @ B ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) ) @ ( image @ B @ A ) @ C ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2_finite__imageI) ).
thf(370,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ B @ bool ) @ bool @ ( finite_finite @ B ) @ D ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) ) @ ( image @ B @ A ) @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(122,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ B @ bool ) @ bool @ ( hAPP @ B @ ( fun @ ( fun @ B @ bool ) @ bool ) @ ( member @ B ) @ E ) @ F ) )
=> ( ( ( ti @ A @ C )
= ( hAPP @ B @ A @ D @ E ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) ) @ ( image @ B @ A ) @ D ) @ F ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_rev__image__eqI) ).
thf(502,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ B @ bool ) @ bool @ ( hAPP @ B @ ( fun @ ( fun @ B @ bool ) @ bool ) @ ( member @ B ) @ E ) @ F ) )
=> ( ( ( ti @ A @ C )
= ( hAPP @ B @ A @ D @ E ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) ) @ ( image @ B @ A ) @ D ) @ F ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(108,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less_eq @ nat ) @ A ) @ ( hAPP @ nat @ nat @ suc @ B ) ) )
=> ( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less_eq @ nat ) @ A ) @ B ) )
=> ( A
= ( hAPP @ nat @ nat @ suc @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_le__SucE) ).
thf(463,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less_eq @ nat ) @ A ) @ ( hAPP @ nat @ nat @ suc @ B ) ) )
=> ( ~ ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less_eq @ nat ) @ A ) @ B ) )
=> ( A
= ( hAPP @ nat @ nat @ suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(63,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ C ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ B ) ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( combs @ A @ bool @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ ( fun @ bool @ bool ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ A ) @ fconj ) @ C ) ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_finite__Collect__conjI) ).
thf(338,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ C ) ) )
| ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ B ) ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( collect @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( combs @ A @ bool @ bool ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ ( fun @ bool @ bool ) ) @ ( hAPP @ ( fun @ bool @ ( fun @ bool @ bool ) ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ ( fun @ bool @ bool ) ) ) @ ( combb @ bool @ ( fun @ bool @ bool ) @ A ) @ fconj ) @ C ) ) @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(53,axiom,
( ( ti @ ( fun @ nat @ ( fun @ nat @ nat ) ) @ ( minus_minus @ nat ) )
= ( minus_minus @ nat ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_Groups_Ominus__class_Ominus_res) ).
thf(314,plain,
( ( ti @ ( fun @ nat @ ( fun @ nat @ nat ) ) @ ( minus_minus @ nat ) )
= ( minus_minus @ nat ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(154,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ A @ B @ C @ ( ti @ A @ D ) )
= ( hAPP @ A @ B @ C @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_hAPP_arg2) ).
thf(612,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ A @ B @ C @ ( ti @ A @ D ) )
= ( hAPP @ A @ B @ C @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(120,axiom,
! [A: $i,B: $i] :
( ( hAPP @ nat @ nat @ ( hAPP @ nat @ ( fun @ nat @ nat ) @ ( minus_minus @ nat ) @ ( hAPP @ nat @ nat @ suc @ A ) ) @ ( hAPP @ nat @ nat @ suc @ B ) )
= ( hAPP @ nat @ nat @ ( hAPP @ nat @ ( fun @ nat @ nat ) @ ( minus_minus @ nat ) @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_diff__Suc__Suc) ).
thf(497,plain,
! [A: $i,B: $i] :
( ( hAPP @ nat @ nat @ ( hAPP @ nat @ ( fun @ nat @ nat ) @ ( minus_minus @ nat ) @ ( hAPP @ nat @ nat @ suc @ A ) ) @ ( hAPP @ nat @ nat @ suc @ B ) )
= ( hAPP @ nat @ nat @ ( hAPP @ nat @ ( fun @ nat @ nat ) @ ( minus_minus @ nat ) @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(102,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ A @ B @ ( hAPP @ ( fun @ A @ C ) @ ( fun @ A @ B ) @ ( hAPP @ ( fun @ A @ ( fun @ C @ B ) ) @ ( fun @ ( fun @ A @ C ) @ ( fun @ A @ B ) ) @ ( combs @ A @ C @ B ) @ D ) @ E ) @ F )
= ( hAPP @ C @ B @ ( hAPP @ A @ ( fun @ C @ B ) @ D @ F ) @ ( hAPP @ A @ C @ E @ F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBS_1_1_U) ).
thf(446,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ A @ B @ ( hAPP @ ( fun @ A @ C ) @ ( fun @ A @ B ) @ ( hAPP @ ( fun @ A @ ( fun @ C @ B ) ) @ ( fun @ ( fun @ A @ C ) @ ( fun @ A @ B ) ) @ ( combs @ A @ C @ B ) @ D ) @ E ) @ F )
= ( hAPP @ C @ B @ ( hAPP @ A @ ( fun @ C @ B ) @ D @ F ) @ ( hAPP @ A @ C @ E @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(145,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less_eq @ nat ) @ A ) @ ( hAPP @ nat @ nat @ suc @ B ) ) )
<=> ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less_eq @ nat ) @ A ) @ B ) )
| ( A
= ( hAPP @ nat @ nat @ suc @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_le__Suc__eq) ).
thf(571,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less_eq @ nat ) @ A ) @ ( hAPP @ nat @ nat @ suc @ B ) ) )
=> ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less_eq @ nat ) @ A ) @ B ) )
| ( A
= ( hAPP @ nat @ nat @ suc @ B ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less_eq @ nat ) @ A ) @ B ) )
| ( A
= ( hAPP @ nat @ nat @ suc @ B ) ) )
=> ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less_eq @ nat ) @ A ) @ ( hAPP @ nat @ nat @ suc @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(27,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ C ) )
<=> ( hBOOL @ ( hAPP @ A @ bool @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_mem__def) ).
thf(231,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ C @ B ) ) )
& ( ( hBOOL @ ( hAPP @ A @ bool @ C @ B ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(160,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( ti @ ( fun @ A @ bool ) @ B )
= ( ti @ ( fun @ A @ bool ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_equalityD1) ).
thf(627,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ti @ ( fun @ A @ bool ) @ B )
= ( ti @ ( fun @ A @ bool ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(72,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_finite__subset) ).
thf(363,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(119,axiom,
! [A: $i] :
( ( hBOOL @ A )
| ( hBOOL @ ( hAPP @ bool @ bool @ fNot @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fNot_2_1_U) ).
thf(495,plain,
! [A: $i] :
( ( hBOOL @ A )
| ( hBOOL @ ( hAPP @ bool @ bool @ fNot @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(115,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ nat @ nat @ suc @ A )
= ( hAPP @ nat @ nat @ suc @ B ) )
<=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_nat_Oinject) ).
thf(482,plain,
! [A: $i,B: $i] :
( ( ( ( hAPP @ nat @ nat @ suc @ A )
= ( hAPP @ nat @ nat @ suc @ B ) )
=> ( A = B ) )
& ( ( A = B )
=> ( ( hAPP @ nat @ nat @ suc @ A )
= ( hAPP @ nat @ nat @ suc @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ x_a @ bool ) @ bool @ ( hAPP @ ( fun @ x_a @ bool ) @ ( fun @ ( fun @ x_a @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ x_a @ bool ) ) @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( fun @ x_a @ bool ) @ bool @ ( hAPP @ ( fun @ x_a @ bool ) @ ( fun @ ( fun @ x_a @ bool ) @ bool ) @ p @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_assms_I1_J) ).
thf(203,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ x_a @ bool ) @ bool @ ( hAPP @ ( fun @ x_a @ bool ) @ ( fun @ ( fun @ x_a @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ x_a @ bool ) ) @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( fun @ x_a @ bool ) @ bool @ ( hAPP @ ( fun @ x_a @ bool ) @ ( fun @ ( fun @ x_a @ bool ) @ bool ) @ p @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(127,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( ti @ ( fun @ A @ bool ) @ B )
= ( ti @ ( fun @ A @ bool ) @ C ) )
<=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ B ) @ C ) )
& ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_set__eq__subset) ).
thf(517,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( ti @ ( fun @ A @ bool ) @ B )
= ( ti @ ( fun @ A @ bool ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ B ) @ C ) )
& ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ C ) @ B ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ B ) @ C ) )
& ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ C ) @ B ) ) )
=> ( ( ti @ ( fun @ A @ bool ) @ B )
= ( ti @ ( fun @ A @ bool ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(34,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ A @ B @ ( hAPP @ ( fun @ A @ C ) @ ( fun @ A @ B ) @ ( hAPP @ ( fun @ C @ B ) @ ( fun @ ( fun @ A @ C ) @ ( fun @ A @ B ) ) @ ( combb @ C @ B @ A ) @ D ) @ E ) @ F )
= ( hAPP @ C @ B @ D @ ( hAPP @ A @ C @ E @ F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_COMBB_1_1_U) ).
thf(258,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ A @ B @ ( hAPP @ ( fun @ A @ C ) @ ( fun @ A @ B ) @ ( hAPP @ ( fun @ C @ B ) @ ( fun @ ( fun @ A @ C ) @ ( fun @ A @ B ) ) @ ( combb @ C @ B @ A ) @ D ) @ E ) @ F )
= ( hAPP @ C @ B @ D @ ( hAPP @ A @ C @ E @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(162,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ D ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ B ) )
=> ( ( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ D )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ B ) )
<=> ( ( ti @ ( fun @ A @ bool ) @ D )
= ( ti @ ( fun @ A @ bool ) @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_insert__ident) ).
thf(632,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ D ) )
=> ( ~ ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ B ) )
=> ( ( ( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ D )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ B ) )
=> ( ( ti @ ( fun @ A @ bool ) @ D )
= ( ti @ ( fun @ A @ bool ) @ B ) ) )
& ( ( ( ti @ ( fun @ A @ bool ) @ D )
= ( ti @ ( fun @ A @ bool ) @ B ) )
=> ( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ D )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(6,axiom,
preorder @ nat,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Opreorder) ).
thf(171,plain,
preorder @ nat,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(91,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ nat @ nat @ suc @ A )
= ( hAPP @ nat @ nat @ suc @ B ) )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_Suc__inject) ).
thf(418,plain,
! [A: $i,B: $i] :
( ( ( hAPP @ nat @ nat @ suc @ A )
= ( hAPP @ nat @ nat @ suc @ B ) )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(97,axiom,
( ( ti @ ( fun @ pname @ x_a ) @ mgt_call )
= mgt_call ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_v_mgt__call_res) ).
thf(433,plain,
( ( ti @ ( fun @ pname @ x_a ) @ mgt_call )
= mgt_call ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(67,axiom,
! [A: $i] :
( ( ti @ ( fun @ A @ A ) @ ( combi @ A ) )
= ( combi @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_COMBI_res) ).
thf(346,plain,
! [A: $i] :
( ( ti @ ( fun @ A @ A ) @ ( combi @ A ) )
= ( combi @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(132,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ B @ bool ) @ bool @ ( finite_finite @ B ) @ E ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ B @ bool ) @ bool @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ ( fun @ B @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ B @ bool ) ) @ E ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) ) @ ( image @ A @ B ) @ C ) @ D ) ) )
=> ? [F: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ F ) @ D ) )
& ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ F ) )
& ( ( ti @ ( fun @ B @ bool ) @ E )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) ) @ ( image @ A @ B ) @ C ) @ F ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_finite__subset__image) ).
thf(536,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ B @ bool ) @ bool @ ( finite_finite @ B ) @ E ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ B @ bool ) @ bool @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ ( fun @ B @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ B @ bool ) ) @ E ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) ) @ ( image @ A @ B ) @ C ) @ D ) ) )
=> ? [F: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ F ) @ D ) )
& ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ F ) )
& ( ( ti @ ( fun @ B @ bool ) @ E )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) @ ( hAPP @ ( fun @ A @ B ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ B @ bool ) ) @ ( image @ A @ B ) @ C ) @ F ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(157,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ B @ bool ) @ bool @ ( finite_finite @ B ) @ D ) )
=> ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less_eq @ nat ) @ ( hAPP @ ( fun @ A @ bool ) @ nat @ ( finite_card @ A ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) ) @ ( image @ B @ A ) @ C ) @ D ) ) ) @ ( hAPP @ ( fun @ B @ bool ) @ nat @ ( finite_card @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4_card__image__le) ).
thf(620,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ B @ bool ) @ bool @ ( finite_finite @ B ) @ D ) )
=> ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less_eq @ nat ) @ ( hAPP @ ( fun @ A @ bool ) @ nat @ ( finite_card @ A ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) ) @ ( image @ B @ A ) @ C ) @ D ) ) ) @ ( hAPP @ ( fun @ B @ bool ) @ nat @ ( finite_card @ B ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(12,axiom,
( ( ti @ ( fun @ bool @ bool ) @ fNot )
= fNot ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',tsy_c_fNot_res) ).
thf(190,plain,
( ( ti @ ( fun @ bool @ bool ) @ fNot )
= fNot ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(153,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ C ) @ D ) )
<=> ( ( ( ti @ A @ B )
= ( ti @ A @ D ) )
| ( hBOOL @ ( hAPP @ A @ bool @ C @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_insert__code) ).
thf(603,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ C ) @ D ) )
=> ( ( ( ti @ A @ B )
= ( ti @ A @ D ) )
| ( hBOOL @ ( hAPP @ A @ bool @ C @ D ) ) ) )
& ( ( ( ( ti @ A @ B )
= ( ti @ A @ D ) )
| ( hBOOL @ ( hAPP @ A @ bool @ C @ D ) ) )
=> ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ C ) @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(64,axiom,
finite_finite_1 @ bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Finite__Set_Ofinite) ).
thf(341,plain,
finite_finite_1 @ bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(38,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ D ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ D ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ B ) ) )
<=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ D ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_subset__insert) ).
thf(268,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ C ) @ D ) )
=> ( ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ D ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ B ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ D ) @ B ) ) )
& ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ D ) @ B ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ D ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ B ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(71,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less_eq @ nat ) @ ( hAPP @ nat @ nat @ suc @ A ) ) @ ( hAPP @ nat @ nat @ suc @ B ) ) )
<=> ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less_eq @ nat ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_Suc__le__mono) ).
thf(358,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less_eq @ nat ) @ ( hAPP @ nat @ nat @ suc @ A ) ) @ ( hAPP @ nat @ nat @ suc @ B ) ) )
=> ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less_eq @ nat ) @ A ) @ B ) ) )
& ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less_eq @ nat ) @ A ) @ B ) )
=> ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less_eq @ nat ) @ ( hAPP @ nat @ nat @ suc @ A ) ) @ ( hAPP @ nat @ nat @ suc @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(112,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( ti @ A @ B )
!= ( ti @ A @ C ) )
| ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( fequal @ A ) @ B ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',help_fequal_2_1_T) ).
thf(474,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ti @ A @ B )
!= ( ti @ A @ C ) )
| ( hBOOL @ ( hAPP @ A @ bool @ ( hAPP @ A @ ( fun @ A @ bool ) @ ( fequal @ A ) @ B ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(84,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ C ) )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_insert__absorb2) ).
thf(400,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ C ) )
= ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(29,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less_eq @ nat ) @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less_eq @ nat ) @ B ) @ A ) )
=> ( ( hAPP @ nat @ nat @ ( hAPP @ nat @ ( fun @ nat @ nat ) @ ( minus_minus @ nat ) @ ( hAPP @ nat @ nat @ ( hAPP @ nat @ ( fun @ nat @ nat ) @ ( minus_minus @ nat ) @ C ) @ B ) ) @ ( hAPP @ nat @ nat @ ( hAPP @ nat @ ( fun @ nat @ nat ) @ ( minus_minus @ nat ) @ A ) @ B ) )
= ( hAPP @ nat @ nat @ ( hAPP @ nat @ ( fun @ nat @ nat ) @ ( minus_minus @ nat ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40_Nat_Odiff__diff__eq) ).
thf(239,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less_eq @ nat ) @ B ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less_eq @ nat ) @ B ) @ A ) )
=> ( ( hAPP @ nat @ nat @ ( hAPP @ nat @ ( fun @ nat @ nat ) @ ( minus_minus @ nat ) @ ( hAPP @ nat @ nat @ ( hAPP @ nat @ ( fun @ nat @ nat ) @ ( minus_minus @ nat ) @ C ) @ B ) ) @ ( hAPP @ nat @ nat @ ( hAPP @ nat @ ( fun @ nat @ nat ) @ ( minus_minus @ nat ) @ A ) @ B ) )
= ( hAPP @ nat @ nat @ ( hAPP @ nat @ ( fun @ nat @ nat ) @ ( minus_minus @ nat ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(30,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ D ) ) )
<=> ( ( ( ti @ A @ B )
= ( ti @ A @ C ) )
| ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ D ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_insert__iff) ).
thf(242,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ D ) ) )
=> ( ( ( ti @ A @ B )
= ( ti @ A @ C ) )
| ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ D ) ) ) )
& ( ( ( ( ti @ A @ B )
= ( ti @ A @ C ) )
| ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ D ) ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( member @ A ) @ B ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ C ) @ D ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(159,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ A ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( image @ A @ A ) @ ( combi @ A ) ) @ B )
= ( ti @ ( fun @ A @ bool ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_image__ident) ).
thf(624,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ A @ A ) @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( image @ A @ A ) @ ( combi @ A ) ) @ B )
= ( ti @ ( fun @ A @ bool ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(150,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less_eq @ nat ) @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less_eq @ nat ) @ ( hAPP @ nat @ nat @ ( hAPP @ nat @ ( fun @ nat @ nat ) @ ( minus_minus @ nat ) @ B ) @ A ) ) @ ( hAPP @ nat @ nat @ ( hAPP @ nat @ ( fun @ nat @ nat ) @ ( minus_minus @ nat ) @ C ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_diff__le__mono) ).
thf(596,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less_eq @ nat ) @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less_eq @ nat ) @ ( hAPP @ nat @ nat @ ( hAPP @ nat @ ( fun @ nat @ nat ) @ ( minus_minus @ nat ) @ B ) @ A ) ) @ ( hAPP @ nat @ nat @ ( hAPP @ nat @ ( fun @ nat @ nat ) @ ( minus_minus @ nat ) @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(1,conjecture,
hBOOL @ ( hAPP @ ( fun @ x_a @ bool ) @ bool @ ( hAPP @ ( fun @ x_a @ bool ) @ ( fun @ ( fun @ x_a @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ x_a @ bool ) ) @ ( hAPP @ ( fun @ x_a @ bool ) @ ( fun @ x_a @ bool ) @ ( hAPP @ x_a @ ( fun @ ( fun @ x_a @ bool ) @ ( fun @ x_a @ bool ) ) @ ( insert @ x_a ) @ ( hAPP @ pname @ x_a @ mgt_call @ pn ) ) @ g ) ) @ ( hAPP @ ( fun @ pname @ bool ) @ ( fun @ x_a @ bool ) @ ( hAPP @ ( fun @ pname @ x_a ) @ ( fun @ ( fun @ pname @ bool ) @ ( fun @ x_a @ bool ) ) @ ( image @ pname @ x_a ) @ mgt_call ) @ u ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_6) ).
thf(2,negated_conjecture,
~ ( hBOOL @ ( hAPP @ ( fun @ x_a @ bool ) @ bool @ ( hAPP @ ( fun @ x_a @ bool ) @ ( fun @ ( fun @ x_a @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ x_a @ bool ) ) @ ( hAPP @ ( fun @ x_a @ bool ) @ ( fun @ x_a @ bool ) @ ( hAPP @ x_a @ ( fun @ ( fun @ x_a @ bool ) @ ( fun @ x_a @ bool ) ) @ ( insert @ x_a ) @ ( hAPP @ pname @ x_a @ mgt_call @ pn ) ) @ g ) ) @ ( hAPP @ ( fun @ pname @ bool ) @ ( fun @ x_a @ bool ) @ ( hAPP @ ( fun @ pname @ x_a ) @ ( fun @ ( fun @ pname @ bool ) @ ( fun @ x_a @ bool ) ) @ ( image @ pname @ x_a ) @ mgt_call ) @ u ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(163,plain,
~ ( hBOOL @ ( hAPP @ ( fun @ x_a @ bool ) @ bool @ ( hAPP @ ( fun @ x_a @ bool ) @ ( fun @ ( fun @ x_a @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ x_a @ bool ) ) @ ( hAPP @ ( fun @ x_a @ bool ) @ ( fun @ x_a @ bool ) @ ( hAPP @ x_a @ ( fun @ ( fun @ x_a @ bool ) @ ( fun @ x_a @ bool ) ) @ ( insert @ x_a ) @ ( hAPP @ pname @ x_a @ mgt_call @ pn ) ) @ g ) ) @ ( hAPP @ ( fun @ pname @ bool ) @ ( fun @ x_a @ bool ) @ ( hAPP @ ( fun @ pname @ x_a ) @ ( fun @ ( fun @ pname @ bool ) @ ( fun @ x_a @ bool ) ) @ ( image @ pname @ x_a ) @ mgt_call ) @ u ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(62,axiom,
order @ bool,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Oorder) ).
thf(337,plain,
order @ bool,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(110,axiom,
! [A: $i,B: $i] :
( ( ( finite_finite_1 @ B )
& ( finite_finite_1 @ A ) )
=> ( finite_finite_1 @ ( fun @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_fun___Finite__Set_Ofinite) ).
thf(469,plain,
! [A: $i,B: $i] :
( ( ( finite_finite_1 @ B )
& ( finite_finite_1 @ A ) )
=> ( finite_finite_1 @ ( fun @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(51,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ B @ bool ) @ bool @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ ( fun @ B @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ B @ bool ) ) @ D ) @ E ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) ) @ ( image @ B @ A ) @ C ) @ D ) ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) ) @ ( image @ B @ A ) @ C ) @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_image__mono) ).
thf(309,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ B @ bool ) @ bool @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ ( fun @ B @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ B @ bool ) ) @ D ) @ E ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) ) @ ( image @ B @ A ) @ C ) @ D ) ) @ ( hAPP @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ ( fun @ B @ A ) @ ( fun @ ( fun @ B @ bool ) @ ( fun @ A @ bool ) ) @ ( image @ B @ A ) @ C ) @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(134,axiom,
! [A: $i] : ( hBOOL @ ( hAPP @ ( fun @ nat @ bool ) @ bool @ ( finite_finite @ nat ) @ ( hAPP @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) @ ( collect @ nat ) @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( hAPP @ ( fun @ nat @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ ( fun @ nat @ bool ) ) @ ( combc @ nat @ nat @ bool ) @ ( ord_less_eq @ nat ) ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12_finite__Collect__le__nat) ).
thf(543,plain,
! [A: $i] : ( hBOOL @ ( hAPP @ ( fun @ nat @ bool ) @ bool @ ( finite_finite @ nat ) @ ( hAPP @ ( fun @ nat @ bool ) @ ( fun @ nat @ bool ) @ ( collect @ nat ) @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( hAPP @ ( fun @ nat @ ( fun @ nat @ bool ) ) @ ( fun @ nat @ ( fun @ nat @ bool ) ) @ ( combc @ nat @ nat @ bool ) @ ( ord_less_eq @ nat ) ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(141,axiom,
hBOOL @ ( hAPP @ ( fun @ x_a @ bool ) @ bool @ ( hAPP @ ( fun @ x_a @ bool ) @ ( fun @ ( fun @ x_a @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ x_a @ bool ) ) @ g ) @ ( hAPP @ ( fun @ pname @ bool ) @ ( fun @ x_a @ bool ) @ ( hAPP @ ( fun @ pname @ x_a ) @ ( fun @ ( fun @ pname @ bool ) @ ( fun @ x_a @ bool ) ) @ ( image @ pname @ x_a ) @ mgt_call ) @ u ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_1) ).
thf(560,plain,
hBOOL @ ( hAPP @ ( fun @ x_a @ bool ) @ bool @ ( hAPP @ ( fun @ x_a @ bool ) @ ( fun @ ( fun @ x_a @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ x_a @ bool ) ) @ g ) @ ( hAPP @ ( fun @ pname @ bool ) @ ( fun @ x_a @ bool ) @ ( hAPP @ ( fun @ pname @ x_a ) @ ( fun @ ( fun @ pname @ bool ) @ ( fun @ x_a @ bool ) ) @ ( image @ pname @ x_a ) @ mgt_call ) @ u ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(117,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_finite_OinsertI) ).
thf(491,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ C ) )
=> ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) @ ( hAPP @ A @ ( fun @ ( fun @ A @ bool ) @ ( fun @ A @ bool ) ) @ ( insert @ A ) @ B ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(24,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( ti @ ( fun @ A @ bool ) @ B )
= ( ti @ ( fun @ A @ bool ) @ C ) )
=> ~ ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ B ) @ C ) )
=> ~ ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ C ) @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_equalityE) ).
thf(222,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ti @ ( fun @ A @ bool ) @ B )
= ( ti @ ( fun @ A @ bool ) @ C ) )
=> ~ ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ B ) @ C ) )
=> ~ ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ C ) @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(149,axiom,
! [A: $i,B: $i] :
( ( A = B )
=> ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less_eq @ nat ) @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_eq__imp__le) ).
thf(592,plain,
! [A: $i,B: $i] :
( ( A = B )
=> ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less_eq @ nat ) @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(105,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less_eq @ nat ) @ ( hAPP @ nat @ nat @ suc @ A ) ) @ B ) )
=> ? [C: $i] :
( B
= ( hAPP @ nat @ nat @ suc @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_Suc__le__D) ).
thf(454,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less_eq @ nat ) @ ( hAPP @ nat @ nat @ suc @ A ) ) @ B ) )
=> ? [C: $i] :
( B
= ( hAPP @ nat @ nat @ suc @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(32,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less_eq @ nat ) @ ( hAPP @ ( fun @ A @ bool ) @ nat @ ( finite_card @ A ) @ B ) ) @ ( hAPP @ ( fun @ A @ bool ) @ nat @ ( finite_card @ A ) @ C ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_card__mono) ).
thf(254,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( finite_finite @ A ) @ C ) )
=> ( ( hBOOL @ ( hAPP @ ( fun @ A @ bool ) @ bool @ ( hAPP @ ( fun @ A @ bool ) @ ( fun @ ( fun @ A @ bool ) @ bool ) @ ( ord_less_eq @ ( fun @ A @ bool ) ) @ B ) @ C ) )
=> ( hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less_eq @ nat ) @ ( hAPP @ ( fun @ A @ bool ) @ nat @ ( finite_card @ A ) @ B ) ) @ ( hAPP @ ( fun @ A @ bool ) @ nat @ ( finite_card @ A ) @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(25,axiom,
hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less_eq @ nat ) @ ( hAPP @ nat @ nat @ suc @ na ) ) @ ( hAPP @ ( fun @ x_a @ bool ) @ nat @ ( finite_card @ x_a ) @ ( hAPP @ ( fun @ pname @ bool ) @ ( fun @ x_a @ bool ) @ ( hAPP @ ( fun @ pname @ x_a ) @ ( fun @ ( fun @ pname @ bool ) @ ( fun @ x_a @ bool ) ) @ ( image @ pname @ x_a ) @ mgt_call ) @ u ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_2) ).
thf(227,plain,
hBOOL @ ( hAPP @ nat @ bool @ ( hAPP @ nat @ ( fun @ nat @ bool ) @ ( ord_less_eq @ nat ) @ ( hAPP @ nat @ nat @ suc @ na ) ) @ ( hAPP @ ( fun @ x_a @ bool ) @ nat @ ( finite_card @ x_a ) @ ( hAPP @ ( fun @ pname @ bool ) @ ( fun @ x_a @ bool ) @ ( hAPP @ ( fun @ pname @ x_a ) @ ( fun @ ( fun @ pname @ bool ) @ ( fun @ x_a @ bool ) ) @ ( image @ pname @ x_a ) @ mgt_call ) @ u ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(675,plain,
$false,
inference(cvc4,[status(thm)],[365,479,555,170,276,449,379,440,384,500,174,417,320,372,587,344,196,460,421,284,325,228,289,316,261,216,164,179,443,211,514,411,428,452,512,529,201,534,334,349,598,561,297,424,192,630,435,329,493,551,615,403,356,526,489,590,471,256,622,393,457,569,266,205,508,311,541,398,264,279,375,601,176,286,281,545,413,466,236,187,406,172,219,377,567,303,271,208,477,387,367,323,251,198,306,299,431,167,505,438,426,531,548,617,342,355,553,194,557,580,282,327,409,331,370,502,463,338,314,612,497,446,571,231,627,363,495,482,203,517,258,632,171,418,433,346,536,620,190,603,341,268,358,474,400,239,242,624,596,163,337,469,309,543,560,491,222,592,454,254,227]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWW473+5 : TPTP v8.1.2. Released v5.3.0.
% 0.11/0.15 % Command : run_Leo-III %s %d
% 0.16/0.35 % Computer : n010.cluster.edu
% 0.16/0.35 % Model : x86_64 x86_64
% 0.16/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.35 % Memory : 8042.1875MB
% 0.16/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.35 % CPULimit : 300
% 0.16/0.35 % WCLimit : 300
% 0.16/0.35 % DateTime : Thu May 18 22:16:27 EDT 2023
% 0.16/0.36 % CPUTime :
% 0.94/0.89 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.80/1.11 % [INFO] Parsing done (218ms).
% 1.80/1.12 % [INFO] Running in sequential loop mode.
% 2.24/1.32 % [INFO] eprover registered as external prover.
% 2.24/1.32 % [INFO] cvc4 registered as external prover.
% 2.24/1.32 % [INFO] Scanning for conjecture ...
% 2.81/1.44 % [INFO] Found a conjecture and 160 axioms. Running axiom selection ...
% 3.27/1.53 % [INFO] Axiom selection finished. Selected 160 axioms (removed 0 axioms).
% 3.94/1.73 % [INFO] Problem is first-order (TPTP FOF).
% 3.94/1.75 % [INFO] Type checking passed.
% 3.94/1.75 % [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 ...
% 10.92/3.56 % External prover 'cvc4' found a proof!
% 10.92/3.56 % [INFO] Killing All external provers ...
% 10.92/3.56 % Time passed: 3039ms (effective reasoning time: 2437ms)
% 10.92/3.56 % 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)>
% 10.92/3.56 % 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
% 10.92/3.56 % No. of inferences in proof: 324
% 10.92/3.57 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 3039 ms resp. 2437 ms w/o parsing
% 12.05/3.71 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 12.05/3.71 % [INFO] Killing All external provers ...
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